Rational quantum integrable systems of D_N type with polarized spin reversal operators
arXiv:1503.08231 · doi:10.1016/j.nuclphysb.2015.06.016
Abstract
We study the spin Calogero model of D_N type with polarized spin reversal operators, as well as its associated spin chain of Haldane-Shastry type, both in the antiferromagnetic and ferromagnetic cases. We compute the spectrum and the partition function of the former model in closed form, from which we derive an exact formula for the chain's partition function in terms of products of partition functions of Polychronakos-Frahm spin chains of type A. Using a recursion relation for the latter partition functions that we derive in the paper, we are able to numerically evaluate the partition function, and thus the spectrum, of the D_N-type spin chain for relatively high values of the number of spins N. We analyze several global properties of the chain's spectrum, such as the asymptotic level density, the distribution of consecutive spacings of the unfolded spectrum, and the average degeneracy. In particular, our results suggest that this chain is invariant under a suitable Yangian group, and that its spectrum coincides with that of a Yangian-invariant vertex model with linear energy function and dispersion relation.
arXiv comment26 pages, 5 figures, typeset in LaTeX
References in corpus (37)
- Yang-Baxter equation in spin chains with long range interactions
- Lattice Integrable Systems of Haldane-Shastry Type
- On Models with Inverse-Square Exchange
- Integrable Systems for Particles with Internal Degrees of Freedom
- Infinite matrix product states, Conformal Field Theory and the Haldane-Shastry model
- Exact Spectrum of SU(n) Spin Chain with Inverse-Square Exchange
- Spectrum of a spin chain with inverse square exchange
- Quantum spin Hamiltonians for the SU(2)_k WZW model
- Exact Solution of Long-Range Interacting Spin Chains with Boundaries
- Quantum vs Classical Integrability in Calogero-Moser Systems
- Global properties of the spectrum of the Haldane-Shastry spin chain
- The SU(n)_1 WZW Models: Spinon Decomposition and Yangian Structure
- Exact partition function of SU(m|n) supersymmetric Haldane-Shastry spin chain
- Haldane-Shastry spin chains of BC_N type
- Orthogonal Polynomials of Types A and B and Related Calogero Models
- A_N-type Dunkl operators and new spin Calogero-Sutherland models
- Skew Young diagram method in spectral decomposition of integrable lattice models
- Supersymmetric Polychronakos Spin Chain: Motif, Distribution Function, and Character
- Integrable Spin Chain with Reflecting End
- Low energy properties of the SU(m|n) supersymmetric Haldane-Shastry spin chain
- New spin Calogero-Sutherland models related to B_N-type Dunkl operators
- Exact spectrum and partition function of SU(m|n) supersymmetric Polychronakos model
- Is there an attraction between spinons in the Haldane--Shastry model?
- The Polychronakos-Frahm spin chain of BC_N type and Berry-Tabor's conjecture
- The Berry-Tabor conjecture for spin chains of Haldane-Shastry type
- Exactly solvable D_N-type quantum spin models with long-range interaction
- Boson-fermion duality in SU(m|n) supersymmetric Haldane-Shastry spin chain
- An exactly solvable supersymmetric spin chain of BC_N type
- On the level density of spin chains of Haldane--Shastry type
- Entanglement in a spin system with inverse square statistical interaction
- Yangian-invariant spin models and Fibonacci numbers
- Spectral properties of supersymmetric Polychronakos spin chain associated with A_{N-1} root system
- The spin Sutherland model of D_N type and its associated spin chain
- The exactly solvable spin Sutherland model of B_N type and its related spin chain
- 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