publications | Justin H. Wilson

2025

Frustration-Free Control and Absorbing-State Transport in Entangled State Preparation

T. Dörstel, T. Iadecola, J. H. Wilson, and 1 more author

arXiv preprint, Oct 2025

Abs DOI arXiv

We study frustration-free control, a measurement-feedback protocol for quantum state preparation that extends the concept of frustration-free Hamiltonians to stochastic dynamics. The protocol drives many-body systems into highly entangled target states, common dark states of all measurement projectors, through minimal local unitary corrections that realize an absorbing-state dynamics without post-selection. We show that relaxation to the target state is governed by emergent transport of nonlocal charges, such as singlet excitations in SU\(2)\-symmetric dynamics. While measurement-feedback annihilates compatible charge configurations, both measurement and scrambling unitaries induce charge transport and thus determine the convergence time. Mapping a baseline model of SU\(N) SWAP measurements with local corrections to a solvable absorbing random walk yields a runtime scaling \t ∼L^z with transport exponent \z=2\. Simulations of Motzkin and Fredkin chains reveal subdiffusive scaling \z \ge \tfrac{8}{3} confirming the transport picture and suggesting strategies for controlled entangled-state preparation and charge-transport probing in monitored quantum dynamics.
Order from Chaos with Adaptive Circuits on Quantum Hardware

Bibek Pokharel, Haining Pan, Kemal Aziz, and 8 more authors

arXiv preprint, Sep 2025

Comment: 21 pages, 11 figures

Abs DOI arXiv

Programmable quantum devices provide a platform to control the coherent dynamics of quantum wavefunctions. Here we experimentally realize adaptive monitored quantum circuits, which incorporate conditional feedback into non-unitary evolution, to control quantum chaotic dynamics using a combination of local mid-circuit measurements and resets. The experiments are performed with an IBM superconducting quantum processor using up to 100 qubits that samples a quantum version of the classically chaotic Bernoulli map. This map scrambles quantum information, while local measurements and feedback attempt to steer the dynamics toward a state that is a fixed point of the map. This competition drives a dynamical phase transition between quantum and classical dynamics that we observe experimentally and describe theoretically using noisy simulations, matrix product states, and mappings to statistical mechanics models. Estimates of the universal critical properties are obtained to high accuracy on the quantum computer thanks to the large number of qubits utilized in the calculation. By successfully applying up to nearly 5000 entangling gates and 5000 non-unitary mid-circuit operations on systems up to 100 qubits, this experiment serves as a signpost on the route towards fault tolerance.
Universality of Stochastic Control of Quantum Chaos with Measurement and Feedback

Andrew A. Allocca, Devesh K. Verma, Sriram Ganeshan, and 1 more author

arXiv preprint, Jun 2025

Abs DOI arXiv

We investigate quantum dynamics in the vicinity of an unstable fixed point subjected to stochastic control. The stochastic competition between the system’s inherent instability (pushing trajectories away) and engineered control dynamics (drawing them back to the same point) forms the core of probabilistic control in chaotic systems. Recent studies reveal that this interplay underlies a family of measurement- and feedback-driven dynamical quantum phase transitions. To capture its universal features, we consider the inverted harmonic oscillator, a canonical model whose operator amplitudes diverge. Our control scheme, a quantum version of classical attractor dynamics, employs non-unitary evolution via measurements and conditional resets. By combining numerical simulations, a semiclassical Fokker-Planck analysis, and direct spectra of the quantum channel, we map out the control transition and uncover quantum-specific signatures of the underlying dynamics. We demonstrate the universality of our results within the quantum Arnold cat map, a paradigmatic model of quantum chaos.
Bridging Classical and Quantum Information Scrambling with the Operator Entanglement Spectrum

Ben T. McDonough, Claudio Chamon, Justin H. Wilson, and 1 more author

arXiv preprint, May 2025

Abs DOI arXiv

Universal features of chaotic quantum dynamics underlie our understanding of thermalization in closed quantum systems and the complexity of quantum computations. Reversible automaton circuits, comprised of classical logic gates, have emerged as a tractable means to study such dynamics. Despite generating no entanglement in the computational basis, these circuits nevertheless capture many features expected from fully quantum evolutions. In this work, we demonstrate that the differences between automaton dynamics and fully quantum dynamics are revealed by the operator entanglement spectrum, much like the entanglement spectrum of a quantum state distinguishes between the dynamics of states under Clifford and Haar random circuits. While the operator entanglement spectrum under random unitary dynamics is governed by the eigenvalue statistics of random Gaussian matrices, we show evidence that under random automaton dynamics it is described by the statistics of Bernoulli random matrices, whose entries are random variables taking values \0 or \1\. We study the crossover between automaton and generic unitary operator dynamics as the automaton circuit is doped with gates that introduce superpositions, namely Hadamard or \R_x = e^{-i\frac{\pi}{4}X} gates. We find that a constant number of superposition-generating gates is sufficient to drive the operator dynamics to the random-circuit universality class, similar to earlier results on Clifford circuits doped with \T gates. This establishes the operator entanglement spectrum as a useful tool for probing the chaoticity and universality class of quantum dynamics.
Controlling a Quantum Point Junction on the Surface of an Antiferromagnetic Topological Insulator

Jedediah Pixley, Nicodemos Varnava, David Vanderbilt, and 1 more author

May 2025

Abs

Various embodiments include an electrical device comprising an antiferromagnetic topological insulator having a surface comprising a bulk domain wall configured to support a first type of 1D chiral channel, a surface step configured to support a second 1D chiral channel and intersecting the bulk domain wall to form thereat a quantum point junction.
Concomitant Entanglement and Control Criticality Driven by Collective Measurements

Thomas Iadecola, Justin H. Wilson, and J.H. Pixley

PRX Quantum, Mar 2025

Abs DOI

Adaptive quantum circuits—where a quantum many-body state is controlled using measurements and conditional unitary operations—are a powerful paradigm for state preparation and quantum error-correction tasks. They can support two types of nonequilibrium quantum phase transitions: measurement-induced transitions between volume- and area-law-entangled steady states and control-induced transitions where the system falls into an absorbing state or, more generally, an orbit visiting several absorbing states. Within this context, nonlocal conditional operations can alter the critical properties of the two transitions and the topology of the phase diagram. Here, we consider the scenario where the measurements are , in order to engineer efficient control onto dynamical trajectories. Motivated by Rydberg-atom arrays, we consider a locally constrained model with global sublattice magnetization measurements and local correction operations to steer the system’s dynamics onto a many-body orbit with finite recurrence time. The model has a well-defined classical limit, which we leverage to aid our analysis of the control transition. As a function of the density of local correction operations, we find control and entanglement transitions with continuously varying critical exponents. For sufficiently high densities of local correction operations, we find that both transitions acquire a dynamical critical exponent z < 1 , reminiscent of criticality in long-range power-law interacting systems. At low correction densities, we find that the criticality reverts to a short-range nature with z ≳ 1 . In the long-range regime, the control and entanglement transitions are indistinguishable to within the resolution of our finite-size numerics, while in the short-range regime we find evidence that the transitions become distinct. We conjecture that the effective long-range criticality mediated by collective measurements is essential in driving the two transitions together. Published by the American Physical Society 2025
Defect Bound States in the Continuum of Bilayer Electronic Materials without Symmetry Protection

Daniel Massatt, Stephen P. Shipman, Ilya Vekhter, and 1 more author

Phys. Rev. B, Feb 2025

DOI
Critical Filaments and Superconductivity in Quasiperiodic Twisted Bilayer Graphene

Xinghai Zhang, Justin H. Wilson, and Matthew S. Foster

Phys. Rev. B, Jan 2025

DOI

2024

Statistical Mechanics of Stochastic Quantum Control: D-Adic Rényi Circuits

Andrew A. Allocca, Conner LeMaire, Thomas Iadecola, and 1 more author

Phys. Rev. E, Aug 2024

DOI
Local and Nonlocal Stochastic Control of Quantum Chaos: Measurement- and Control-Induced Criticality

Haining Pan, Sriram Ganeshan, Thomas Iadecola, and 2 more authors

Phys. Rev. B, Aug 2024

DOI
Charge and Entanglement Criticality in a U(1)-Symmetric Hybrid Circuit of Qubits

Ahana Chakraborty, Kun Chen, Aidan Zabalo, and 2 more authors

Phys. Rev. B, Jul 2024

DOI
Separate Measurement- and Feedback-Driven Entanglement Transitions in the Stochastic Control of Chaos

Conner LeMaire, Andrew A. Allocca, J. H. Pixley, and 2 more authors

Phys. Rev. B, Jul 2024

DOI
Absence of Quantization in the Circular Photogalvanic Effect in Disordered Chiral Weyl Semimetals

Ang-Kun Wu, Daniele Guerci, Yixing Fu, and 2 more authors

Phys. Rev. B, Jul 2024

DOI
Critical Filaments and Superconductivity in Quasiperiodic Twisted Bilayer Graphene

Xinghai Zhang, Justin H. Wilson, and Matthew S. Foster

arXiv preprint, Jun 2024

Comment: 6 + 21 pages, 5 + 7 figures

Abs arXiv

Moir\’e materials can exhibit electronic topological features yet are inherently quasiperiodic. Nonetheless, the localizing tendency of quasiperiodicity can be prevented by topology. We consider a quasiperiodic variant of the chiral Bistritzer-MacDonald model for twisted bilayer graphene with two incommensurate moir\’e potentials. We observe "filaments" linking magic angles with enhanced density of states and fractal wave functions that evade localization; states away from the filaments mimic fractal surface states of dirty topological superconductors. We demonstrate that topological quasiperiodicity can broadly enhance superconductivity without magic-angle fine-tuning.
Direct Topological Insulator Transitions in Three Dimensions Are Destabilized by Nonperturbative Effects of Disorder

Yixing Fu, Justin H. Wilson, David A. Huse, and 1 more author

Phys. Rev. B, May 2024

DOI
Statistical Mechanics of Stochastic Quantum Control: \d\-Adic R\’enyi Circuits

Andrew A. Allocca, Conner LeMaire, Thomas Iadecola, and 1 more author

arXiv preprint, Apr 2024

Comment: 14+3 pages, 13+1 figures, 3+4 tables

Abs arXiv

The dynamics of quantum information in many-body systems with large onsite Hilbert space dimension admits an enlightening description in terms of effective statistical mechanics models. Motivated by this fact, we reveal a connection between three separate models: the classically chaotic \d\-adic R\’{e}nyi map with stochastic control, a quantum analog of this map for qudits, and a Potts model on a random graph. The classical model and its quantum analog share a transition between chaotic and controlled phases, driven by a randomly applied control map that attempts to order the system. In the quantum model, the control map necessitates measurements that concurrently drive a phase transition in the entanglement content of the late-time steady state. To explore the interplay of the control and entanglement transitions, we derive an effective Potts model from the quantum model and use it to probe information-theoretic quantities that witness both transitions. The entanglement transition is found to be in the bond-percolation universality class, consistent with other measurement-induced phase transitions, while the control transition is governed by a classical random walk. These two phase transitions merge as a function of model parameters, consistent with behavior observed in previous small-size numerical studies of the quantum model.
Connecting the Avoided Quantum Critical Point to the Magic-Angle Transition in Three-Dimensional Weyl Semimetals

J. H. Pixley, David A. Huse, and Justin H. Wilson

Phys. Rev. B, Apr 2024

DOI
Entanglement in an Expanding Toroidal Bose-Einstein Condensate

Anshuman Bhardwaj, Ivan Agullo, Dimitrios Kranas, and 2 more authors

Phys. Rev. A, Jan 2024

DOI

2023

Imaging Self-aligned Moiré Crystals and Quasicrystals in Magic-angle Bilayer Graphene on hBN Heterostructures

Xinyuan Lai, Daniele Guerci, Guohong Li, and 5 more authors

arXiv preprint, Nov 2023

Abs arXiv

Using scanning-tunneling-microscopy and theoretical modeling on heterostructures of twisted bilayer graphene and hexagonal Boron-Nitride, we show that the emergent super-moire structures display a rich landscape of moire-crystals and quasicrystals. We reveal a phase-diagram comprised of commensurate moire-crystals embedded in swaths of moire quasicrystals. The 1:1 commensurate crystal, expected to be a Chern insulator, should only exist at one point on the phase-diagram, implying that it ought to be practically undetectable. Surprisingly we find that the commensurate crystals exist over a much wider than predicted range, providing evidence of an unexpected self-alignment mechanism that is explained using an elastic-network model. The remainder of the phase-diagram, where we observe tunable quasicrystals, affords a new platform for exploring the unique electronic-properties of these rarely found in nature structures.
Measurement and Feedback Driven Entanglement Transition in the Probabilistic Control of Chaos

Thomas Iadecola, Sriram Ganeshan, J. H. Pixley, and 1 more author

Phys. Rev. Lett., Aug 2023

DOI
Infinite-Randomness Criticality in Monitored Quantum Dynamics with Static Disorder

Aidan Zabalo, Justin H. Wilson, Michael J. Gullans, and 4 more authors

Phys. Rev. B, Jun 2023

DOI
Magic Angles and Correlations in Twisted Nodal Superconductors

Pavel A. Volkov, Justin H. Wilson, Kevin P. Lucht, and 1 more author

Phys. Rev. B, May 2023

DOI
Current- and Field-Induced Topology in Twisted Nodal Superconductors

Pavel A. Volkov, Justin H. Wilson, Kevin P. Lucht, and 1 more author

Phys. Rev. Lett., May 2023

DOI

2022

Entanglement and Charge-Sharpening Transitions in U(1) Symmetric Monitored Quantum Circuits

Utkarsh Agrawal, Aidan Zabalo, Kun Chen, and 5 more authors

Phys. Rev. X, Oct 2022

DOI
PRA

Analog Spacetimes from Nonrelativistic Goldstone Modes in Spinor Condensates

Justin H. Wilson, Jonathan B. Curtis, and Victor M. Galitski

Phys. Rev. A, Apr 2022

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It is well established that linear dispersive modes in a flowing quantum fluid behave as though they are coupled to an Einstein-Hilbert metric and exhibit a host of phenomena coming from quantum field theory in curved space, including Hawking radiation. We extend this analogy to any nonrelativistic Goldstone mode in a flowing spinor Bose-Einstein condensate. In addition to showing the linear dispersive result for all such modes, we show that the quadratically dispersive modes couple to a special nonrelativistic spacetime called a Newton-Cartan geometry. The kind of spacetime (Einstein-Hilbert or Newton-Cartan) is intimately linked to the mean-field phase of the condensate. To illustrate the general result, we further provide the specific theory in the context of a pseudo-spin-1/2 condensate where we can tune between relativistic and nonrelativistic geometries. We uncover the fate of Hawking radiation upon such a transition: it vanishes and remains absent in the Newton-Cartan geometry despite the fact that any fluid flow creates a horizon for certain wave numbers. Finally, we use the coupling to different spacetimes to compute and relate various energy and momentum currents in these analog systems. While this result is general, present day experiments can realize these different spacetimes including the magnon modes for spin-1 condensates such as Rb-87, Li-7, K-41 (Newton-Cartan), and Na-23 (Einstein-Hilbert).
PRL

Operator Scaling Dimensions and Multifractality at Measurement-Induced Transitions

A. Zabalo, M. J. Gullans, J. H. Wilson, and 5 more authors

Phys. Rev. Lett., Feb 2022

Abs DOI arXiv PDF Supp

Repeated local measurements of quantum many-body systems can induce a phase transition in their entanglement structure. These measurement-induced phase transitions (MIPTs) have been studied for various types of dynamics, yet most cases yield quantitatively similar critical exponents, making it unclear how many distinct universality classes are present. Here, we probe the properties of the conformal field theories governing these MIPTs using a numerical transfer-matrix method, which allows us to extract the effective central charge, as well as the first few low-lying scaling dimensions of operators at these critical points for (1+1)-dimensional systems. Our results provide convincing evidence that the generic and Clifford MIPTs for qubits lie in different universality classes and that both are distinct from the percolation transition for qudits in the limit of large on-site Hilbert space dimension. For the generic case, we find strong evidence of multifractal scaling of correlation functions at the critical point, reflected in a continuous spectrum of scaling dimensions.

2021

PRL

Magnetic Weyl Semimetallic Phase in Thin Films of Eu2Ir2O7

Xiaoran Liu, Shiang Fang, Yixing Fu, and 17 more authors

Phys. Rev. Lett., Dec 2021

Abs DOI arXiv PDF Supp

The interplay between electronic interactions and strong spin-orbit coupling is expected to create a plethora of fascinating correlated topological states of quantum matter. Of particular interest are magnetic Weyl semimetals originally proposed in the pyrochlore iridates, which are only expected to reveal their topological nature in thin film form. To date, however, direct experimental demonstrations of these exotic phases remain elusive, due to the lack of usable single crystals and the insufficient quality of available films. Here, we report on the discovery of signatures for the long-sought magnetic Weyl semimetallic phase in (111)-oriented Eu2Ir2O7 high-quality epitaxial thin films. We observed an intrinsic anomalous Hall effect with colossal coercivity but vanishing net magnetization, which emerges right below the onset of a peculiar magnetic phase with all-in-all-out (AIAO) antiferromagnetic ordering. The anomalous Hall conductivity obtained experimentally is consistent with the theoretical prediction, likely arising from the nonzero Berry curvature emanated by Weyl node pairs near the Fermi level that act as sources and sinks of Berry flux, activated by broken cubic crystal symmetry at the top and bottom terminations of the thin film.
AnnPhys

Rare Regions and Avoided Quantum Criticality in Disordered Weyl Semimetals and Superconductors

J.H. Pixley and Justin H. Wilson

Ann. Phys. (N. Y.), Dec 2021

Abs DOI arXiv

Disorder in Weyl semimetals and superconductors is surprisingly subtle, attracting attention and competing theories in recent years. In this brief review, we discuss the current theoretical understanding of the effects of short-ranged, quenched disorder on the low energy-properties of three-dimensional, topological Weyl semimetals and superconductors. We focus on the role of non-perturbative rare region effects on destabilizing the semimetal phase and rounding the expected semimetal-to-diffusive metal transition into a cross over. Furthermore, the consequences of disorder on the resulting nature of excitations, transport, and topology are reviewed. New results on a bipartite random hopping model are presented that confirm previous results in a p+ip Weyl superconductor, demonstrating that particle–hole symmetry is insufficient to help stabilize the Weyl semimetal phase in the presence of disorder. The nature of the avoided transition in a model for a single Weyl cone in the continuum is discussed. We close with a discussion of open questions and future directions.
NatComm

Controllable Quantum Point Junction on the Surface of an Antiferromagnetic Topological Insulator

Nicodemos Varnava, Justin H. Wilson, J. H. Pixley, and 1 more author

Nat. Commun., Dec 2021

Abs DOI arXiv PDF Supp

Abstract Engineering and manipulation of unidirectional channels has been achieved in quantum Hall systems, leading to the construction of electron interferometers and proposals for low-power electronics and quantum information science applications. However, to fully control the mixing and interference of edge-state wave functions, one needs stable and tunable junctions. Encouraged by recent material candidates, here we propose to achieve this using an antiferromagnetic topological insulator that supports two distinct types of gapless unidirectional channels, one from antiferromagnetic domain walls and the other from single-height steps. Their distinct geometric nature allows them to intersect robustly to form quantum point junctions, which then enables their control by magnetic and electrostatic local probes. We show how the existence of stable and tunable junctions, the intrinsic magnetism and the potential for higher-temperature performance make antiferromagnetic topological insulators a promising platform for electron quantum optics and microelectronic applications.
PRB

Flat Topological Bands and Eigenstate Criticality in a Quasiperiodic Insulator

Yixing Fu, Justin H. Wilson, and J. H. Pixley

Phys. Rev. B, Jul 2021

Abs DOI arXiv PDF Supp

The effects of downfolding a Brillouin zone can open gaps and quench the kinetic energy by flattening bands. Quasiperiodic systems are extreme examples of this process, which leads to new phases and critical eigenstates. We analytically and numerically investigate these effects in a two-dimensional topological insulator with a quasiperiodic potential and discover a complex phase diagram. We study the nature of the resulting eigenstate quantum phase transitions; a quasiperiodic potential can make a trivial insulator topological and induce topological insulator-to-metal phase transitions through a unique universality class distinct from random systems. This wealth of critical behavior occurs concomitantly with the quenching of the kinetic energy, resulting in flat topological bands that could serve as a platform to realize the fractional quantum Hall effect without a magnetic field.
PRB

Moiré Superlattice on the Surface of a Topological Insulator

Jennifer Cano, Shiang Fang, J. H. Pixley, and 1 more author

Phys. Rev. B, Apr 2021

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Twisting van der Waals heterostructures to induce correlated many body states provides a novel tuning mechanism in solid state physics. In this work, we theoretically investigate the fate of the surface Dirac cone of a three-dimensional topological insulator subject to a superlattice potential. Using a combination of diagrammatic perturbation theory, lattice model simulations, and ab initio calculations we elucidate the unique aspects of twisting a single Dirac cone with an induced moiré potential and the role of the bulk topology on the reconstructed surface band structure. We report a dramatic renormalization of the surface Dirac cone velocity as well as demonstrate a topological obstruction to the formation of isolated minibands. Due to the topological nature of the bulk, surface band gaps cannot open; instead additional satellite Dirac cones emerge, which can be highly anisotropic and made quite flat. We discuss the implications of our findings for future experiments.

2020

Berry Phase Manipulation in Ultrathin SrRuO 3 Films

Liang Wu, Fangdi Wen, Yixing Fu, and 7 more authors

Phys. Rev. B, Dec 2020

DOI arXiv
Mana in Haar-random States

Christopher David White and Justin H. Wilson

arXiv preprint, Nov 2020

Abs DOI arXiv

Mana is a measure of the amount of non-Clifford resources required to create a state; the mana of a mixed state on \\ell qudits bounded by \\le \frac 1 2 (\ell \ln d - S_2); \S_2 the state’s second Renyi entropy. We compute the mana of Haar-random pure and mixed states and find that the mana is nearly logarithmic in Hilbert space dimension: that is, extensive in number of qudits and logarithmic in qudit dimension. In particular, the average mana of states with less-than-maximal entropy falls short of that maximum by \\ln \pi/2\. We then connect this result to recent work on near-Clifford approximate \t\-designs; in doing so we point out that mana is a useful measure of non-Clifford resources precisely because it is not differentiable.
npj

Magic-Angle Semimetals

Yixing Fu, Elio J. König, Justin H. Wilson, and 2 more authors

npj Quantum Materials, Oct 2020

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Breakthroughs in two-dimensional van der Waals heterostructures have revealed that twisting creates a moiré pattern that quenches the kinetic energy of electrons, allowing for exotic many-body states. We show that cold atomic, trapped ion, and metamaterial systems can emulate the effects of a twist in many models from one to three dimensions. Further, we demonstrate at larger angles (and argue at smaller angles) that by considering incommensurate effects, the magic-angle effect becomes a single-particle quantum phase transition (including in a model for twisted bilayer graphene in the chiral limit). We call these models “magic-angle semimetals”. Each contains nodes in the band structure and an incommensurate modulation. At magic-angle criticality, we report a nonanalytic density of states, flat bands, multifractal wave functions that Anderson delocalize in momentum space, and an essentially divergent effective interaction scale. As a particular example, we discuss how to observe this effect in an ultracold Fermi gas.
Avoided Quantum Criticality in Exact Numerical Simulations of a Single Disordered Weyl Cone

Justin H. Wilson, David A. Huse, S. Das Sarma, and 1 more author

Phys. Rev. B, Sep 2020

Abs DOI

Existing theoretical works differ on whether three-dimensional Dirac and Weyl semimetals are stable to a short-range-correlated random potential. Numerical evidence suggests the semimetal to be unstable, while some field-theoretic instanton calculations have found it to be stable. The differences go beyond method: the continuum field-theoretic works use a single, perfectly linear Weyl cone, while numerical works use tight-binding lattice models which inherently have band curvature and multiple Weyl cones. In this work, we bridge this gap by performing exact numerics on the same model used in analytic treatments, and we find that all phenomena associated with rare regions near the Weyl node energy found in lattice models persist in the continuum theory: The density of states is nonzero and exhibits an avoided transition. In addition to characterizing this transition, we find rare states and show that they have the expected behavior. The simulations utilize sparse matrix techniques with formally dense matrices; doing so allows us to reach Hilbert space sizes upwards of 107 states, substantially larger than anything achieved before.
Magic-Angle Semimetals with Chiral Symmetry

Yang-Zhi Chou, Yixing Fu, Justin H. Wilson, and 2 more authors

Phys. Rev. B, Jun 2020

Abs DOI

We construct and solve a two-dimensional, chirally symmetric model of Dirac cones subjected to a quasiperiodic modulation. In real space, this is realized with a quasiperiodic hopping term. This hopping model, as we show, at the Dirac node energy has a rich phase diagram with a semimetal-to-metal phase transition at intermediate amplitude of the quasiperiodic modulation, and a transition to a phase with a diverging density of states (DOS) and subdiffusive transport when the quasiperiodic hopping is strongest. We further demonstrate that the semimetal-to-metal phase transition can be characterized by the multifractal structure of eigenstates in momentum space and can be considered as a unique “unfreezing” transition. This unfreezing transition in momentum space generates flat bands with a dramatically renormalized bandwidth in the metallic phase similar to the phenomena of the band structure of twisted bilayer graphene at the magic angle. We characterize the nature of this transition numerically as well as analytically in terms of the formation of a band of topological zero modes. For pure quasiperiodic hopping, we provide strong numerical evidence that the low-energy DOS develops a divergence and the eigenstates exhibit Chalker (quantum-critical) scaling despite the model not being random. At particular commensurate limits the model realizes higher-order topological insulating phases. We discuss how these systems can be realized in experiments on ultracold atoms and metamaterials.
Disorder in Twisted Bilayer Graphene

Justin H. Wilson, Yixing Fu, S. Das Sarma, and 1 more author

Phys. Rev. Research, Jun 2020

Abs DOI

We develop a theory for a type of disorder in condensed matter systems arising from local twist-angle fluctuations in two strongly coupled van der Waals monolayers twisted with respect to each other to create a flat-band moiré superlattice. The paradigm of “twist-angle disorder” arises from the currently ongoing intense research activity in the physics of twisted bilayer graphene. In experimental samples of pristine twisted bilayer graphene, which are nominally free of impurities and defects, the main source of disorder is believed to arise from the unavoidable and uncontrollable nonuniformity of the twist angle across the sample. To address this physics of twist-angle disorder, we develop a real-space, microscopic model of twisted bilayer graphene where the angle enters as a free parameter. In particular, we focus on the size of single-particle energy gaps separating the miniband from the rest of the spectrum, the Van Hove peaks, the renormalized Dirac cone velocity near charge neutrality, and the minibandwidth. We find that the energy gaps and minibandwidth are strongly affected by disorder while the renormalized velocity remains virtually unchanged. We discuss the implications of our results for the ongoing experiments on twisted bilayer graphene. Our theory is readily generalized to future studies of twist-angle disorder effects on all electronic properties of moiré superlattices created by twisting two coupled van der Waals materials with respect to each other.
Tidal and Nonequilibrium Casimir Effects in Free Fall

Justin H. Wilson, Francesco Sorge, and Stephen A. Fulling

Phys. Rev. D, Mar 2020

Abs DOI

In this work, we consider a Casimir apparatus that is put into free fall (e.g., falling into a black hole). Working in 1+1D1+1D, we find that two main effects occur: First, the Casimir energy density experiences a tidal effect where negative energy is pushed toward the plates and the resulting force experienced by the plates is increased. Second, the process of falling is inherently nonequilibrium and we treat it as such, demonstrating that the Casimir energy density moves back and forth between the plates after being “dropped,” with the force modulating in synchrony. In this way, the Casimir energy behaves as a classical liquid might, putting (negative) pressure on the walls as it moves about in its container. In particular, we consider this in the context of a black hole and the multiple vacua that can be achieved outside of the apparatus.
PRB

Critical Properties of the Measurement-Induced Transition in Random Quantum Circuits

Aidan Zabalo, Michael J. Gullans, Justin H. Wilson, and 3 more authors

Phys. Rev. B, Feb 2020

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We numerically study the measurement-driven quantum phase transition of Haar-random quantum circuits in 1+1 dimensions. By analyzing the tripartite mutual information we are able to make a precise estimate of the critical measurement rate pc=0.17(1). We extract estimates for the associated bulk critical exponents that are consistent with the values for percolation, as well as those for stabilizer circuits, but differ from previous estimates for the Haar-random case. Our estimates of the surface order parameter exponent appear different from those for stabilizer circuits or percolation, but we cannot definitively rule out the scenario where all exponents in the three cases match. Moreover, in the Haar case the prefactor for the entanglement entropies Sn depends strongly on the Rényi index n; for stabilizer circuits and percolation this dependence is absent. Results on stabilizer circuits are used to guide our study and identify measures with weak finite-size effects. We discuss how our numerical estimates constrain theories of the transition.

2019

Casimir Effect in Free Fall towards a Schwarzschild Black Hole

Francesco Sorge and Justin H. Wilson

Phys. Rev. D, Nov 2019

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2018

The Equivalence Principle at Work in Radiation from Unaccelerated Atoms and Mirrors

S. A. Fulling and J. H. Wilson

Phys. Scr., Nov 2018

Abs DOI

The equivalence principle is a perennial subject of controversy, especially in connection with radiation by a uniformly accelerated classical charge, or a freely falling charge observed by a supported detector. Recently, related issues have been raised in connection with the Unruh radiation associated with accelerated detectors (including two-level atoms and resonant cavities). A third type of system, very easy to analyze because of conformal invariance, is a two-dimensional scalar field interacting with perfectly reflecting boundaries (mirrors). After reviewing the issues for atoms and cavities, we investigate a stationary mirror from the point of view of an accelerated detector in ‘Rindler space’. In keeping with the conclusions of earlier authors about the electromagnetic problem, we find that a radiative effect is indeed observed; from an inertial point of view, the process arises from a collision of the negative vacuum energy of Rindler space with the mirror. There is a qualitative symmetry under interchange of accelerated and inertial subsystems (a vindication of the equivalence principle), but it hinges on the accelerated detector’s being initially in its own ‘Rindler vacuum’. This observation is consistent with the recent work on the Unruh problem.
Do the Surface Fermi Arcs in Weyl Semimetals Survive Disorder?

Justin H. Wilson, J. H. Pixley, David A. Huse, and 2 more authors

Phys. Rev. B, Jun 2018

Abs DOI

We theoretically study the topological robustness of the surface physics induced by Weyl Fermi-arc surface states in the presence of short-ranged quenched disorder and surface-bulk hybridization. This is investigated with numerically exact calculations on a lattice model exhibiting Weyl Fermi arcs. We find that the Fermi-arc surface states, in addition to having a finite lifetime from disorder broadening, hybridize with nonperturbative bulk rare states making them no longer bound to the surface (i.e., they lose their purely surface spectral character). Thus, we provide strong numerical evidence that the Weyl Fermi arcs are not topologically protected from disorder. Nonetheless, the surface chiral velocity is robust and survives in the presence of strong disorder, persisting all the way to the Anderson-localized phase by forming localized current loops that live within the localization length of the surface. Thus, the Weyl semimetal is not topologically robust to the presence of disorder, but the surface chiral velocity is.
Weyl Semimetal to Metal Phase Transitions Driven by Quasiperiodic Potentials

J. H. Pixley, Justin H. Wilson, David A. Huse, and 1 more author

Phys. Rev. Lett., May 2018

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We explore the stability of three-dimensional Weyl and Dirac semimetals subject to quasiperiodic potentials. We present numerical evidence that the semimetal is stable for weak quasiperiodic potentials, despite being unstable for weak random potentials. As the quasiperiodic potential strength increases, the semimetal transitions to a metal, then to an “inverted” semimetal, and then finally to a metal again. The semimetal and metal are distinguished by the density of states at the Weyl point, as well as by level statistics, transport, and the momentum-space structure of eigenstates near the Weyl point. The critical properties of the transitions in quasiperiodic systems differ from those in random systems: we do not find a clear critical scaling regime in energy; instead, at the quasiperiodic transitions, the density of states appears to jump abruptly (and discontinuously to within our resolution).

2017

Quantum Phases of Disordered Three-Dimensional Majorana-Weyl Fermions

Justin H. Wilson, J. H. Pixley, Pallab Goswami, and 1 more author

Phys. Rev. B, Apr 2017

DOI

2016

Real-Space Mean-Field Theory of a Spin-1 Bose Gas in Synthetic Dimensions

Hilary M. Hurst, Justin H. Wilson, J. H. Pixley, and 2 more authors

Phys. Rev. A, Dec 2016

DOI
Remnant Geometric Hall Response in a Quantum Quench

Justin H. Wilson, Justin C. W. Song, and Gil Refael

Phys. Rev. Lett., Nov 2016

Abs DOI

Out-of-equilibrium systems can host phenomena that transcend the usual restrictions of equilibrium systems. Here, we unveil how out-of-equilibrium states, prepared via a quantum quench in a two-band system, can exhibit a nonzero Hall-type current—a remnant Hall response—even when the instantaneous Hamiltonian is time reversal symmetric (in contrast to equilibrium Hall currents). Interestingly, the remnant Hall response arises from the coherent dynamics of the wave function that retain a remnant of its quantum geometry postquench, and can be traced to processes beyond linear response. Quenches in two-band Dirac systems are natural venues for realizing remnant Hall currents, which exist when either mirror or time-reversal symmetry are broken (before or after the quench). Its long time persistence, sensitivity to symmetry breaking, and decoherence-type relaxation processes allow it to be used as a sensitive diagnostic of the complex out-of-equilibrium dynamics readily controlled and probed in cold-atomic optical lattice experiments.

2015

Quantum Interference Phenomena in the Casimir Effect

Andrew A. Allocca, Justin H. Wilson, and Victor M. Galitski

Phys. Rev. A, Jun 2015

DOI
Repulsive Casimir Force between Weyl Semimetals

Justin H. Wilson, Andrew A. Allocca, and Victor Galitski

Phys. Rev. B, Jun 2015

DOI
Optical and Casimir Effects in Topological Materials

Justin Howard Wilson

2015

Abs DOI

Two major electromagnetic phenomena, magneto-optical effects and the Casimir effect, have seen much theoretical and experimental use for many years. On the other hand, recently there has been an explosion of theoretical and experimental work on so-called topological materials, and a natural question to ask is how such electromagnetic phenomena change with these novel materials. Specifically, we will consider are topological insulators and Weyl semimetals. When Dirac electrons on the surface of a topological insulator are gapped or Weyl fermions in the bulk of a Weyl semimetal appear due to time-reversal symmetry breaking, there is a resulting quantum anomalous Hall effect (2D in one case and bulk 3D in the other, respectively). For topological insulators, we investigate the role of localized in-gap states which can leave their own fingerprints on the magneto-optics and can therefore be probed. We have shown that these states resonantly contribute to the Hall conductivity and are magneto-optically active. For Weyl semimetals we investigate the Casimir force and show that with thickness, chemical potential, and magnetic field, a \emph{repulsive and tunable} Casimir force can be obtained. Additionally, various values of the parameters can give various combinations of traps and antitraps. We additionally probe the topological transition called a Lifshitz transition in the band structure of a material and show that in a Casimir experiment, one can observe a non-analytic “kink” in the Casimir force across such a transition. The material we propose is a spin-orbit coupled semiconductor with large \g\-factor that can be magnetically tuned through such a transition. Additionally, we propose an experiment with a two-dimensional metal where weak localization is tuned with an applied field in order to definitively test the effect of diffusive electrons on the Casimir force—an issue that is surprisingly unresolved to this day. Lastly, we show how the time-continuous coherent state path integral breaks down for both the single-site Bose-Hubbard model and the spin path integral. Specifically, when the Hamiltonian is quadratic in a generator of the algebra used to construct coherent states, the path integral fails to produce correct results following from an operator approach. We note that the problems do not arise in the time-discretized version of the path integral, as expected.

2014

Resonant Faraday and Kerr Effects Due to In-Gap States on the Surface of a Topological Insulator

Justin H. Wilson, Dmitry K. Efimkin, and Victor M. Galitski

Phys. Rev. B, Nov 2014

DOI
Probing the Structure of Entanglement with Entanglement Moments

Justin H. Wilson, Joe Mitchell, and Victor Galitski

Solid State Communications, Oct 2014

DOI
Nonanalytic Behavior of the Casimir Force across a Lifshitz Transition in a Spin-Orbit-Coupled Material

Andrew A. Allocca, Justin H. Wilson, and Victor Galitski

Phys. Rev. B, Aug 2014

DOI

2012

Entanglement Dynamics in a Non-Markovian Environment: An Exactly Solvable Model

Justin H. Wilson, Benjamin M. Fregoso, and Victor M. Galitski

Phys. Rev. B, May 2012

Abs DOI

We study the non-Markovian effects on the dynamics of entanglement in an exactly solvable model that involves two independent oscillators, each coupled to its own stochastic noise source. First, we develop Lie algebraic and functional integral methods to find an exact solution to the single-oscillator problem which includes an analytic expression for the density matrix and the complete statistics, i.e., the probability distribution functions for observables. For long bath time correlations, we see nonmonotonic evolution of the uncertainties in observables. Further, we extend this exact solution to the two-particle problem and find the dynamics of entanglement in a subspace. We find the phenomena of “sudden death” and “rebirth” of entanglement. Interestingly, all memory effects enter via the functional form of the energy and hence the time of death and rebirth is controlled by the amount of noisy energy added into each oscillator. If this energy increases above (decreases below) a threshold, we obtain sudden death (rebirth) of entanglement.

2011

Breakdown of the Coherent State Path Integral: Two Simple Examples

Justin H. Wilson and Victor Galitski

Phys. Rev. Lett., Mar 2011

Abs DOI

We show how the time-continuous coherent state path integral breaks down for both the single-site Bose-Hubbard model and the spin-path integral. Specifically, when the Hamiltonian is quadratic in a generator of the algebra used to construct coherent states, the path integral fails to produce correct results following from an operator approach. As suggested by previous authors, we note that the problems do not arise in the time-discretized version of the path integral.

2009

Mathematical Aspects of Vacuum Energy on Quantum Graphs

G Berkolaiko, J M Harrison, and J H Wilson

J. Phys. A: Math. Theor., Jan 2009

DOI

2007

Index Theorems for Quantum Graphs

S A Fulling, P Kuchment, and J H Wilson

J. Phys. A: Math. Theor., Nov 2007

DOI
Vacuum Energy and Repulsive Casimir Forces in Quantum Star Graphs

S. A. Fulling, L. Kaplan, and J. H. Wilson

Phys. Rev. A, Jul 2007

DOI
Vacuum Energy in Quantum Graphs

Justin H Wilson

2007