Quantum scars in spin-1/2 isotropic Heisenberg clusters

TL;DR

This paper explores how external fields affect energy level statistics and quantum scars in finite spin-1/2 Heisenberg clusters, revealing non-thermalized states with potential for quantum information processing.

Contribution

It demonstrates the persistence of quantum scars under symmetry-breaking fields and proposes experimental detection methods in finite quantum spin clusters.

Findings

Level statistics transition from Poisson to Wigner-Dyson with transverse fields.

Largest towers remain approximately intact, indicating quantum scars.

Non-thermalized states include GHZ and W states with revival features.

Abstract

We investigate the influence of the external fields on the statistics of energy levels and towers of eigenstates in spin-1/2 isotropic Heisenberg clusters, including chain, ladder, square and triangular lattices. In the presence of uniform field in one direction, the SU(2) symmetry of the system allows that almost whole spectrum consists of a large number of towers with identical level spacing. Exact diagonalization on finite clusters shows that random transverse fields in other two directions drive the level statistics from Poisson to Wigner-Dyson distributions with different values of mean level spacing ratio, indicating the transition from integrability to non-integrability. However, for the three types of clusters, it is found that the largest tower still hold approximately even the symmetry is broken, resulting to a quantum scar. Remarkably, the non-thermalized states cover the Greenberger-Horn-Zeilinger and W states, which maintain the feature of revival while a Neel state decays fast in the dynamic processes. In addition, some dynamic schemes for experimental detection are proposed. Our finding reveals the possibility of quantum information processing that is immune to the thermalization in finite size quantum spin clusters.