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Search for Many-Body Localization in translation invariant systems

François Huveneers, Wojciech De Roeck

Published May 13, 2014• 0 citations
OpenAlex

Abstract

We investigate the possibility of many-body localization in translation invariant Hamiltonian systems. A key feature of many-body localized disordered systems is recovered, namely the fact that resonant spots are rare and far-between. However, we point out that resonant spots are mobile, unlike in models with quenched disorder, and that they could therefore in principle delocalize the system. The motion of these resonant spots is reminiscent of motion in kinetically constrained models, the frustration effect being caused by a mismatch of energies rather than by geometric constraints. We provide examples where, in first order in the hopping, the resonant spots are effectively trapped (analogous to a jammed phase) and therefore localization is not ruled out, but we also have examples where, despite the rareness of resonant spots, the resonant spots are not trapped and hence this obvious scenario for many-body localization is not realized. We comment on the analysis of higher orders, but we did not reach a final conclusion yet.

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We investigate the possibility of many-body localization in translation invariant Hamiltonian systems. A key feature of many-body localized disordered systems is recovered, namely the fact that resonant spots are rare and far-between. However, we point out that resonant spots are mobile, unlike in models with quenched disorder, and that they could therefore in principle delocalize the system. The motion of these resonant spots is reminiscent of motion in kinetically constrained models, the frustration effect being caused by a mismatch of energies rather than by geometric constraints. We provide examples where, in first order in the hopping, the resonant spots are effectively trapped (analogous to a jammed phase) and therefore localization is not ruled out, but we also have examples where, despite the rareness of resonant spots, the resonant spots are not trapped and hence this obvious scenario for many-body localization is not realized. We comment on the analysis of higher orders, but we did not reach a final conclusion yet.
We investigate the possibility of many-body localization in translation-invariant Hamiltonian systems, which was recently brought up by several authors. A key feature of many-body localized disordered systems is recovered, namely the fact that resonant spots are rare and far-between. However, we point out that resonant spots are mobile, unlike in models with strong quenched disorder, and that these mobile spots constitute a possible mechanism for delocalization, albeit possibly only on very long timescales. In some models, this argument for delocalization can be made very explicit in first order of perturbation theory in the hopping. For models where this does not work, we present instead a nonperturbative argument that relies solely on ergodicity inside the resonant spots.
Recently it has been suggested that many-body localization (MBL) can occur in translationally-invariant systems, and candidate 1D models have been proposed. We find that such models typically exhibit strong finite-size effects due to the presence of two or more vastly different energy scales, including an artificial separation of density of states into bands separated by large energy gaps. By carefully choosing the parameters of the models such that finite-size effects are minimized, we perform extensive numerical studies of small systems using exact diagonalization. Based on the variety of diagnostics, including entanglement properties and the behavior of local observables, we find the systems exhibit thermal (ergodic), rather than MBL-like behavior. Our results suggest that MBL in translationally-invariant systems with two very different energy scales is less robust than perturbative arguments suggest, possibly pointing to the importance of non-perturbative effects which induce delocalization in the thermodynamic limit.
The phenomenon of localization is usually accompanied with the presence of quenched disorder. To what extent disorder is necessary for localization is a well-known open problem. In this paper, we prove the instability of localization in translation-invariant systems. For any translation-invariant local Hamiltonian exhibiting either Anderson or many-body localization, an arbitrarily small translation-invariant random local perturbation almost surely leads to the following manifestations of delocalization: (i) Transport: For any (inhomogeneous) initial state, the spatial distribution of energy or any other local conserved quantity becomes uniform at late times. (ii) Scrambling: The out-of-time-ordered correlator of any traceless local operators decays to zero at late times. (iii) Thermalization: Random product states locally thermalize to the infinite temperature state with overwhelming probability.
We explore the possibility for translationally invariant quantum many-body systems to undergo a dynamical glass transition, at which ergodicity and translational invariance break down spontaneously, driven entirely by quantum effects. In contrast to analogous classical systems, where the existence of such an ideal glass transition remains a controversial issue, a genuine phase transition is predicted in the quantum regime. This ideal quantum glass tran-sition can be regarded as a many-body localization transition due to self-generated disorder. Despite their lack of thermalization, these disorder-free quantum glasses do not possess an extensive set of local conserved operators, unlike what is conjectured for many-body localized systems with strong quenched disorder. 1
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 possibility for translationally invariant quantum many-body systems to undergo a dynamical glass transition, at which ergodicity and translational invariance break down spontaneously, driven entirely by quantum effects.In contrast to analogous classical systems, where the existence of such an ideal glass transition remains a controversial issue, a genuine phase transition is predicted in the quantum regime.This ideal quantum glass transition can be regarded as a manybody localization transition due to self-generated disorder.Despite their lack of thermalization, these disorder-free quantum glasses do not possess an extensive set of local conserved operators, unlike what is conjectured for many-body localized systems with strong quenched disorder.