Related papers: An exactly solvable supersymmetric spin chain of B…
We introduce a new class of open, translationally invariant spin chains with long-range interactions depending on both spin permutation and (polarized) spin reversal operators, which includes the Haldane-Shastry chain as a particular…
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,…
The Haldane-Shastry spin chain has a myriad of remarkable properties, including Yangian symmetry and, for spin $1/2$, explicit highest-weight eigenvectors featuring (the case $\alpha = 1/2$ of) Jack polynomials. This stems from the…
By using the technique of supersymmetric quantum mechanics, we study a quasi exactly solvable extension of the N-particle rational Calogero model with harmonic confining interaction. Such quasi exactly solvable many particle system, whose…
Although QCD can be treated perturbatively in the high energy limit, lower energies requre uses of nonperturbative methods such as ADS/CFT and/or Abelian reduction.These methods are not equivalent. In this paper we provide arguments in…
Several topics related to quantum spin models of Calogero-Sutherland type, partially solvable spin chains and Polychronakos's "freezing trick" are rigorously studied.
We analyze the thermodynamics and criticality properties of four families of su$(m|n)$ supersymmetric spin chains of Haldane-Shastry (HS) type, related to both the $A_{N-1}$ and the $BC_N$ classical root systems. Using a known formula…
In a series of recently published papers we reanalyzed the existing treatments of Veneziano and Veneziano-like amplitudes and the models associated with these amplitudes. In this work we demonstrate that the already obtained new partition…
We present a new lattice integrable system in one dimension of the Haldane-Shastry type. It consists of spins positioned at the static equilibrium positions of particles in a corresponding classical Calogero system and interacting through…
New exactly solvable nineteen vertex models and related quantum spin-1 chains are solved. Partition functions, excitation energies, correlation lengths, and critical exponents are calculated. It is argued that one of the non-critical…
Based on Richardson's exact solution of the pairing model and the Gaudin model for spin systems we derive a new class of exactly solvable models for finite boson system. As an example we solve a particular hamiltonian which displays a…
We present a new and simpler expression for the Hamiltonian of the partially isotropic (XXZ-like) version of the Haldane-Shastry model, which was derived by D. Uglov over two decades ago in an apparently little-known preprint. While…
We discuss relation between the cluster integrable systems and spin chains in the context of their correspondence with 5d supersymmetric gauge theories. It is shown that $\mathfrak{gl}_N$ XXZ-type spin chain on $M$ sites is isomorphic to a…
The use of exactly-solvable Richardson-Gaudin (R-G) models to describe the physics of systems with strong pair correlations is reviewed. We begin with a brief discussion of Richardson's early work, which demonstrated the exact solvability…
We review some recent results on quasi-exactly solvable spin models presenting near-neighbors interactions. These systems can be understood as cyclic generalizations of the usual Calogero-Sutherland models. A nontrivial modification of the…
We refine the recently introduced notion of eclectic spin chains by including a maximal number of deformation parameters. These models are integrable, nearest-neighbor n-state spin chains with exceedingly simple non-hermitian Hamiltonians.…
We construct a class of interacting spin Calogero-Moser type systems. They can be regarded as a many particle system with spin degrees of freedom and as an integrable spin chain of Gaudin type. We prove that these Hamiltonian systems are…
The spectrum of the integrable spin-S Heisenberg chains is completely characterized in terms of spin-1/2 spinons. In the continuum limit they form a quasi-particle basis to the higher level SU(2) Wess-Zumino-Witten (WZW) models. Enumerating…
This monograph introduces an exact model for a critical spin chain with arbitrary spin S, which includes the Haldane--Shastry model as the special case S=1/2. While spinons in the Haldane--Shastry model obey abelian half-fermi statistics,…
The Heisenberg spin chain is a canonical integrable model. As such, it features stable ballistically propagating quasiparticles, but spin transport is sub-ballistic at any nonzero temperature: an initially localized spin fluctuation spreads…