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Eigenstate Transition between Constrained and Diagonal Many-Body Localization: Hierarchy of Many-Body-Localized Dynamical Phases of Matter

Chun Chen, Yan Chen

Published Nov 18, 2020• 0 citations
OpenAlex

Abstract

We study the full many-body localization (MBL) in the Rydberg atomic quantum simulator with quasiperiodic modulation. Employing both exact diagonalization (ED) and time-evolving block decimation (TEBD) methods, we identify evidence of a constrained many-body-localized phase stabilized by a pure quasirandom field transverse to the direction of the projection. Intriguingly, through the lens of quantum dynamics, we find that rotating the modulated field from parallel towards perpendicular to the projection axis induces an eigenstate transition between the diagonal and the constrained MBL phases. Remarkably, the growth of the entanglement entropy in constrained MBL follows a double-logarithmic form, whereas it changes to a power law in the diagonal limit. Although the diagonal MBL steered by a strong modulation along the projection direction can be understood by extending the phenomenology of local integrals of motion, a thorough analysis of the constrained MBL calls for the new ingredients. As a preliminary first step, we unveil the significance of confined nonlocal effects in the integrals of motion of the constrained MBL phase, which potentially challenges the established framework of the unconstrained MBL. Since the quasiperiodic modulation has been achievable in cold-atom laboratories, the constrained and diagonal MBL regimes, as well as the eigenstate transition between them, should be within reach of the ongoing Rydberg experiments.

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We study the full many-body localization (MBL) in the Rydberg atomic quantum simulator with quasiperiodic modulation. Employing both exact diagonalization (ED) and time-evolving block decimation (TEBD) methods, we identify evidence of a constrained many-body-localized phase stabilized by a pure quasirandom field transverse to the direction of the projection. Intriguingly, through the lens of quantum dynamics, we find that rotating the modulated field from parallel towards perpendicular to the projection axis induces an eigenstate transition between the diagonal and the constrained MBL phases. Remarkably, the growth of the entanglement entropy in constrained MBL follows a double-logarithmic form, whereas it changes to a power law in the diagonal limit. Although the diagonal MBL steered by a strong modulation along the projection direction can be understood by extending the phenomenology of local integrals of motion, a thorough analysis of the constrained MBL calls for the new ingredients. As a preliminary first step, we unveil the significance of confined nonlocal effects in the integrals of motion of the constrained MBL phase, which potentially challenges the established framework of the unconstrained MBL. Since the quasiperiodic modulation has been achievable in cold-atom laboratories, the constrained and diagonal MBL regimes, as well as the eigenstate transition between them, should be within reach of the ongoing Rydberg experiments.
We study the full many-body localization (MBL) in the Rydberg atomic quantum simulator with quasiperiodic modulation. Employing both exact diagonalization (ED) and time-evolving block decimation (TEBD) methods, we identify evidence of a constrained many-body-localized phase stabilized by a pure quasirandom field transverse to the direction of the projection. Intriguingly, through the lens of quantum dynamics, we find that rotating the modulated field from parallel towards perpendicular to the projection axis induces an eigenstate transition between the diagonal and the constrained MBL phases. Remarkably, the growth of the entanglement entropy in constrained MBL follows a double-logarithmic form, whereas it changes to a power law in the diagonal limit. Although the diagonal MBL steered by a strong modulation along the projection direction can be understood by extending the phenomenology of local integrals of motion, a thorough analysis of the constrained MBL calls for the new ingredients. As a preliminary first step, we unveil the significance of confined nonlocal effects in the integrals of motion of the constrained MBL phase, which potentially challenges the established framework of the unconstrained MBL. Since the quasiperiodic modulation has been achievable in cold-atom laboratories, the constrained and diagonal MBL regimes, as well as the eigenstate transition between them, should be within reach of the ongoing Rydberg experiments.
Abstract We study many-body localization (MBL) in a spin-chain model mimicking the Rydberg-blockade quantum simulator with infinite-strength projection and moderate quasiperiodic modulation. Employing exact diagonalization, Krylov-typicality technique, and time-evolving block decimation, we identify evidence for a constrained MBL phase stabilized by a pure quasirandom transverse field. Intriguingly, the constrained MBL transition may embody a discontinuous eigenstate phase transition, whose discontinuity nature significantly suppresses finite-size drifts that plague most numerical studies of conventional MBL transition. Through quantum dynamics, we find that rotating the modulated field from parallel toward perpendicular to the projection axis induces an eigenstate transition between diagonal and constrained MBL phases. The entanglement-entropy growth in constrained MBL follows a double-log form, whereas it changes to a power law in approaching the diagonal limit. By unveiling confined nonlocal effects in integrals of motion of constrained MBL, we show this insulating state is not a many-body Anderson insulator. Our predictions are testable in Rydberg experiments.
At low energy, the dynamics of excitations of many physical systems are locally constrained. Examples include frustrated antiferromagnets, fractional quantum Hall fluids, and Rydberg atoms in the blockaded regime. Can such locally constrained systems be fully many-body localized? In this Letter, we answer this question affirmatively and elucidate the structure of the accompanying quasilocal integrals of motion. By studying disordered spin chains subject to a projection constraint in the z direction, we show that full many-body localization (MBL) is stable at strong z-field disorder and identify a new mechanism of localization through resonance at strong transverse disorder. However, MBL is not guaranteed; the constraints can "frustrate" the tendency of the spins to align with the transverse fields and lead to full thermalization or criticality. We further provide evidence that the transition is discontinuous in local observables with large sample-to-sample variations. Our dynamical phase diagram is accessible in current Rydberg atomic experiments which realize programmable constrained Ising Hamiltonians.
Study how quantum information propagates through spacetime manifold provides a means of identifying, distinguishing, and classifying novel phases of matter fertilized by many-body effects in strongly interacting systems in and out of equilibrium. Via a fuller characterization of key aspects regarding dynamic behaviors of information, we perform such an analysis on constrained many-body localization -- a newly proposed fully localized state under infinite-interaction limit -- in quasirandom Rydberg blockade spin chain models using thermal out-of-time-order commutators (OTOCs). The OTOC light cones predict a hitherto unknown Lieb-Robinson bound for constrained many-body localization, which is qualitatively different from that of unconstrained many-body Anderson insulators stabilized at weak-interaction limit. Our corroborated numeric and analytic study suggests that constrained many-body localization is a distinct dynamical eigenstate phase whose nonergodicity is beyond local-integral-of-motion phenomenology. Together, these findings consolidate the hierarchy of unconventional quantum dynamics encompassing constrained, unconstrained, and diagonal many-body-localized regimes.
Study how quantum information propagates through the spacetime manifold may provide a useful means of identifying, distinguishing, and classifying the unconventional phases of matter fertilized by many-body effects in strongly interacting systems in and out of equilibrium. Via a fuller characterization of the key aspects regarding the descendent novel dynamical processes, we performed such an analysis on the constrained many-body-localized phase -- a newly-discovered fully localized state in the infinite-interaction limit -- in the quasirandom Rydberg-blockaded spin chains using the thermal out-of-time-ordered commutators (OTOCs). The calculated OTOC lightcone contours predict a new and hitherto unknown Lieb-Robinson bound for the constrained many-body localization, which is qualitatively different from that of the conventional unconstrained many-body Anderson insulators normally arising in the weak-interaction limit. Our combined numerical and analytical investigation thus suggests that the constrained many-body localization is a distinct dynamical phase of matter in constrained quantum systems whose underlying mechanism of nonergodicity is beyond the existing phenomenology of quasilocal integrals of motion. Further, it also consolidates the hierarchy of unconventional quantum dynamics that encompasses constrained, unconstrained, and diagonal many-body-localized states.
We consider disordered many-body systems with periodic time-dependent Hamiltonians in one spatial dimension. By studying the properties of the Floquet eigenstates, we identify two distinct phases: (i) a many-body localized (MBL) phase, in which almost all eigenstates have area-law entanglement entropy, and the eigenstate thermalization hypothesis (ETH) is violated, and (ii) a delocalized phase, in which eigenstates have volume-law entanglement and obey the ETH. The MBL phase exhibits logarithmic in time growth of entanglement entropy when the system is initially prepared in a product state, which distinguishes it from the delocalized phase. We propose an effective model of the MBL phase in terms of an extensive number of emergent local integrals of motion, which naturally explains the spectral and dynamical properties of this phase. Numerical data, obtained by exact diagonalization and time-evolving block decimation methods, suggest a direct transition between the two phases.