# Gumbel statistics for entanglement spectra of many-body localized eigenstates

## TL;DR

This paper investigates the extreme value statistics of entanglement spectra in many-body localized eigenstates, revealing Gumbel distribution behavior that offers a new analytical perspective on these quantum states.

## Contribution

It introduces the first observation of Gumbel statistics in entanglement spectra of many-body localized states, providing a novel, parameter-free analytical characterization.

## Key findings

- Entanglement spectra are dominated by the smallest elements.
- Gumbel distribution accurately describes the extreme value statistics.
- Provides a new analytical framework for understanding many-body localization.

## Abstract

An entanglement spectrum encodes statistics beyond the entanglement entropy, of which several have been studied in the context of many-body localization. We numerically study the extreme value statistics of entanglement spectra of many-body localized eigenstates. The physical information encoded in these spectra is almost fully carried by the few smallest elements, suggesting the extreme value statistics to have physical significance. We report the surprising observation of Gumbel statistics. Our result provides an analytical, parameter-free characterization of many-body localized eigenstates.