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

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 $B{C}_N$ 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 $m\lesssim 10$ 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.

12 pages, 2 figures

References in corpus (5)

• Low energy properties of the SU(m|n) supersymmetric Haldane-Shastry spin chain
• The Berry-Tabor conjecture for spin chains of Haldane-Shastry type
• Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models
• One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane-Shastry Like Spin Chains
• The open Haldane-Shastry chain: thermodynamics and criticality