Weak-ergodicity-breaking via lattice supersymmetry

Federica Maria Surace,Marcello Dalmonte,Giuliano Giudici

doi:10.22331/q-2020-10-07-339

Abstract

We study the spectral properties of D-dimensional N=2 supersymmetric lattice models. We find systematic departures from the eigenstate thermalization hypothesis (ETH) in the form of a degenerate set of ETH-violating supersymmetric (SUSY) doublets, also referred to as many-body scars, that we construct analytically. These states are stable against arbitrary SUSY-preserving perturbations, including inhomogeneous couplings. For the specific case of two-leg ladders, we provide extensive numerical evidence that shows how those states are the only ones violating the ETH, and discuss their robustness to SUSY-violating perturbations. Our work suggests a generic mechanism to stabilize quantum many-body scars in lattice models in arbitrary dimensions.

Highlights

In many-body theories, generic phenomena are often associated to and characterized by the presence of symmetries [1]
A paradigmatic phenomenon that - in a sense we specify below - lies ’in- between’ equilibrium and out-of-equilibrium is represented by eigenstates of quantum Hamiltonians that, despite belonging to the middle of the energy spectrum, feature properties that are at odds with theoretical expectations based on the eigenstate thermalization hypothesis (ETH) [6,7,8,9]
We have shown that N = 2 supersymmetric lattice models display weak-ergodicity breaking in the form of scarred eigenstates in any D-dimensional hypercubic lattice

Summary

Introduction

In many-body theories, generic phenomena are often associated to and characterized by the presence of symmetries [1]. A paradigmatic phenomenon that - in a sense we specify below - lies ’in- between’ equilibrium and out-of-equilibrium is represented by eigenstates of quantum Hamiltonians that, despite belonging to the middle of the energy spectrum, feature properties that are at odds with theoretical expectations based on the eigenstate thermalization hypothesis (ETH) [6,7,8,9]. These states, recently dubbed quantum many-body scars [10], have finite energy density above the ground state and sub-extensive entanglement entropy.

Supersymmetric lattice models

Exact eigenstates at finite energy density: two-leg ladders

Exact scars in d-dimensional hypercubic lattices

Spectral statistics in two-leg ladders

Robustness to perturbations and connection to the Shiraishi-Mori construction

Conclusions and outlook