Phase Structure of XX0 Spin Chain and Nonintersecting Brownian Motion

TL;DR

This paper investigates the phase structure of the XX0 Heisenberg spin chain in the asymptotic limit, revealing new phase transitions through connections to random matrix theory and nonintersecting Brownian motion.

Contribution

It introduces a novel analysis of the XX0 spin chain's phase structure using integrable combinatorics and probability, uncovering second- and third-order phase transitions.

Findings

Partition function governed by Tracy-Widom distribution

Discovery of new second- and third-order phase transitions

Distinct dynamical features of spin configurations in different phases

Abstract

We study finite size and temperature XX0 Heisenberg spin chain in weak and strong coupling regimes. By using an elegant connection of the model to integrable combinatorics and probability, we explore and interpret a possible phase structure of the model in asymptotic limit: the limit of large inverse temperature and size. First, partition function and free energy of the model are derived by using techniques and results from random matrix models and nonintersecting Brownian motion. We show that, in the asymptotic limit, partition function of the model, written in terms of matrix integral, is governed by the Tracy-Widom distribution. Second, the exact analytic results for the free energy, which is obtained by the asymptotic analysis of the Tracy-Widom distribution, indicate a completely new and sophisticated phase structure of the model. This phase structure consists of second- and third-order phase transitions. Finally, to shed light on our new results, we provide a possible interpretation of the phase structure in terms of dynamical behavior of magnons in the spin chain. We demonstrate distinct features of the phases with schematic spin configurations which have definite features in each region of the phase diagram.