The antiferromagnetic Ising chain in a mixed transverse and longitudinal magnetic field

TL;DR

This paper investigates the phase diagram and critical properties of the antiferromagnetic Ising chain subjected to both transverse and longitudinal magnetic fields, revealing an order-disorder transition and universality class characteristics.

Contribution

It provides a detailed phase diagram using DMRG and finite-size scaling, and analyzes the critical behavior near key points with perturbation theory.

Findings

Identification of an order-disorder transition line in the phase diagram.

Critical properties belong to the 2D Ising universality class.

Linear form of the transition line near the multicritical point.

Abstract

We have studied the antiferromagnetic Ising chain in a transverse magnetic field $h_{x}$ and uniform longitudinal field $h_{z}$. Using the density matrix renormalization group calculation combined with a finite-size scaling the ground state phase diagram in ($h_{x},h_{z}$) plane is determined. It is shown that there is an order-disordered transition line in this plane and the critical properties belong to the universality class of the two-dimensional Ising model. Based on the perturbation theory in $h_{z}$ the scaling behavior of the mass gap in the vicinity of the critical point ($h_{x}=1/2,h_{z}=0$) is established. It is found that the form of the transition line near the classical multicritical point ($h_{x}=0,h_{z}=1$) is linear. The connection of the considered quantum model with the quasi-one-dimensional classical Ising model in the magnetic field is discussed.