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 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 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.
This dissertation presents new results on two problems concerning the dynamics of certainclasses of interacting many-body systems in quantum mechanics. Chapter 1 is an introduction,\nwhich includes mathematical preliminaries and a summary of the results.\nIn Chapter 2 we introduce the notion of transmission time to study the dynamics of disordered\nquantum spin chains and prove results relating its behavior to many-body localization properties.\nWe also study two versions of the so-called Local Integrals of Motion (LIOM) representation of\nspin chain Hamiltonians and their relation to dynamical many-body localization. We prove that\nuniform-in-time dynamical localization expressed by a zero-velocity Lieb-Robinson bound implies\nthe existence of a LIOM representation of the dynamics as well as a weak converse of this statement.\nWe also prove that for a class of spin chains satisfying a form of exponential dynamical localization,\nsparse perturbations result in a dynamics in which transmission times diverge at least as a power\nlaw of distance, with a power for which we provide lower bound that diverges with increasing\nsparseness of the perturbation.\nIn Chapter 3 we introduce a class of UV-regularized two-body interactions for fermions in Rd\nand prove a Lieb-Robinson estimate for the dynamics of this class of many-body systems. As a\nstep toward this result, we also prove a propagation bound of Lieb-Robinson type for Schrodinger\noperators. We apply the propagation bound to prove the existence of infnite-volume dynamics as\na strongly continuous group of automorphisms on the CAR algebra.
In many-body localized systems, propagation of information forms a light cone that grows logarithmically with time. However, local changes in energy or other conserved quantities are expected to spread only within a finite distance. Is it possible to detect the logarithmic light cone using local observables, starting from thermal states or eigenstates? Here we show that this is indeed the case, but only in an out-of-time-ordered way. In particular, we numerically calculate various correlators in a prototypical model of many-body localization. While correlators of local operators A(t=0) and B(t>0) ordered in time sequence -- e.g., A(t=0)B(t>0) -- are not sensitive to the unbounded information propagation, those with out-of-time order -- e.g., A(t=0)B(t>0)A(t=0)B(t>0) -- can detect the logarithmic light cone. We demonstrate the connection between out-of-time-ordered correlators and the Lieb-Robinson bound in many-body localized systems, and explain how to saturate the latter by measuring the involved commutator on specially designed initial states. Moreover, out-of-time-ordered correlators also allow us to study the temperature dependence of the light cones and we observe an increase of propagation velocity with increasing temperature.