Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session W33: Quantum Thermalization |
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Sponsoring Units: DCMP Chair: Michael Gullans, Joint Center for Quantum Information and Computer Science Room: Room 225 |
Thursday, March 9, 2023 3:00PM - 3:12PM |
W33.00001: The statistical properties of eigenstates in chaotic many-body quantum systems Dominik Hahn, David Luitz, John T Chalker We consider the statistical properties of eigenstates of the Hamiltonian or of the time-evolution |
Thursday, March 9, 2023 3:12PM - 3:24PM |
W33.00002: Statistical properties of the off-diagonal matrix elements of observables in eigenstates of integrable systems Yicheng Zhang, Lev Vidmar, Marcos Rigol We study the statistical properties of the off-diagonal matrix elements of observables in the energy eigenstates of integrable quantum systems. They have been found to be dense in the spin-1/2 XXZ chain, while they are sparse in noninteracting systems. We focus on the quasimomentum occupation of hard-core bosons in one dimension, and show that the distributions of the off-diagonal matrix elements are well described by generalized Gamma distributions, in both the presence and absence of translational invariance but not in the presence of localization. We also show that the results obtained for the off-diagonal matrix elements of observables in the spin-1/2 XXZ model are well described by a generalized Gamma distribution. |
Thursday, March 9, 2023 3:24PM - 3:36PM |
W33.00003: Conserved Quantities in Generalized Gibbs Ensemble from Entanglement Hamiltonian Hao Chen, Biao Lian The description and understanding of relaxation and thermalization of isolated quantum many-body systems have been elusive for decades. It has been shown that a subset of conserved quantities may lead an integrable system to relax into a nonthermal state described by a generalized Gibbs ensemble (GGE), however, which sets of conserved quantities constrain the relaxation and which do not is still unclear. Recently, a method of getting subregionally (quasi)local conserved quantities from the entanglement Hamiltonian of a bipartite system has been proposed. We find that the conserved quantities which constrain the relaxation of a 1+1d free-fermion system can be got by the same method while making the system a "coarse-grained subsystem" of a larger system. Generically, these conserved quantities may not commute to each other but should all be included in GGE. |
Thursday, March 9, 2023 3:36PM - 3:48PM |
W33.00004: Relaxation dynamics after a global quench in the massive XXZ chain Imke Schneider, Flávia B Ramos, Jesko Sirker, Andrew Urichuk While there have been great advances in understanding the final equilibration of integrable systems after a quantum quench, relatively little is known about their precise relaxation towards the steady state. In this context, the XXZ chain provides a playground |
Thursday, March 9, 2023 3:48PM - 4:00PM |
W33.00005: Generalized thermalization in quantum-chaotic quadratic Hamiltonians Lev Vidmar, Patrycja Lydzba, Marcos Rigol, Marcin Mierzejewski Thermalization (generalized thermalization) in nonintegrable (integrable) quantum systems requires two ingredients, equilibration and an agreement with the predictions of the Gibbs (generalized Gibbs) ensemble. We prove that observables that exhibit eigenstate thermalization in single-particle sector equilibrate in many-body sectors of quantum-chaotic quadratic models. Remarkably, the same observables do not exhibit eigenstate thermalization in many-body sectors (we establish that there are exponentially many outliers). Hence, the generalized Gibbs ensemble is generally needed to describe their expectation values after equilibration, and it is characterized by Lagrange multipliers that are smooth functions of single-particle energies. |
Thursday, March 9, 2023 4:00PM - 4:12PM |
W33.00006: Superdiffusive Energy Transport in Kinetically Constrained Models Jean-Yves M Desaules, Marko Ljubotina, Maksym Serbyn, Zlatko Papic Universal nonequilibrium properties of isolated quantum systems are typically probed by studying transport of conserved quantities, such as charge or spin, while transport of energy has received considerably less attention. Here, we study infinite-temperature energy transport in the kinetically-constrained PXP model describing Rydberg atom quantum simulators. Our state-of-the-art numerical simulations, including exact diagonalization and time-evolving block decimation methods, reveal the existence of two distinct transport regimes. At moderate times, the energy-energy correlation function displays periodic oscillations due to families of eigenstates forming different su(2) representations hidden within the spectrum. These families of eigenstates generalize the quantum many-body scarred states found in previous works and leave an imprint on the infinite-temperature energy transport. At later times, we observe a broad superdiffusive transport regime that we attribute to the proximity of a nearby integrable point. Intriguingly, strong deformations of the PXP model by the chemical potential do not restore diffusion, but instead lead to a stable superdiffusive exponent z≈3/2. Our results suggest constrained models to be potential hosts of novel transport regimes and call for developing an analytic understanding of their energy transport. |
Thursday, March 9, 2023 4:12PM - 4:24PM |
W33.00007: Scrambling of quantum information in interacting integrable systems Neha Zaidi, Laimei Nie Scrambling or delocalization of quantum information is an important indicator of how chaotic a many-body quantum dynamics is, and can be quantified by the Tri-partite Operator Mutual Information (TOMI), defined through the entanglement of the unitary evolution operator. While TOMI has been thoroughly studied in the contexts of systems exhibiting either simple or maximally chaotic dynamics, its behavior in systems with "intermediate" dynamics is yet to be understood. One example of such systems is the interacting integrable models, where the interplay of interactions and extensive number of conserved charges may lead to interesting scrambling behavior. Here we look at various interacting integrable models, including the XXZ spin chain and the one-dimensional Hubbard model. We begin by performing a numerical analysis of TOMI in these systems, focusing on the scaling behavior of its late-time saturation value. We then present an analytical interpretation using the recently developed tool invoking Bethe Ansatz, and make connections and comparisons with chaotic dynamics with a finite number of conserved charges. |
Thursday, March 9, 2023 4:24PM - 4:36PM |
W33.00008: Field theory approach to eigenstate thermalization in random quantum circuits Yunxiang Liao, Victor M Galitski Eigenstate thermalization hypothesis (ETH) explains the emergence of the statistical mechanics behavior in isolated quantum systems, and relates thermalization to the statistics of energy eigenstates. In this work, we investigate the statistics of quasienergy eigenstates in Floquet random quantum circuits where each qudit is coupled with all its neighboring qudits by independent Haar random unitaries at arbitrary and distinct substeps. Within the supersymmetric sigma-model framework, we prove that the correlation function of the quasienergy eigenstates agrees with that of the circular unitary ensemble to the leading order in the Hilbert space dimension N. This result shows that the matrix elements of local traceless operators in the quasienergy eigenbasis have small variance of the order of 1/N, consistent with ETH. Moreover, the eigenstate correlation function allows for the investigation of the temporal relaxation of physical observables to their thermal expectation values. |
Thursday, March 9, 2023 4:36PM - 4:48PM |
W33.00009: Dynamical purifcation and deep thermalization Matteo Ippoliti, Wen Wei Ho Quantum thermalization in a many-body system is defined by the approach of local expectation values towards universal, equlibrium values. Recently, it was demonstrated that universal statistics can emerge not just in expectation values, but also in distributions of states on a subsystem obtained by projectively measuring the complementary subsystem. Specifically, this ensemble of states, known as the projected ensemble, can under certain conditions mimic the behavior of a uniformly random ensemble, a phenomenon dubbed deep thermalization. We investigate the dynamical process underlying this novel emergent universality. Leveraging a space-time duality mapping for one-dimensional quantum circuits, we argue that the physics of dynamical purification, which arises in the context of monitored quantum systems, constrains deep thermalization. In particular we show that dynamical purification can lead to a separation of timescales between the equilibration of different moments of the projected ensemble: moment k=1 corresponding to regular thermalization, and high moments k»1 corresponding to deep thermalization. Our results suggest that the projected ensemble can probe nuanced features of quantum dynamics inaccessible to regular thermalization, such as quantum information scrambling. |
Thursday, March 9, 2023 4:48PM - 5:00PM |
W33.00010: Solvable model of deep thermalization with distinct design times Wen Wei Ho, Matteo Ippoliti We study the emergence over time of a universal, uniform distribution of quantum states on a finite subsystem, induced by projectively measuring the rest of the system. Dubbed deep thermalization, this phenomenon represents a form of equilibration in quantum many-body systems stronger than regular thermalization, which only constrains the ensemble-averaged values of observables. While there exist quantum circuit models of dynamics in one dimension where this phenomenon can be shown to arise exactly, these are special in that deep thermalization occurs at precisely the same time as regular thermalization. Here, we present an exactly-solvable model of chaotic dynamics where the two processes can be shown to occur over different time scales. The model is composed of a finite subsystem coupled to an infinite random-matrix bath through a small constriction, and highlights the role of locality and imperfect thermalization in constraining the formation of such universal wavefunction distributions. We test our analytical predictions against exact numerical simulations, finding excellent agreement. |
Thursday, March 9, 2023 5:00PM - 5:12PM |
W33.00011: Non-local nature of deep thermalization Harshank Shrotriya, Wen Wei Ho Quantum thermalization in a many-body system refers to the approach of local observables toward universal values, captured by a thermal Gibbs state. Recently, a novel generalized form of quantum thermalization was introduced, wherein a local subsystem is described by an ensemble of pure states, each of which is associated with a projective measurement outcome of the complementary subsystem. Remarkably, it was shown that the distribution of such states can under certain conditions approach a maximally entropic, uniform form, dubbed "deep thermalization". Here, we study the role of boundary conditions in governing the emergence of this dynamical phenomenon. Focusing on the maximally chaotic (1+1)-d kicked Ising model, we show that deep thermalization arises at late times for a small subsystem contained within the bulk of an infinitely large system, irrespective of the global topology. At finite times though, boundary effects do lead to observable differences: deep thermalization happens twice as fast for a system with periodic boundaries than with open boundaries. Our results reveal an inherent non-local feature associated with deep thermalization, in contrast to regular thermalization which is insensitive to boundary effects, owing to constraints placed on information propagation by Lieb-Robinson bounds. |
Thursday, March 9, 2023 5:12PM - 5:24PM |
W33.00012: Robust non-equilibrium surface currents with and without band topology Mark T Mitchison, Ángel Rivas, Miguel Angel Martin-Delgado We study two-dimensional bosonic and fermionic lattice systems under nonequilibrium conditions corresponding to a sharp gradient of temperature imposed by two thermal baths. In particular, we consider a lattice model with broken time-reversal symmetry that exhibits both topologically trivial and nontrivial phases. For both bosonic and fermionic systems, we find chiral edge currents that are robust against coupling to reservoirs and to the presence of defects on the boundary or in the bulk. This robustness not only originates from topological effects at zero temperature but, remarkably, also persists as a result of dissipative symmetries in regimes where band topology plays no role. Chirality of the edge currents implies that energy locally flows against the temperature gradient without any external work input. Therefore, an observer living on the boundary of the system sees very peculiar behaviour: the heat current locally flows from cold to hot, despite the second law of thermodynamics being obeyed overall. This novel boundary effect is found to persist in three-dimensional systems. We provide an explanation for the phenomenon in terms of the erasure effect --- currents in the bulk cancel while they add constructively on the boundary --- whose emergence is dictated by the nonequilibrium distribution function and the underlying symmetries of the lattice. |
Thursday, March 9, 2023 5:24PM - 5:36PM |
W33.00013: Charge-conserving equilibration of quantum Hall edge states. Eugene Sukhorukov We address the problem of the equilibration of quantum Hall (QH) edge states under the additional constraint of charge conservation.This question applies generally to any chiral quasi-one dimensional states, but it naturally arises in the context of resent experiments with quantum Hall systems. This is because QH edge states carry charge excitations with approximately constant speed, and in a typical mesoscopic experiment, to finite distances. Therefore, edge states dynamics must depend on the initial generally non-equilibrium state via boundary condition. Thus even in the case of a strong coupling of edge states to the bath of neutral excitations, their complete equilibration is not possible. In order to investigate the equilibration process under such conditions, we propose the model describing QH edge states a chiral bosonic channel strongly coupled to an array of identical Ohmic contacts with small capacitances. Such model effectively describes a chiral one-dimensional charged channel with dissipation. Asymptotically close to the equilibrium state, the electron distribution function acquires an almost equilibrium form with the universal correction, which is a function of the energy and distance form the injection point, where a non-equilibrium state is created. |
Thursday, March 9, 2023 5:36PM - 5:48PM |
W33.00014: Hydrodynamic description of Non-Equilibrium Radiation Eric Akkermans Non-equilibrium radiation is addressed theoretically by means of a stochastic lattice-gas model. We consider a resonating transmission line composed of a chain of radiation resonators, each at a local equilibrium, whose boundaries are in thermal contact with two blackbody reservoirs at different temperatures. In the long chain limit, the stationary state of the non-equilibrium radiation is obtained in a closed form. The corresponding spectral energy density departs from the Planck expression, yet it obeys a useful scaling form. A macroscopic fluctuating hydrodynamic limit is obtained leading to a Langevin equation whose transport parameters are calculated. In this macroscopic limit, we identify a local temperature which characterises the spectral energy density. The generality of our approach is discussed and applications for the interaction of non-equilibrium radiation with matter are suggested. |
Thursday, March 9, 2023 5:48PM - 6:00PM |
W33.00015: Quantum thermodynamics at strong system-reservoir coupling Nicholas Anto-Sztrikacs, Ahsan Nazir, Dvira Segal At the nanoscale, strong system-reservoir interactions are ubiquitous and could play a significant role in the development of nanoscale quantum machines. As a result, a formulation of thermodynamics which is valid in the quantum regime must incorporate the effects of strong system-reservoir couplings. The reaction coordinate (RC) mapping tackles the strong coupling regime by reshaping the system-environment boundary to include a collective degree of freedom from the environment. This results in an enlarged system, which in turn, is weakly coupled to its surroundings, thus allowing the use of weak-coupling tools for simulations. Nevertheless, this approach is limited due to the growing Hilbert space of the extended system, and the lack of analytical insights into the strong coupling regime. |
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