Systematic construction of asymptotic quantum many-body scar states and their relation to supersymmetric quantum mechanics

TL;DR

This paper introduces a systematic method for constructing asymptotic quantum many-body scar states, revealing their connection to supersymmetric quantum mechanics and their relation to QMBS states as low-lying excited states.

Contribution

The authors develop a formalism to construct AQMBS states as low-lying excited states linked to a parent Hamiltonian with a QMBS ground state, and connect this to SUSY quantum mechanics.

Findings

AQMBS states can be obtained as low-lying gapless excited states.

A connection between QMBS and SUSY quantum mechanics is established.

QMBS states can be interpreted as SUSY-unbroken ground states.

Abstract

We develop a systematic method for constructing asymptotic quantum many-body scar (AQMBS) states. While AQMBS states are closely related to quantum many-body scar (QMBS) states, they exhibit key differences. Unlike QMBS states, AQMBS states are not energy eigenstates of the Hamiltonian, making their construction more challenging. We demonstrate that, under appropriate conditions, AQMBS states can be obtained as low-lying gapless excited states of a parent Hamiltonian, which has a QMBS state as its ground state. Furthermore, our formalism reveals a connection between QMBS and supersymmetric (SUSY) quantum mechanics. The QMBS state can be interpreted as a SUSY-unbroken ground state.