Thermodynamics and criticality of su($m$) spin chains of Haldane-Shastry type

TL;DR

This paper analyzes the thermodynamic properties and critical behavior of su(m) Haldane-Shastry spin chains, deriving explicit formulas for thermodynamic quantities and identifying conditions for criticality related to conformal field theory.

Contribution

It provides closed-form expressions for thermodynamic functions of su(m) spin chains and clarifies their criticality and low-energy behavior across different cases.

Findings

Specific heat exhibits a Schottky peak approximated by m-level systems.

Low-temperature free energy matches a conformal field theory with central charge c=m-1.

Models are critical only in the antiferromagnetic case, with some exceptions.

Abstract

We study the thermodynamics and critical behavior of su($m$) spin chains of Haldane-Shastry type at zero chemical potential, both in the $A_{N-1}$ and $BC_N$ cases. We evaluate in closed form the free energy per spin for arbitrary values of $m$, from which we derive explicit formulas for the energy, entropy and specific heat per spin. In particular, we find that the specific heat features a single Schottky peak, whose temperature is well approximated for $m\lesssim10$ by the corresponding temperature for an $m$-level system with uniformly spaced levels. We show that at low temperatures the free energy per spin of the models under study behaves as that of a one-dimensional conformal field theory with central charge $c=m-1$ (with the only exception of the Frahm-Inozemtsev chain with zero value of its parameter). However, from a detailed study of the ground state degeneracy and the low-energy excitations, we conclude that these models are only critical in the antiferromagnetic case, with a few exceptions that we fully specify.