Exact bounds for dynamical critical exponents of transverse-field Ising chains with a correlated disorder

TL;DR

This paper analytically determines finite bounds for the dynamical critical exponent in transverse-field Ising chains with correlated disorder, revealing differences from uncorrelated disorder cases and dependence on the tuning process.

Contribution

It provides the first analytical bounds for the dynamical critical exponent in correlated disordered Ising chains, highlighting the impact of disorder correlations.

Findings

Correlated disorder yields a finite dynamical critical exponent.

Uncorrelated disorder results in an infinite dynamical critical exponent.

The critical exponent depends on how the transverse field is tuned.

Abstract

This study investigates the dynamical critical exponent of disordered Ising chains under transverse fields to examine the effect of a correlated disorder on quantum phase transitions. The correlated disorder, where the on-site transverse field depends on the nearest-neighbor coupling strengths connecting the site, gives a qualitatively different result from the uncorrelated disorder. In the uncorrelated disorder cases where the transverse field is either homogeneous over sites or random independently of the nearest-neighbor coupling strengths, the dynamical critical exponent is infinite. In contrast, in the presence of the correlated disorder, we analytically show that the dynamical critical exponent is finite. We also show that the dynamical critical exponent depends on the tuning process of the transverse field strengths.