Unconventional Thermalization of a Localized Chain Interacting with an Ergodic Bath

TL;DR

The paper investigates how an Anderson localized chain can be destabilized by coupling to a small ergodic bath using the Anderson Quantum Sun (AQS) model. By analyzing both eigenvalue statistics and eigenstate entanglement across parameters ${J}$ and ${\alpha}$, it uncovers unconventional regimes: a Poisson-like spectral phase with sub-volume entanglement and rare-event correlations, and a fully thermal eigenstate with volume-law entanglement yet intermediate spectral statistics, revealing ergodicity-breaking pathways beyond standard MBL-ETH. The findings are supported by detailed numerical analysis (ED and POLFED) of gap ratios ${r}$, entanglement entropy ${S}$ normalized by ${S_P}$, and correlation functions, as well as phase-diagram mappings. These results challenge the conventional correspondence between localization and spectral statistics and point to new mechanisms for ergodicity breaking, with potential experimental realizations in controllable quantum simulators.

Abstract

The study of many-body localized (MBL) phases intrinsically links spectral properties with eigenstate characteristics: localized systems exhibit Poisson level statistics and area-law entanglement entropy, while ergodic systems display volume-law entanglement and follow random matrix theory predictions, including level repulsion. Here, we introduce the interacting Anderson Quantum Sun model, which significantly deviates from these conventional expectations. In addition to standard localized and ergodic phases, we identify a regime that exhibits volume-law entanglement coexisting with intermediate spectral statistics. We also identify another nonstandard regime marked by Poisson level statistics, sub-volume entanglement growth, and rare-event-dominated correlations, indicative of emerging ergodic instabilities. These results highlight unconventional routes of ergodicity breaking and offer fresh perspectives on how Anderson localization may be destabilized.

Figures (13)

• Figure 1: Schematic of the AQS model Eq. \ref{['eq:model_hamiltonian']}. An ergodic bath is coupled to an Anderson chain via exponentially decaying interactions.
• Figure 2: Phase diagram of the AQS model. (a): gap ratio extrapolated to the thermodynamic limit $r^\infty$. (b): power in the power-law dependence of entropy growth $S\propto L^b$ extrapolated to the thermodynamic limit $b^\infty$. Curves on both plots represent spectral (dashed black, $\alpha^{\rm c}_{r,\infty}$) and eigenstate (solid black, $\alpha^{\rm c}_{S,\infty}$) phase transition, regimes of the model are labeled with [A-D]. The dotted-dashed green analytical line indicates the onset of ergodic instabilities.
• Figure 3: High energy indicators of ergodicity-breaking, as a function of parameter $\alpha$, for a fixed value of $J$. (a, b): gap ratio $r$, black circles show extrapolations to the thermodynamic limit $L=\infty$. (c, d): rescaled half-chain entanglement entropy of eigenstates $S/S_P$. Dashed lines indicate the prediction of the GOE and Poisson ensembles, while dotted lines indicate transitions. Different colors represent different system sizes - see color bar. Regimes are labeled [A-D] in accordance with Fig. \ref{['fig:phase_diagram']}.
• Figure 4: Horizontal scan of the phase diagram at $\alpha=0.35$. (a): Gap ratio $r$. (b): Rescaled entropy $S/S_P$. (c): Entanglement entropy $S$. (d): Correlation length ratio $\xi_x/\xi_z$ of $C_{1,L}$, for different choices of the fitting window of system sizes $[L-2,L+2]$, with $L$ indicated by the color bar. In panels (a, b), dashed horizontal lines indicate the Poisson limit, and the black solid curve in (a) represents the extrapolation to the thermodynamic limit. The dotted line indicates [B]-[C] transition based on $S/S_P$, while the gray band corresponds to the onset of power law $S$-dependence in [A]-[B] transition. Data points for $L=12$–$14$ in (d) at $J=0$ are omitted, as they contain events with $C_{1,L}$ below numerical precision.
• Figure 5: Multifractal dimension $D_1$ of eigenstates in the AQS model. For explanations of the lines, see Fig. \ref{['fig:phase_diagram']} of the main text.