Exact results for quantum phase transitions in random XY spin chains

TL;DR

This paper provides exact analytical results for quantum phase transitions in disordered XY spin chains, confirming previous numerical findings and exploring the impact of a transverse field on universality classes.

Contribution

It offers exact solutions for critical behavior in disordered XY chains, validating real space renormalization group results and analyzing the effects of transverse fields.

Findings

Exact expressions for dynamical critical exponent, specific heat, and susceptibility.

Confirmation of the accuracy of Fisher's real space RG approach.

Transverse field alters the universality class of the transition.

Abstract

The effect of disorder on the quantum phase transitions induced by a transverse field, anisotropy, and dimerization in XY spin chains is investigated. The low-energy behavior near the critical point is described by a Dirac-type equation with a random mass for which an exact analytic treatment is possible. Results obtained for the dynamical critical exponent, the specific heat, and transverse susceptibility agree with results recently obtained using a real space renormalization group decimation technique, supporting Fisher's claim that it is exact. A non-zero transverse field changes the universality class of the anisotropy transition.