# Disorder-Free Localization

## TL;DR

This paper introduces a translationally invariant quantum model where localization occurs without quenched disorder, challenging the traditional view that disorder is essential for localization phenomena.

## Contribution

The work demonstrates a model with self-generated disorder leading to localization, providing new insights into many-body localization without quenched disorder.

## Key findings

- Localization arises in a translationally invariant model.
- The system generates its own disorder dynamically.
- Provides new understanding of disorder's role in localization.

## Abstract

The venerable phenomena of Anderson localization, along with the much more recent many-body localization, both depend crucially on the presence of disorder. The latter enters either in the form of quenched disorder in the parameters of the Hamiltonian, or through a special choice of a disordered initial state. Here we present a model with localization arising in a very simple, completely translationally invariant quantum model, with only local interactions between spins and fermions. By identifying an extensive set of conserved quantities, we show that the system generates purely dynamically its own disorder, which gives rise to localization of fermionic degrees of freedom. Our work gives an answer to a decades old question whether quenched disorder is a necessary condition for localization. It also offers new insights into the physics of many-body localization, lattice gauge theories, and quantum disentangled liquids.