Density matrix renormalization group analysis of the spin 1/2 XXZ chain in an XY symmetric random magnetic field

TL;DR

This paper uses DMRG to analyze the phase diagram of the spin 1/2 XXZ chain in a random magnetic field, identifying regions of quasi-long-range order and superfluid density based on spin correlations.

Contribution

It provides a detailed numerical study of the phase diagram of the XXZ chain with random fields, highlighting the critical region and order parameters.

Findings

Identification of the critical region with infinite correlation length

Estimation of superfluid density in the presence of randomness

Mapping of phase boundaries as a function of anisotropy and field strength

Abstract

The spin 1/2 XXZ chain in a random magnetic field pointing in the Z direction is numerically studied using the Density Matrix Renormalization Group (DMRG) method. The phase diagram as a function of the anisotropy of the XXZ Hamiltonian and the strength of the random field is analyzed by computing the spin correlations and the superfluid density. To obtain the superfluid density we consider a superblock configuration representing a closed system with an arbitrary twist at the boundary. This allows us to estimate the size of the critical region where the quasi-long-range order persists, that is, where the spin correlation length is infinite and the superfluid density is non-zero.