Thermodynamics and criticality of su (m ) spin chains of HaldaneShastry type
Abstract
We study the thermodynamics and critical behavior of su (m ) spin chains of HaldaneShastry 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 ≲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 onedimensional conformal field theory with central charge c =m −1 (with the only exception of the FrahmInozemtsev chain at zero value of its parameter). However, from a detailed study of the groundstate degeneracy and the lowenergy excitations, we conclude that these models are only critical in the antiferromagnetic case, with a few exceptions that we fully specify.
 Publication:

Physical Review E
 Pub Date:
 November 2022
 DOI:
 10.1103/PhysRevE.106.054120
 arXiv:
 arXiv:2208.04014
 Bibcode:
 2022PhRvE.106e4120F
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Mathematical Physics;
 Quantum Physics
 EPrint:
 12 pages, 2 figures