publications | Justin H. Wilson

2022

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

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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

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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

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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

Shared under CC BY 4.0

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

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

arXiv:2107.10279 [cond-mat, physics:quant-ph], Jul 2021

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Monitored quantum circuits can exhibit an entanglement transition as a function of the rate of measurements, stemming from the competition between scrambling unitary dynamics and disentangling projective measurements. We study how entanglement dynamics in non-unitary quantum circuits can be enriched in the presence of charge conservation, using a combination of exact numerics and a mapping onto a statistical mechanics model of constrained hard-core random walkers. We uncover a charge-sharpening transition that separates different scrambling phases with volume-law scaling of entanglement, distinguished by whether measurements can efficiently reveal the total charge of the system. We find that while R\’enyi entropies grow sub-ballistically as \\sqrt{t} in the absence of measurement, for even an infinitesimal rate of measurements, all average R\’enyi entropies grow ballistically with time \∼t\. We study numerically the critical behavior of the charge-sharpening and entanglement transitions in U(1) circuits, and show that they exhibit emergent Lorentz invariance and can also be diagnosed using scalable local ancilla probes. Our statistical mechanical mapping technique readily generalizes to arbitrary Abelian groups, and offers a general framework for studying dissipatively-stabilized symmetry-breaking and topological orders.
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

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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

Magic Angles and Current-Induced Topology in Twisted Nodal Superconductors

Pavel A. Volkov, Justin H. Wilson, and J. H. Pixley

Dec 2020

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Motivated by the recent achievements in the realization of strongly correlated and topological phases in twisted van der Waals heterostructures, we study the low-energy properties of a twisted bilayer of nodal superconductors. It is demonstrated that the spectrum of the superconducting Dirac quasiparticles close to the gap nodes is strongly renormalized by twisting and can be controlled with magnetic fields, current, or interlayer voltage. In particular, the application of an interlayer current transforms the system into a topological superconductor, opening a topological gap and resulting in a quantized thermal Hall effect with gapless, neutral edge modes. Close to the "magic angle," where the Dirac velocity of the quasiparticles is found to vanish, a correlated superconducting state breaking time-reversal symmetry is shown to emerge. Estimates for a number of superconducting materials, such as cuprate, heavy fermion, and organic nodal superconductors, show that twisted bilayers of nodal superconductors can be readily realized with current experimental techniques.
Berry Phase Manipulation in Ultrathin SrRuO 3 Films

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

Phys. Rev. B, Dec 2020
Mana in Haar-random States

Christopher David White, and Justin H. Wilson

arXiv:2011.13937 [cond-mat, physics:quant-ph], Nov 2020

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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

Shared under CC BY 4.0

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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

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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.
Controlling a Quantum Point Junction on the Surface of an Antiferromagnetic Topological Insulator

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

arXiv:2008.03316 [cond-mat], Aug 2020

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The abstract notion of topology has led to profound insights into real materials. Notably, the surface and edges of topological materials can host physics, such as unidirectional charge or spin transport, that is unavailable in isolated one- and two-dimensional systems. However, to fully control the mixing and interference of edge-state wave functions, one needs robust and tunable junctions. We propose to achieve this control using an antiferromagnetic topological insulator that supports two distinct types of gapless unidirectional channels on its surface, one from antiferromagnetic domain walls and the other from single-height steps. The distinct geometric nature of these edge modes allows them to intersect robustly to form quantum point junctions, and their presence at the surface makes them subject to control by magnetic and electrostatic tips like those used in scanning probe microscopes. Prospects for realizing such junctions are encouraged by recent material candidate proposals, potentially leading to exciting applications in quantum computing and sensing.
Magic-Angle Semimetals with Chiral Symmetry

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

Phys. Rev. B, Jun 2020

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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

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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

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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

arXiv:1909.07357 [gr-qc], Sep 2019

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In this paper we discuss the Casimir effect in a small cavity, freely falling from spatial infinity in spacetime geometry outside of a Schwarzschild black hole. Our main goal is to search for possible changes in the vacuum energy, as well as particle creation inside the falling cavity, with respect to a comoving observer. Working in the Lema\textbackslashître chart and assuming a cavity size Ł much smaller than the Schwarzschild radius (Ł/r_g≪1\), we solve the Klein-Gordon equation for a massless scalar field confined within the cavity in the reference frame of the comoving observer. We follow Schwinger’s proper time approach, evaluating the one-loop effective action for the field in the falling cavity hence evaluating the corrections to the vacuum energy. We find a small reduction in the absolute value of Casimir energy as the cavity approaches the black hole horizon due to the changing spacetime geometry. Since the spacetime geometry for the cavity changes dynamically, we further find the energy density of the created particles due to the dynamical Casimir effect. These dynamical contributions exactly match the deficit to the static Casimir energy. Combined, the observer measures a net increase in energy within the cavity as she falls.

2018

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

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

Phys. Scr., Nov 2018

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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

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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

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
Remnant Geometric Hall Response in a Quantum Quench

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

Phys. Rev. Lett., Nov 2016

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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
Repulsive Casimir Force between Weyl Semimetals

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

Phys. Rev. B, Jun 2015

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
Probing the Structure of Entanglement with Entanglement Moments

Justin H. Wilson, Joe Mitchell, and Victor Galitski

Solid State Communications, Oct 2014
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

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

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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

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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

2007

Index Theorems for Quantum Graphs

S A Fulling, P Kuchment, and J H Wilson

J. Phys. A: Math. Theor., Nov 2007
Vacuum Energy and Repulsive Casimir Forces in Quantum Star Graphs

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

Phys. Rev. A, Jul 2007