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arXiv:1911.11711 · Physical Review Letters

Nucleation of Ergodicity by a Single Mobile Impurity in Supercooled Insulators

Ulrich Krause, Théo Pellegrin, Piet W. Brouwer, Dmitry A. Abanin, Michele Filippone

Published Jan 21, 2021• 14 citations
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Abstract

We consider a disordered Hubbard model and show that, at sufficiently weak disorder, a single spin-down mobile impurity can thermalize an extensive initially localized system of spin-up particles. Thermalization is enabled by resonant processes that involve correlated hops of the impurity and localized particles. This effect indicates that Anderson localized insulators behave as "supercooled" systems, with mobile impurities acting as ergodic seeds. We provide analytical estimates, supported by numerical exact diagonalization, showing how the critical disorder strength for such mechanism depends on the particle density of the localized system. In the U→∞ limit, doublons are stable excitations, and they can thermalize mesoscopic systems by a similar mechanism. The emergence of an additional conservation law leads to an eventual localization of doublons. Our predictions apply to fermionic and bosonic systems and are readily accessible in ongoing experiments simulating synthetic quantum lattices with tunable disorder.

DOI
10.1103/physrevlett.126.030603

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We consider a disordered Hubbard model and show that, at sufficiently weak disorder, a single spin-down mobile impurity can thermalize an extensive initially localized system of spin-up particles. Thermalization is enabled by resonant processes that involve correlated hops of the impurity and localized particles. This effect indicates that Anderson localized insulators behave as "supercooled" systems, with mobile impurities acting as ergodic seeds. We provide analytical estimates, supported by numerical exact diagonalization, showing how the critical disorder strength for such mechanism depends on the particle density of the localized system. In the U→∞ limit, doublons are stable excitations, and they can thermalize mesoscopic systems by a similar mechanism. The emergence of an additional conservation law leads to an eventual localization of doublons. Our predictions apply to fermionic and bosonic systems and are readily accessible in ongoing experiments simulating synthetic quantum lattices with tunable disorder.
We illustrate a remarkably simple mechanism in which single doublon excitations in interacting lattice systems with large on-site interaction UUU trigger the generation of ergodic bubbles, which thermalize extensive localized systems. Such phenomenon shows how localized insulators behave as supercooled systems, in which doublons act as ergodic seeds. We provide analytical estimates showing how the critical disorder strength for such mechanism depends on singlon densities, which are supported by numerical exact-diagonalization simulations. Our predictions apply to both fermionic and bosonic systems and are readily accessible in ongoing experiments simulating synthetic quantum lattice systems with tunable disorder.
Thermalizing and localized many-body quantum systems present two distinct dynamical phases of matter. Recently the fate of a localized system coupled to a thermalizing system viewed as a quantum bath received significant theoretical and experimental attention. In this work, we study a mobile impurity, representing a small quantum bath, that interacts locally with an Anderson insulator with a finite density of localized particles. Using static Hartree approximation to obtain an effective disorder strength, we formulate an analytic criterion for the perturbative stability of the localization. Next, we use an approximate dynamical Hartree method and the quasi-exact time-evolved block decimation (TEBD) algorithm to study the dynamics of the system. We find that the dynamical Hartree approach which completely ignores entanglement between the impurity and localized particles predicts the delocalization of the system. In contrast, the full numerical simulation of the unitary dynamics with TEBD suggests the stability of localization on numerically accessible timescales. Finally, using an extension of the density matrix renormalization group algorithm to excited states (DMRG-X), we approximate the highly excited eigenstates of the system. We find that the impurity remains localized in the eigenstates and entanglement is enhanced in a finite region around the position of the impurity, confirming the dynamical predictions. Dynamics and the DMRG-X results provide compelling evidence for the stability of localization.
We investigate dynamics of a single mobile impurity immersed in a bath of Anderson localized particles and focus on the regime of relatively strong disorder and interactions. In that regime, the dynamics of the system is particularly slow, suggesting, at short times, an occurrence of many-body localization. Considering longer timescales, we show that the latter is a transient effect and that, eventually, the impurity spreads subdiffusively and induces a gradual delocalization of the Anderson insulator. The phenomenology of the system in the considered regime of slow dynamics includes a subdiffusive growth of mean square displacement of the impurity, power-law decay of density correlation functions of the Anderson insulator, and a power-law growth of entanglement entropy in the system. We observe a similar regime of slow dynamics also when the disorder in the system is replaced by a sufficiently strong quasiperiodic potential.
Recent work by De Roeck et al. [Phys. Rev. B 95, 155129 (2017)] has argued that many-body localization is unstable in two and higher dimensions due to a thermalization avalanche triggered by rare regions of weak disorder. To examine these arguments, we construct several models of a finite ergodic bubble coupled to an Anderson insulator of noninteracting fermions. We first describe the ergodic region using a Gaussian orthogonal ensemble random matrix and perform an exact diagonalization study of small systems. The results are in excellent agreement with a refined theory of the thermalization avalanche that includes transient finite-size effects, lending strong support to the avalanche scenario. We then explore the limit of large system sizes by modeling the ergodic region via a Hubbard model with all-to-all random hopping: the combined system, consisting of the bubble and the insulator, can be reduced to an effective Anderson impurity problem. We find that the spectral function of a local operator in the ergodic region changes dramatically when coupling to a large number of localized fermionic states; this occurs even when the localized sites are weakly coupled to the bubble. In principle, for a given size of the ergodic region, this may arrest the avalanche. However, this back-action effect is suppressed and the avalanche can be recovered if the ergodic bubble is large enough. Thus, the main effect of the back-action is to renormalize the critical bubble size.
An interacting many-body system being localized in the presence of disorder can fail to serve as its own bath. In an electronic system, the charge and spin degrees of freedom can act as thermal baths for each other. In this paper, we study the stability of an Anderson insulator in the spin sector with respect to charge doping. We consider one-dimensional two-component fermions in a lattice with large onsite repulsion (t−JXXt-J_{XX}t−JXX​ model) and with a single hole in a random magnetic field. In the absence of the hole the spin sector is localized in arbitrarily weak random magnetic fields. We argue that a single hole thermalizes the spin chain in the weak disorder limit. In this regime our numerical results indicate ergodicity of the system as a whole and delocalization of the hole. At larger magnetic fields the hole eventually localizes with a finite localization length, and the Anderson spin insulator is restored.
Many-body localization (MBL) is an example of a dynamical phase of matter that avoids thermalization. While the MBL phase is robust to weak local perturbations, the fate of an MBL system coupled to a thermalizing quantum system that represents a ``heat bath'' is an open question that is actively investigated theoretically and experimentally. In this work, we consider the stability of an Anderson insulator with a finite density of particles interacting with a single mobile impurity---a small quantum bath. We give perturbative arguments that support the stability of localization in the strong interaction regime. Large-scale tensor network simulations of dynamics are employed to corroborate the presence of the localized phase and give quantitative predictions in the thermodynamic limit. We develop a phenomenological description of the dynamics in the strong interaction regime, and we demonstrate that the impurity effectively turns the Anderson insulator into an MBL phase, giving rise to nontrivial entanglement dynamics well captured by our phenomenology.