Exact solution of a spin-1/2 $XX$ chain with three-site interactions in a random transverse field: Influence of randomness on quantum phase transition

TL;DR

This paper provides exact solutions for a spin-1/2 XX chain with three-site interactions under a random transverse field, analyzing how randomness affects quantum phase transitions and critical behavior.

Contribution

It offers the first exact analysis of the impact of Lorentzian randomness on quantum criticality in a spin chain with three-site interactions.

Findings

Randomness smears out zero-temperature quantum phase transition features.

Signatures of quantum criticality persist at low temperatures with weak randomness.

Weak randomness can slightly enlarge the quantum critical region.

Abstract

We present exact results for the ground-state and thermodynamic properties of the spin-1/2 $XX$ chain with three-site interactions in a random (Lorentzian) transverse field. We discuss the influence of randomness on the quantum critical behavior known to be present in the nonrandom model. We find that at zero temperature the characteristic features of the quantum phase transition, such as kinks in the magnetization versus field curve, are smeared out by randomness. However, at low but finite temperatures signatures of the quantum critical behavior are preserved if the randomness is not too large. Even the quantum critical region may be slightly enlarged for very weak randomness. In addition to the exact results for Lorentzian randomness we present a more general discussion of an arbitrarily random transverse magnetic field based on the inspection of the moments of the density of states.