The open Haldane-Shastry chain: thermodynamics and criticality

TL;DR

This paper analyzes the thermodynamics and critical behavior of the su(m|n) Haldane-Shastry chain of BC_N type, deriving spectrum descriptions, partition functions, and identifying critical intervals and phases with unique low-energy excitations.

Contribution

It provides a complete spectrum description, closed-form thermodynamic functions, and characterizes critical phases with novel low-energy excitation features for the first time.

Findings

Derived spectrum in terms of BC_N motifs

Obtained closed-form free energy expressions for m,n≤2

Identified critical intervals and computed Fermi velocities

Abstract

We study the thermodynamics and criticality of the su($m|n$) Haldane-Shastry chain of $BC_N$ type with a general chemical potential term. We first derive a complete description of the spectrum of this model in terms of $BC_N$-type motifs, from which we deduce a representation for the partition function as the trace of a product of site-dependent transfer matrices. In the thermodynamic limit, this formula yields a simple expression for the free energy per spin in terms of the Perron-Frobenius eigenvalue of the continuum limit of the transfer matrix. Evaluating this eigenvalue we obtain closed-form expressions for the thermodynamic functions of the chains with $m,n\le2$. Using the motif-based description of the spectrum derived here, we study in detail the ground state of these models and their low energy excitations. In this way we identify the critical intervals in chemical potential space and compute their corresponding Fermi velocities. By contrast with previously studied models of this type, we find in some cases two types of low energy excitations with linear energy-quasimomentum relation. Finally, we determine the central charge of all the critical phases by analyzing the low-temperature behavior of the expression for the free energy per spin.