An exactly solvable supersymmetric spin chain of BC_N type

TL;DR

This paper introduces a new exactly solvable supersymmetric spin chain related to BC_N root systems, deriving its partition function, spectrum properties, and demonstrating its non-Poissonian level spacings, highlighting its integrability features.

Contribution

The paper constructs a novel BC_N supersymmetric spin chain, provides explicit partition functions, and reveals unique spectral properties, including a boson-fermion duality and non-Poissonian level spacings.

Findings

Partition functions derived in closed form.

Spectrum exhibits a normal distribution of level density.

Level spacings follow a simple analytic distribution fitting numerical data.

Abstract

We construct a new exactly solvable supersymmetric spin chain related to the BC_N extended root system, which includes as a particular case the BC_N version of the Polychronakos-Frahm spin chain. We also introduce a supersymmetric spin dynamical model of Calogero type which yields the new chain in the large coupling limit. This connection is exploited to derive two different closed-form expressions for the chain's partition function by means of Polychronakos's freezing trick. We establish a boson-fermion duality relation for the new chain's spectrum, which is in fact valid for a large class of (not necessarily integrable) spin chains of BC_N type. The exact expressions for the partition function are also used to study the chain's spectrum as a whole, showing that the level density is normally distributed even for a moderately large number of particles. We also determine a simple analytic approximation to the distribution of normalized spacings between consecutive levels which fits the numerical data with remarkable accuracy. Our results provide further evidence that spin chains of Haldane-Shastry type are exceptional integrable models, in the sense that their spacings distribution is not Poissonian, as posited by the Berry-Tabor conjecture for "generic'' quantum integrable systems.