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arXiv:2103.14020 · Physical Review Letters

Constraint-Induced Delocalization

Piotr Sierant, Eduardo González Lazo, Marcello Dalmonte, Antonello Scardicchio, Jakub Zakrzewski

Published Sep 14, 2021• 35 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.127.126603

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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.
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 explore the dynamics of Rydberg excitations in an optical tweezer array under antiblockade (or facilitation) conditions. Because of the finite temperature the atomic positions are randomly spread, an effect that leads to quenched correlated disorder in the interatomic interaction strengths. This drastically affects the facilitation dynamics as we demonstrate experimentally on the elementary example of two atoms. To shed light on the role of disorder in a many-body setting we show that here the dynamics is governed by an Anderson-Fock model, i.e., an Anderson model formulated on a lattice with sites corresponding to many-body Fock states. We first consider a one-dimensional atom chain in a limit that is described by a one-dimensional Anderson-Fock model with disorder on every other site, featuring both localized and delocalized states. We then illustrate the effect of disorder experimentally in a situation in which the system maps on a two-dimensional Anderson-Fock model on a trimmed square lattice. We observe a clear suppression of excitation propagation, which we ascribe to the localization of the many-body wave functions in Hilbert space.
retical explanation: local observables do not thermalize when prepared in specific initial states.This evidence points at a new kind of ETH violation, dubbed "weak" since it only affects a small fraction of energy eigenstates, now called many-body quantum scars [26].After fully characterizing the phase diagram of the constraint Rydberg atom chain, we will uncover a profound connection between this system and a U (1) lattice gauge theory (LGT) [27].Achieving experimental control on synthetic gauge fields is one of the pillars of quantum simulations, and a crucial step to deepen our understanding of fundamental interactions.However, there is presently no experimental evidence that atomic systems can be used to simulate lattice gauge theories at large scales.This limitation stems from the very characteristic aspect that distinguishes lattice gauge theories from other statistical mechanics models, i.e, the presence of local constraints on the possible configurations, in the form of a Gauss law, which cannot be easily implemented in actual experimental realizations.These local constraints turn out to be naturally mapped into the Rydberg blockade, and the experimental setup of Ref. [25] represents the first large-scale quantum simulation of a lattice gauge theory.Motivated by the connection between LGTs and weak ETH violations, in the last part of Chapter 3, we will move to study the interplay between the Gauss constraint and strong ETH violations in disordered systems.This will be done through an extensive analysis of the spectral properties of a disordered version of one-dimensional quantum electrodynamics [28].
For a quantum system to be permanently out-of-equilibrium, some non-trivial mechanism must be at play, to counteract the general tendency of entropy increase and flow toward equilibration. Among the possible ways to protect a system against local thermalization, the phenomenon of localization induced by quenched disorder appears to be one of the most promising. Although the problem of localization was introduced almost sixty years ago, its many-body version is still partly unresolved, despite the recent theoretical effort to tackle it. In this thesis we address a few aspects of the localized phase, mainly focusing on the interacting case. A large part of the thesis is devoted to investigating the underlying “integrable” structure of many-body localized systems, i.e., the existence of non-trivial conservation laws that prevent ergodicity and thermalization. In particular, we show that such conserved operators can be explicitly constructed by dressing perturbatively the non-interacting conserved quantities, in a procedure that converges when scattering processes are weak enough. This is reminiscent of the quasiparticle theory in Fermi liquids, although in the disordered case the construction extends to the full many-body energy spectrum, and it results in operators that are exactly conserved. As an example of how to use the constructive recipe for the conserved quantities, we compute the long-time limit of an order parameter for the MBL phase in antiferromagnetic spin systems. Similar analytical tools as the ones exploited for the construction of the conserved operators are then applied to the problem of the stability of single-particle localization with respect to the coupling to a finite bath. In this context, we identify a quantum-Zeno-type effect, whereby the bath unexpectedly enhances the particle’s localization. In the final part of the thesis, we discuss several mechanisms by which thermal fluctuations may influence the spatial localization of excitations in interacting many-body states.
Many-body localization in an XY model with a long-range interaction is investigated. We show that in the regime of a high strength of disordering compared to the interaction an off-resonant flip-flop spin-spin interaction (hopping) generates the effective Ising interactions of spins in the third order of perturbation theory in a hopping. The combination of hopping and induced Ising interactions for the power-law distance dependent hopping $V(R)\ensuremath{\propto}{R}^{\ensuremath{-}\ensuremath{\alpha}}$ always leads to the localization breakdown in a thermodynamic limit of an infinite system at $\ensuremath{\alpha}<3d/2$ where ddd is a system dimension. The delocalization takes place due to the induced Ising interactions $U(R)\ensuremath{\propto}{R}^{\ensuremath{-}2\ensuremath{\alpha}}$ of ``extended'' resonant pairs. This prediction is consistent with the numerical finite size scaling in one-dimensional systems. Many-body localization in an XY model is more stable with respect to the long-range interaction compared to a many-body problem with similar Ising and Heisenberg interactions requiring $\ensuremath{\alpha}\ensuremath{\ge}2d$ which makes the practical implementations of this model more attractive for quantum information applications. The full summary of dimension constraints and localization threshold size dependencies for many-body localization in the case of combined Ising and hopping interactions is obtained using this and previous work and it is the subject for the future experimental verification using cold atomic systems.
Disordered quantum systems undergoing a many-body localization (MBL) transition fail to reach thermal equilibrium under their own dynamics. Distinguishing between asymptotically localized or delocalized dynamics based on numerical results is, however, nontrivial due to finite-size effects. Numerical linked cluster expansions (NLCE) provide a means to tackle quantum systems directly in the thermodynamic limit but are challenging for models without translational invariance. Here we demonstrate that NLCE provides a powerful tool to explore MBL by simulating quench dynamics in disordered spin-1/21/21/2 two-leg ladders and Fermi-Hubbard chains. Combining NLCE with an efficient real-time evolution of pure states, we obtain converged results for the decay of the imbalance on long time scales and show that, especially for intermediate disorder below the putative MBL transition, NLCE outperforms direct simulations of finite systems with open or periodic boundaries. Furthermore, while spin is delocalized even in strongly disordered Hubbard chains with frozen charge, we unveil that an additional tilted potential leads to a drastic slowdown of the spin imbalance and nonergodic behavior on accessible times. Our work sheds light on MBL in systems beyond the well-studied disordered Heisenberg chain and emphasizes the usefulness of NLCE for this purpose.