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Localization of interacting fermions at high temperature

Vadim Oganesyan, David A. Huse

TL;DR

The paper investigates whether a true many-body localization phase can persist at nonzero temperature in strongly disordered, interacting fermions by performing exact diagonalization on a one-dimensional spinless fermion model with random potentials and analyzing spectral statistics up to system sizes $L=16$. It uses the adjacent-gap ratio $r_n$ to distinguish GOE-like diffusive behavior from Poisson-like localized behavior and reports a drift in finite-size crossing points with increasing $L$, preventing a clear finite-size conclusion about a finite critical disorder $W_c$. The results show GOE at weak disorder and Poisson at strong disorder, but the drift implies that spectral statistics alone may be insufficient to confirm MBL at $T>0$, raising two plausible interpretations: either a finite-$W_c$ with insulator-like critical statistics or no finite-$W_c$ transition in the high-$T$ regime. The work highlights the challenges of diagnosing high-temperature MBL from spectral data alone and motivates studying dynamical quantities and larger systems to draw firmer conclusions.

Abstract

We suggest that if a localized phase at nonzero temperature $T>0$ exists for strongly disordered and weakly interacting electrons, as recently argued, it will also occur when both disorder and interactions are strong and $T$ is very high. We show that in this high-$T$ regime the localization transition may be studied numerically through exact diagonalization of small systems. We obtain spectra for one-dimensional lattice models of interacting spinless fermions in a random potential. As expected, the spectral statistics of finite-size samples cross over from those of orthogonal random matrices in the diffusive regime at weak random potential to Poisson statistics in the localized regime at strong randomness. However, these data show deviations from simple one-parameter finite-size scaling: the apparent mobility edge ``drifts'' as the system's size is increased. Based on spectral statistics alone, we have thus been unable to make a strong numerical case for the presence of a many-body localized phase at nonzero $T$.

Localization of interacting fermions at high temperature

TL;DR

The paper investigates whether a true many-body localization phase can persist at nonzero temperature in strongly disordered, interacting fermions by performing exact diagonalization on a one-dimensional spinless fermion model with random potentials and analyzing spectral statistics up to system sizes . It uses the adjacent-gap ratio to distinguish GOE-like diffusive behavior from Poisson-like localized behavior and reports a drift in finite-size crossing points with increasing , preventing a clear finite-size conclusion about a finite critical disorder . The results show GOE at weak disorder and Poisson at strong disorder, but the drift implies that spectral statistics alone may be insufficient to confirm MBL at , raising two plausible interpretations: either a finite- with insulator-like critical statistics or no finite- transition in the high- regime. The work highlights the challenges of diagnosing high-temperature MBL from spectral data alone and motivates studying dynamical quantities and larger systems to draw firmer conclusions.

Abstract

We suggest that if a localized phase at nonzero temperature exists for strongly disordered and weakly interacting electrons, as recently argued, it will also occur when both disorder and interactions are strong and is very high. We show that in this high- regime the localization transition may be studied numerically through exact diagonalization of small systems. We obtain spectra for one-dimensional lattice models of interacting spinless fermions in a random potential. As expected, the spectral statistics of finite-size samples cross over from those of orthogonal random matrices in the diffusive regime at weak random potential to Poisson statistics in the localized regime at strong randomness. However, these data show deviations from simple one-parameter finite-size scaling: the apparent mobility edge ``drifts'' as the system's size is increased. Based on spectral statistics alone, we have thus been unable to make a strong numerical case for the presence of a many-body localized phase at nonzero .

Paper Structure

This paper contains 5 sections, 3 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Ensemble of Hamiltonians
  3. Method of analysis
  4. Results
  5. Summary and outlook

Figures (2)

  • Figure 1: (color online) Disorder averaged probability distribution, $P(r)$, for Poisson (solid black line) and GOE distributed eigenvalues goedata (black dots) and for our interacting fermion model at randomness $W=3$ (green, diffusive regime), $W=11$ (red, localized regime) and $W=7$ (blue, intermediate) for length $L=16$.
  • Figure 2: (color online) Size $L$ and disorder $W$ dependence of $r(W,L)$. The curves correspond to $L$=8, 10, 12, 14, 16 from top to bottom for large $W$. Bottom: an enlargement of the crossing region to make the drift of the crossings more visible. Where not visible, the error bars are smaller than the points.