Thermodynamics and short-range correlations of the XXZ chain close to its triple point

TL;DR

This paper investigates the thermodynamics and short-range correlations of the XXZ spin chain near its triple point, revealing significant physical variations driven by quantum fluctuations and providing explicit low-temperature formulas.

Contribution

It offers a detailed analysis of the XXZ chain's behavior near the triple point using exact solutions and perturbation theory, highlighting the scaling of physical quantities.

Findings

Strong variation of physical quantities near the triple point

Explicit low-temperature formulas for magnetization and correlations

Identification of relevant scaling behaviors

Abstract

The XXZ quantum spin chain has a triple point in its ground state $h$-$1/\Delta$ phase diagram. This first order critical point is located at the joint end point of the two second order phase transition lines marking the transition from the gapless phase to the fully polarized phase and to the N\'eel ordered phase, respectively. We explore the magnetization and the short-range correlation functions in its vicinity using the exact solution of the model. In the critical regime above the triple point we observe a strong variation of all physical quantities on a low energy scale of order $1/\Delta$ induced by the transversal quantum fluctuations. We interpret this phenomenon starting from a strong-coupling perturbation theory about the highly degenerate ground state of the Ising chain at the triple point. From the perturbation theory we identify the relevant scaling of the magnetic field and of the temperature. Applying the scaling to the exact solutions we obtain explicit formulae for the magnetization and short-range correlation functions at low temperatures.