Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session T50: Many-Body LocalizationRecordings Available
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Sponsoring Units: DCMP Chair: Dominique Laroche, University of Florida Room: McCormick Place W-474A |
Thursday, March 17, 2022 11:30AM - 11:42AM |
T50.00001: Directly Obtaining Entanglement Dynamics through Quantum Correlation Transfer Functions; Demonstrating the Mechanism of Many-Body Localization Peyman Azodi, Herschel Rabitz We introduce the Quantum Correlation Transfer Function (QCTF) approach to entanglement dynamics in many-body quantum systems and employ this framework to demonstrate the mechanism of Many-Body Localization (MBL). We show that in the QCTF framework, the entanglement dynamics of the two-level particles of a many-body quantum system can be fully characterized directly from the system's Hamiltonian, which circumvents the bottleneck of calculating the many-body system's time-evolution. This result provides a new foundation to study the Eigenstate Thermalization Hypothesis (ETH). By employing the QCTF-based approach, we demonstrate the MBL dynamics in disordered Heisenberg spin chains. Furthermore, we prove the validity of a previous fundamental conjecture regarding the MBL phase by showing that in strongly-disordered spin chains with short-range interaction, the quantum correlation between particles is exponentially attenuated with respect to the site-to-site distance. The QCTF approach can be extended to address general issues regarding non-equilibrium quantum statistics in spin lattices with different geometries. |
Thursday, March 17, 2022 11:42AM - 11:54AM |
T50.00002: Coherent pairs probe disorder-suppressed quantum dynamics in a random dipolar magnet Adrian Beckert, Manuel Grimm, Nino Wili, René Tschaggelar, Gunnar Jeschke, Guy Matmon, Simon Gerber, Markus Müller, Gabriel Aeppli Quantum information processing relies on the persistent coherence of quantum states and holds great potential for application, ranging from computation to communication and metrology. However, uncontrolled interactions among quantum bits (qubits) and with their environment lead to decoherence, i.e., the loss of quantum information [1,2]. Protecting coherence is generally difficult, particularly in quantum systems with magnetic degrees of freedom which directly couple to electron spin fluctuations. Though, many-body localization (MBL) [3,4] and its precursors [5-7] have been predicted to suppress relaxation processes and noise in disordered magnets and, thus, to enhance coherence. |
Thursday, March 17, 2022 11:54AM - 12:06PM |
T50.00003: Entanglement mean field theory and MBL in two dimensions Philip Crowley We present “entanglement mean field theory”, a statistical theory of the subsystem entanglement in eigenstates. This theory applies across the MBL-thermal phase transition to a class of models with “central seed” geometry. The predictions of the theory show good agreement with numerics, even for subsystems which are intermediate to localised and thermal. |
Thursday, March 17, 2022 12:06PM - 12:18PM |
T50.00004: Transient Response of Disordered Systems to an Interaction Quench Eric Dohner, Hanna Terletska, Ka-Ming Tam, Juana Moreno, Herbert F Fotso We present a solution for the nonequilibrium dynamics of an interacting disordered system. The approach adapts the combination of the equilibrium dynamical mean field theory (DMFT) and coherent potential approximation (CPA) methods to the nonequilibrium many-body formalism using the Kadanoff-Baym-Keldysh complex time contour. We use our time domain solution to obtain the equilibrium density of states of the disordered interacting system described by the Anderson-Hubbard model, bypassing the necessity for the cumbersome analytical continuation process. We further apply the nonequilibrium solution to an interaction quench of the isolated disordered system. Here, the interaction is abruptly changed from zero (non-interacting system) to another constant (finite) value at which it is subsequently kept. We observe via the time-dependence of the potential, kinetic, and total energies the effect of disorder on the relaxation of the system as a function of the final interaction strength. The real-time approach has the potential to shed new light on the fundamental role of disorder in the nonequilibrium dynamics of interacting quantum systems. |
Thursday, March 17, 2022 12:18PM - 12:30PM |
T50.00005: Machine learning many-body quantum phases in non-equilibrium systems with single-particle mobility edge Yi-Ting Hsu, Xiao Li, Colin Beveridge The many-body quantum phases in isolated quasi-periodic systems are an intriguing subject that cannot be described by the framework of equilibrium statistical mechanics. One main challenge lies in the fact that there are no well-established order parameters that can definitively determine the number and nature of possible dynamical phases. In particular, a non-ergodic metallic phase has been proposed as a novel phase between the many-body localized and thermalized phases in the Generalized Aubry Andre model, a one-dimensional quasiperiodic chain with single-particle mobility edge (SPME). While the existence and origin of the non-ergodic metal remain elusive, this phase has been conjectured as a natural consequence of the presence of SPME. In this talk, I will present a general machine-learning protocol that can determine the phase diagrams of systems with controversial phases, a situation where the conventional supervised learning is not applicable. By applying our neural-network based method to study multiple different models with SPME, I will discuss the stability of the non-ergodic metal and whether it originates from SPME. |
Thursday, March 17, 2022 12:30PM - 12:42PM |
T50.00006: Probing localization properties of the MBL transition via an imaginary vector potential Liam C O'Brien, Gil Refael Identifying and measuring the ``localization length'' in many-body systems in the vicinity of a many-body localization transition is difficult. Following Hatano and Nelson, a recent work (Heußen, White, Refael, Phys. Rev. B 103, 064201) introduced an ``imaginary vector potential'' to a disordered ring of interacting fermions, in order to measure a localization length corresponding to the end-to-end Green's function of the corresponding open chain. We employ this non-hermitian localization technique to extract the distribution of the localization length at the transition point. We find that the localization-length distributions at the critical points are well-described by extreme value distributions. We explain the appearance of these distributions, as well as connect our study to the localization length identified in the avalanche model of the many-body localization transition. |
Thursday, March 17, 2022 12:42PM - 12:54PM |
T50.00007: Quantum interference and disorder-free localized quantum dynamics in an interacting two-dimensional lattice gauge theory Nilotpal Chakraborty, Markus Heyl, Petr Karpov, Roderich Moessner
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Thursday, March 17, 2022 12:54PM - 1:06PM |
T50.00008: A stabilisation mechanism for many body localisation in 2D Darryl Foo, Nyayabanta Swain, Pinaki Sengupta, Gabriel Lemarie, Shaffique Adam Experiments in cold atom systems see identical signatures of many body localisation (MBL) in both one-dimensional (d=1) and two-dimensional (d=2) systems despite the thermal avalanche hypothesis showing that the MBL phase is unstable for d>1. Underpinning the thermal avalanche argument is the assumption of exponential localisation of local integrals of motion (LIOMs), a result taken from the Furstenberg theorem. In this work we show that the Furstenberg theorem assumptions break down for real experimental systems, resulting in super-exponential localisation of LIOMs. A more careful analysis of the quantum avalanche argument for such realistic systems shows that the critical dimension changes from d=1 to d=2, thereby bridging the divide between the experimental demonstrations of MBL in these systems and existing theoretical arguments that claim that such demonstrations are impossible. |
Thursday, March 17, 2022 1:06PM - 1:18PM |
T50.00009: Theory of growth of number entropy in disordered systems Roopayan Ghosh, Marko Znidaric
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Thursday, March 17, 2022 1:18PM - 1:30PM |
T50.00010: Relaxation at different length-scales in models of many-body localization Jacek Herbrych, Marcin Mierzejewski, Peter Prelovsek We study dynamical correlation functions in the random-field Heisenberg chain, which probes the relaxation times at different length scales. Firstly, we argue that the relaxation time associated with the dynamical imbalance (examining the relaxation at the smallest length scale) decreases with disorder much faster than the one related to the dc conductivity, which probes the global response of the system. We argue that the observed dependence of relaxation on the length scale originates from local nonresonant regions (islands). The latter has particularly long relaxation times or remains frozen, allowing for nonzero dc transport via higher-order processes. Based on the numerical evidence, we introduce a toy model that suggests that the nonresonant islands' asymptotic dynamics are essential for the proper understanding of the disordered chains with many-body interactions. |
Thursday, March 17, 2022 1:30PM - 1:42PM |
T50.00011: Krylov complexity in many-body localization systems Cheng-Ju Lin, Fabian Ballar Trigueros We study the operator growth and Krylov complexity in many-body localization (MBL) systems. Using the Lanczos algorithm, the operator growth problem can be mapped to a single particle hopping problem on a semi-infinite chain with the hopping amplitudes given by the Lanczos coefficients. We find that the hopping amplitudes grow linearly along the chain with a logarithmic correction in both MBL and ergodicity phases. Moreover, in the MBL phase, the hopping amplitudes have an additional even-odd modulation and some effective randomness. We show numerical evidences which suggest that in MBL, the corresponding single particle hopping problem is localized, resulting in its bounded Krylov complexity of the operators. In addition, we obtain the spectral function and auto-correlation function in MBL from the Lanczos algorithm. By extrapolating and modeling the behavior of the Lanczos coefficients, we discuss the possible features of the spectral function in MBL in the thermodynamic limit. |
Thursday, March 17, 2022 1:42PM - 1:54PM |
T50.00012: Probing many-body localization by excited-state VQE Shuo Liu, Shixin Zhang, Chang-Yu Hsieh, Shengyu Zhang, Hong Yao Non-equilibrium physics including many-body localization (MBL) has attracted increasing attentions, but theoretical approaches of reliably studying non-equilibrium properties remain quite limited. We propose a systematic approach to probe MBL phases on a digital quantum computer via the excited-state variational quantum eigensolver (VQE) and demonstrate convincing results of MBL on a quantum hardware, which we believe paves a promising way for future simulations of non-equilibrium systems beyond the reach of classical computations in the noisy intermediate-scale quantum (NISQ) era. Moreover, the MBL probing protocol based on excited-state VQE is NISQ-friendly, as it can successfully differentiate the MBL phase from thermal phases with relatively-shallow quantum circuits, and it is also robust against the effect of quantum noises. |
Thursday, March 17, 2022 1:54PM - 2:06PM |
T50.00013: MBL-Ergodic Transitions in Systems with Correlated Disorder Rajdeep Sensarma, Abhisek Samanta, AHANA CHAKRABORTY We study transitions from many body localized to ergodic phase in one dimensional spin systems with correlated disorder. Using two different parameters to tune the width and correlations of the random couplings separately, we derive a phase diagram in the width-correlation plane. We understand the phase diagram in terms of an effective single parameter related to the sample variance of the couplings. This allows us to track the phase boundary analytically in this model. |
Thursday, March 17, 2022 2:06PM - 2:18PM |
T50.00014: Localization in two-dimensional many-body quasiperiodic models Claudio Castelnovo, Antonio Strkalj, Elmer V Doggen Many-body localization (MBL) provides a mechanism to avoid thermalization in interacting systems. It is well understood that the MBL phase can exist in closed one-dimensional systems subjected to random disorder, quasiperiodic modulations, or homogeneous electric fields. However, the fate of MBL in higher dimensions remains unclear. Although some experiments on randomly disordered two-dimensional (2D) systems observe a stable MBL phase on intermediate time scales, recent theoretical works show that the phenomenon cannot persist forever and in a thermodynamic limit due to the rare regions and the avalanche instability. On the other hand, quasiperiodic systems do not host rare regions, and the avalanche instability is avoided; yet, the existence of an MBL phase in these systems remains to date largely unexplored. Using the numerical method of time-dependent variational principle, we investigate the localization properties of the many-body 2D Aubry-Andre´ quasiperiodic model by studying its out-of-equilibrium dynamics. We show that a stable MBL phase exists in the thermodynamic limit, in contrast to random disorder. Furthermore, we show that deterministic lines of weak potential, which appear in this model, support transport while keeping the localized parts of the system unchanged. |
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