Refined Razumov-Stroganov conjectures for open boundaries

Abstract

Recently it has been conjectured that the ground-state of a Markovian Hamiltonian, with one boundary operator, acting in a link pattern space is related to vertically and horizontally symmetric alternating-sign matrices (equivalently fully-packed loop configurations (FPL) on a grid with special boundaries).We extend this conjecture by introducing an arbitrary boundary parameter. We show that the parameter dependent ground state is related to refined vertically symmetric alternating-sign matrices i.e. with prescribed configurations (respectively, prescribed FPL configurations) in the next to central row. We also conjecture a relation between the ground-state of a Markovian Hamiltonian with two boundary operators and arbitrary coefficients and some doubly refined (dependence on two parameters) FPL configurations. Our conjectures might be useful in the study of ground-states of the O(1) and XXZ models, as well as the stationary states of Raise and Peel models.

11 pages LaTeX, 8 postscript figures

References in corpus (11)

• Spin chains and combinatorics
• The Blob Algebra and the Periodic Temperley-Lieb Algebra
• The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions
• The Importance of being Odd
• Lattice fermion models with supersymmetry
• Spin chains and combinatorics: twisted boundary conditions
• Temperley-Lieb Stochastic Processes
• The raise and peel model of a fluctuating interface
• Nonequilibrium stationary states and equilibrium models with long range interactions
• Raise and Peel Models of fluctuating interfaces and combinatorics of Pascal's hexagon
• The modified XXZ Heisenberg chain, conformal invariance, surface exponents of c<1 systems, and hidden symmetries of the finite chains

Cited by in corpus (4)

• Koornwinder polynomials and the XXZ spin chain
• On the logarithmic bipartite fidelity of the open XXZ spin chain at $\Delta =-1/2$
• The open XXZ chain at $\Delta =-1/2$ and the boundary quantum Knizhnik-Zamolodchikov equations
• Avalanches in the Raise and Peel model in the presence of a wall