# Length scales in the many-body localized phase and their spectral signatures

## TL;DR

This paper investigates the decay lengths of various correlation functions in the many-body localized phase, revealing that they follow normal distributions with linearly growing mean and variance, and discusses how to measure these using interferometric probes.

## Contribution

It provides a detailed analysis of the spectral signatures and distribution of localization lengths in the MBL phase, highlighting their stability and measurement methods.

## Key findings

- Localization lengths are normally distributed with linearly growing mean and variance.
- All localization lengths remain short up to the MBL transition, indicating phase stability.
- Broad distributions of couplings can be experimentally extracted using interferometric techniques.

## Abstract

We compute and compare the decay lengths of several correlation functions and effective coupling constants in the many-body localized (MBL) phase. To this end, we consider the distribution of the logarithms of these couplings and correlators: in each case the log-coupling follows a normal distribution with mean and variance that grow linearly with separation. Thus, a localization length is asymptotically sharply defined for each of these quantities. These localization lengths differ numerically from one another, but all of them remain short up to the numerically observed MBL transition, indicating stability of the MBL phase against isolated ergodic inclusions. We also show how these broad distributions may be extracted using interferometric probes such as double electron-electron resonance (DEER) and the statistics of local spin precession frequencies.