The anisotropic Heisenberg model in a transverse magnetic field

TL;DR

This paper investigates the one-dimensional spin-1/2 XXZ model in a transverse magnetic field, revealing how the field induces a spectral gap, mapping the phase diagram with four phases, and analyzing critical behavior and universality classes.

Contribution

It provides a detailed analysis of the phase diagram, critical exponents, and universality class of the transverse field-induced transitions in the XXZ model.

Findings

Field induces a gap in the spectrum for easy-plane anisotropy.

Four distinct phases with different long-range orders are identified.

Transition lines belong to the transverse Ising universality class.

Abstract

One dimensional spin-1/2 $XXZ$ model in a transverse magnetic field is studied. It is shown that the field induces the gap in the spectrum of the model with easy-plain anisotropy. Using conformal invariance the field dependence of the gap at small fields is found. The ground state phase diagram is obtained. It contains four phases with different types of the long range order (LRO) and a disordered one. These phases are separated by critical lines, where the gap and the long range order vanish. Using scaling estimations and a mean-field approach as well as numerical calculations in the vicinity of all critical lines we found the critical exponents of the gap and the LRO. It is shown that transition line between the ordered and disordered phases belongs to the universality class of the transverse Ising model.