Thermodynamic Properties of XXZ model in a Transverse Field

TL;DR

This study numerically investigates the thermodynamic properties of the spin 1/2 XXZ chain in a transverse magnetic field, analyzing specific heat, correlation functions, and phase diagrams to understand magnetic ordering and energy gaps.

Contribution

It introduces a detailed numerical analysis of the XXZ model in a transverse field, including phase diagram derivation and comparison of computational methods for low-temperature accuracy.

Findings

Exponential decay of specific heat indicates energy gap.

Antiferromagnetic long-range order verified in 3D case.

Low Temperature Lanczos method yields more accurate results at low temperatures.

Abstract

We have numerically studied the thermodynamic properties of the spin 1/2 XXZ chain in the presence of a transverse (non commuting) magnetic field. The thermal, field dependence of specific heat and correlation functions for chains up to 20 sites have been calculated. The area where the specific heat decays exponentially is considered as a measure of the energy gap. We have also obtained the exchange interaction between chains in a bulk material using the random phase approximation and derived the phase diagram of the three dimensional material with this approximation. The behavior of the structure factor at different momenta verifies the antiferromagnetic long range order in y-direction for the three dimensional case. Moreover, we have concluded that the Low Temperature Lanczos results [M. Aichhorn et al., Phys. Rev. B 67, 161103(R) (2003)] are more accurate for low temperatures and closer to the full diagonalization ones than the results of Finite Temperature Lanczos Method [J. Jaklic and P. Prelovsek, Phys. Rev. B 49, 5065 (1994)].