Reflection algebra and functional equations

Abstract

In this work we investigate the possibility of using the reflection algebra as a source of functional equations. More precisely, we obtain functional relations determining the partition function of the six-vertex model with domain-wall boundary conditions and one reflecting end. The model's partition function is expressed as a multiple-contour integral that allows the homogeneous limit to be obtained straightforwardly. Our functional equations are also shown to give rise to a consistent set of partial differential equations for the partition function.

v1: 30 pages. v2: 31 pages, figures added, version accepted for publication in Nucl. Phys. B

References in corpus (6)

• Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors
• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• Correlation functions of the open XXZ chain I
• Correlation functions of the open XXZ chain II
• Functional relations and the Yang-Baxter algebra
• Partial differential equations from integrable vertex models

Cited by in corpus (15)

• Thermodynamic limit of the six-vertex model with reflecting end
• Off-shell scalar products for the $XXZ$ spin chain with open boundaries
• Integral formula for elliptic SOS models with domain walls and a reflecting end
• New differential equations in the six-vertex model
• Differential approach to on-shell scalar products in six-vertex models
• The Functional Method for the Domain-Wall Partition Function
• Boundary Perimeter Bethe Ansatz
• Boundary correlations for the six-vertex model with reflecting end boundary condition
• Six-vertex model and non-linear differential equations I. Spectral problem
• Arctic curve of the free-fermion six-vertex model with reflecting end boundary condition
• Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions
• Scalar products of the elliptic Felderhof model and elliptic Cauchy formula
• Higher rank elliptic partition functions and multisymmetric elliptic functions
• A class of partition functions associated with $E_{\tau ,\eta }(g{l}_3)$ by Izergin-Korepin analysis
• Elliptic free-fermion model with OS boundary and elliptic Pfaffians