Sum rules for the ground states of the O(1) loop model on a cylinder and the XXZ spin chain

Abstract

The sums of components of the ground states of the O(1) loop model on a cylinder or of the XXZ quantum spin chain at Delta=-1/2 (of size L) are expressed in terms of combinatorial numbers. The methods include the introduction of spectral parameters and the use of integrability, a mapping from size L to L+1, and knot-theoretic skein relations.

final version to be published

References in corpus (2)

• Enumeration of Symmetry Classes of Alternating Sign Matrices and Characters of Classical Groups
• On R-matrix representations of Birman-Murakami-Wenzl algebras

Cited by in corpus (10)

• On polynomials interpolating between the stationary state of a O(n) model and a Q.H.E. ground state
• Ground-state properties of a supersymmetric fermion chain
• Bethe roots and refined enumeration of alternating-sign matrices
• Finite-size corrections for universal boundary entropy in bond percolation
• The nineteen-vertex model and alternating sign matrices
• A_k Generalization of the O(1) Loop Model on a Cylinder: Affine Hecke Algebra, q-KZ Equation and the Sum Rule
• Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder
• On the logarithmic bipartite fidelity of the open XXZ spin chain at $\Delta =-1/2$
• Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder II: rotated lattice
• The open XXZ chain at $\Delta =-1/2$ and the boundary quantum Knizhnik-Zamolodchikov equations