Facets of Many Body Localization

TL;DR

MBL represents an ergodicity-breaking dynamical phase in interacting quantum systems, contrasting with ETH by preserving memory, suppressing transport, and displaying Poisson-level statistics. The paper surveys localization physics beyond random onsite disorder, covering quasiperiodic potentials, bond-disordered couplings, and the Quantum Sun model, with emphasis on indicators such as spectral statistics, entanglement scaling, and LIOMs. Key findings include the relative stability and distinct fluctuations in quasiperiodic-driven MBL, the RS RG-X–described behavior in bond-disordered models with integer-peak entanglement distributions, and the Quantum Sun model’s sharp ergodicity transition and mobility edge with exceptionally small finite-size effects. These insights broaden the understanding of ergodicity breaking, offer guidance for experiments with cold atoms and Rydberg arrays, and illuminate the conditions under which MBL may persist or crumble in the thermodynamic limit.

Abstract

Many-body localization (MBL) appears to be a robust example of ergodicity breaking in many-body interacting systems. Here, we review different aspects of MBL, concentrating on various ways the disorder may be introduced into the system studied. In particular, we consider both the random and quasiperiodic diagonal (i.e., on-site) disorder as well as bond disorder as realized in randomly distributed atoms interacting via long-range interactions. We also review the quantum sun model, which seems to be the ideal, albeit artificial, model exhibiting MBL.

Figures (4)

• Figure 1: The paradigmatic XXZ model with $\Delta=1$. (a) Average gap ratio $\langle r\rangle$ as a function of the disorder strength $W$. (b) Estimate of the critical point depending on the method used scales as $1/L$ or as $L$ -- adapted from Sierant20p, @(2020) the American Physical Society. (c) Scaling of the Thouless time $t_{\rm Th}$, black solid line corresponding to scaling \ref{['eq:thouless']} -- adapted from Sierant20b, @(2020) the American Physical Society. (d) Imbalance dynamics of the Neel state for $W=8$, inset showing exponent of the effective power-law decay -- adapted from Sierant22 @(2022) the American Physical Society.
• Figure 2: Key features of MBL with QP potential: (a) Average gap ratio $\langle r \rangle$ as a function of disorder strength $W$ in the Kicked Ising model. The inset shows the derivatives across the transition, with red dots marking the maximum (in absolute value) of the derivatives $\alpha_r$. (b) This maximum scales exponentially with the system size in QP potential as opposed to a linear growth in the random potential -- adapted from Falcao24, @(2024) the American Physical Society. (c) Imbalance in the XXZ model in QP potential reveals strong similarities between different system sizes suggesting MBL -- adapted from Sierant22, @(2024) the American Physical Society.
• Figure 3: Localization properties of the bond-disordered model defined by Hamiltonian (\ref{['eq:bond_disorder_hamiltonian']}) with $m = n = 6$, $J = 1$ and $\Delta = -0.73$. (a) Comparison of the rescaled energies $\varepsilon$ computed from ED and obtained from RSRG-X for a one disorder realization. (b) Normalized distributions of the half-chain entanglement entropy for $L=20$ and several values of $W$. (c) Mean gap ratio as a function of disorder strength $W$. The blue curve shows the RSRG-X predictions ($\expval{r}_{RG}$), while orange corresponds to the ED results ($\expval{r}_{ED}$). The difference between two approaches $\delta_{\expval{r}} = \expval{r}_{ED} - \expval{r}_{RG}$ is shown in the inset -- adapted from Aramthottil24, @(2024) the American Physical Society.
• Figure 4: Ergodicity breaking transition in the U(1) symmetric quantum sun model. (a) Average gap ratio $\expval{r}$ for various system sizes $L$ and interactions $\alpha$ for the energies in the center of the spectrum $\varepsilon=0.5$. (b) Phase diagram of $\alpha$ against $\varepsilon$, with mobility edge highlighted in white dotted line. Solid lines correspond to the estimate of the ergodicity breaking transition for a given system size $L$. (c, d) Average gap ratio $r$ as a function of $\varepsilon$, showing criticality in the center of the spectrum for $\alpha=0.76$ and ergodicity in the spectral bulk at $\alpha=0.8$ -- adapted from Pawlik24, @(2024) the American Physical Society.