A possible combinatorial point for XYZ-spin chain

Abstract

We formulate and discuss a number of conjectures on the ground state vectors of the XYZ-spin chains of odd length with periodic boundary conditions and a special choice of the Hamiltonian parameters. In particular, arguments for the validity of a sum rule for the components, which describes in a sense the degree of antiferromagneticity of the chain, are given.

AMSLaTeX, 15 pages

References in corpus (5)

• The eight-vertex model and Painleve VI
• Sum rules for the ground states of the O(1) loop model on a cylinder and the XXZ spin chain
• Polynomial solutions of qKZ equation and ground state of XXZ spin chain at Delta = -1/2
• A supersymmetric matrix model: III. Hidden SUSY in statistical systems
• Bethe roots and refined enumeration of alternating-sign matrices

Cited by in corpus (18)

• Calculation of multifractal dimensions in spin chains
• Spin chains with dynamical lattice supersymmetry
• The eight-vertex model and lattice supersymmetry
• Exact and simple results for the XYZ and strongly interacting fermion chains
• Ground-state properties of a supersymmetric fermion chain
• Special polynomials related to the supersymmetric eight-vertex model: A summary
• Finite size emptiness formation probability of the XXZ spin chain at $\Delta =-1/2$
• Special polynomials related to the supersymmetric eight-vertex model. II. Schrödinger equation
• Special polynomials related to the supersymmetric eight-vertex model. I. Behaviour at cusps
• The nineteen-vertex model and alternating sign matrices
• On the transfer matrix of the supersymmetric eight-vertex model. II. Open boundary conditions
• On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions
• Elliptic pfaffians and solvable lattice models
• A Combinatorial Description of Certain Polynomials Related to the XYZ Spin Chain
• Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder
• Sum rules for the supersymmetric eight-vertex model
• Theta function solutions of the qKZB equation for a face model
• A Combinatorial Description of Certain Polynomials Related to the XYZ Spin Chain. II. The Polynomials $p_n$