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.
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.
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.
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 impact of quenched disorder on the dynamics of locally constrained quantum spin chains, that describe 1D arrays of Rydberg atoms in both the frozen (Ising-type) and dressed (XY-type) regime. Performing large-scale numerical experiments, we observe no trace of many-body localization even at large disorder. Analyzing the role of quenched disorder terms in constrained systems we show that they act in two, distinct and competing ways: as an on-site disorder term for the basic excitations of the system, and as an interaction between excitations. The two contributions are of the same order, and as they compete (one towards localization, the other against it), one does never enter a truly strong disorder, weak interaction limit, where many-body localization occurs. Such a mechanism is further clarified in the case of XY-type constrained models: there, a term which would represent a bona fide local quenched disorder term acting on the excitations of the clean model must be written as a series of nonlocal terms in the unconstrained variables. Our observations provide a simple picture to interpret the role of quenched disorder that could be immediately extended to other constrained models or quenched gauge theories.
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 study time dynamics of 1D disordered Heisenberg spin-1/2 chain focusing on a regime of large system sizes and a long time evolution. This regime is relevant for observation of many-body localization (MBL), a phenomenon that is expected to freeze the dynamics of the system and prevent it from reaching thermal equilibrium. Performing extensive numerical simulations of the imbalance, a quantity often employed in the experimental studies of MBL, we show that the regime of a slow power-law decay of imbalance persists to disorder strengths exceeding by at least a factor of 2 the current estimates of the critical disorder strength for MBL. Even though we investigate time evolution up to few thousands tunneling times, we observe no signs of the saturation of imbalance that would suggest freezing of system dynamics and provide a smoking gun evidence of MBL. We demonstrate that the situation is qualitatively different when the disorder is replaced by a quasiperiodic potential. In this case, we observe an emergence of a pattern of oscillations of the imbalance that is stable with respect to changes in the system size. This suggests that the dynamics of quasiperiodic systems remain fully local at the longest time scales we reach provided that the quasiperiodic potential is sufficiently strong. Our study identifies challenges in an unequivocal experimental observation of the phenomenon of MBL.