An exactly solvable supersymmetric spin chain of BC_N type

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.

36 pages, 7 figures

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• On the level density of spin chains of Haldane--Shastry type
• Inozemtsev's hyperbolic spin model and its related spin chain
• Spectral properties of supersymmetric Polychronakos spin chain associated with A_{N-1} root system
• Yangian-invariant spin models and Fibonacci numbers
• The exactly solvable spin Sutherland model of B_N type and its related spin chain
• Thermodynamics and criticality of supersymmetric spin chains with long-range interactions
• A new perspective on the integrability of Inozemtsev's elliptic spin chain
• Spin chains of Haldane-Shastry type and a generalized central limit theorem
• $1/f^{\alpha }$ noise and integrable systems
• Level density distribution for one-dimensional vertex models related to Haldane-Shastry like spin chains
• Partition functions of Polychronakos like spin chains associated with polarized spin reversal operators
• Appearance of branched motifs in the spectra of $B{C}_N$ type Polychronakos spin chains
• Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators
• Rational quantum integrable systems of D_N type with polarized spin reversal operators
• The open Haldane-Shastry chain: thermodynamics and criticality
• Super Rogers-Szegö polynomials associated with $B{C}_N$ type of Polychronakos spin chains
• Generalized Lipkin-Meshkov-Glick models of Haldane-Shastry type