Topological many-body scar states in dimensions one, two, and three

Seulgi Ok,Christopher Mudry,Claudio Chamon,Kenny Choo,Claudio Castelnovo,Titus Neupert

doi:10.1103/physrevresearch.1.033144

Abstract

We propose an exact construction for atypical excited states of a class of non-integrable quantum many-body Hamiltonians in one dimension (1D), two dimensions (2D), and three dimensins (3D) that display area law entanglement entropy. These examples of many-body `scar' states have, by design, other properties, such as topological degeneracies, usually associated with the gapped ground states of symmetry protected topological phases or topologically ordered phases of matter.

Highlights

The study of many-body quantum systems has largely focused on ground-state properties and low-energy excitations, implicitly assuming the eigenstate thermalization hypothesis (ETH) dictating that highly excited states of generic nonintegrable models are void of interesting structures [1,2,3,4]
In this work we present a generic construction that places a scar state in the spectrum of nonintegrable many-body quantum systems in one, two, and three dimensons (1D, 2D, and 3D)
We propose a construction to obtain scar states based on stochastic matrix form Hamiltonians [39,41,42]

Summary

INTRODUCTION

The study of many-body quantum systems has largely focused on ground-state properties and low-energy excitations, implicitly assuming the eigenstate thermalization hypothesis (ETH) dictating that highly excited states of generic nonintegrable models are void of interesting structures [1,2,3,4]. With the discovery of quantum systems that violate the ETH, a broader interest in the physics of many-body excited states emerged [5]. Numerical techniques to obtain highly excited states rely on exact diagonalization [27] and, in some cases, matrix-product-state calculations [28] These numerical techniques are limited in that the range of available system sizes is often too small to allow an extrapolation to the thermodynamic limit. In this work we present a generic construction that places a scar state in the spectrum of nonintegrable many-body quantum systems in one, two, and three dimensons (1D, 2D, and 3D). In 3D we present a deformation of the X -cube model [30,31] as an example of a system with scars that display fracton topological order [30,31,32,33,34,35]

CONDITIONS AND GENERAL FORMALISM

A WARMUP EXAMPLE

EXAMPLE IN 2D

CONCLUSIONS