Eigenstate localization in a many-body quantum system

TL;DR

This paper demonstrates the existence of many-body quantum systems with a mobility edge, where low-energy eigenstates are localized in a small part of the Hilbert space, using a construction based on classical codes and quantum perturbations.

Contribution

It introduces a novel construction of many-body Hamiltonians with a mobility edge, showing localization in eigenstates below a certain energy density.

Findings

Existence of many-body Hamiltonians with a mobility edge.

Localization of eigenstates in a small fraction of configurations.

Potential for detecting localization via few-body measurements.

Abstract

We prove the existence of extensive many-body Hamiltonians with few-body interactions and a many-body mobility edge: all eigenstates below a nonzero energy density are localized in an exponentially small fraction of "energetically allowed configurations" within Hilbert space. Our construction is based on quantum perturbations to a classical low-density parity check code. In principle, it is possible to detect this eigenstate localization by measuring few-body correlation functions in efficiently preparable mixed states.