arXiv:solv-int/9608005

Fusion Hierarchies with Open Boundaries and Exactly Solvable Models

Y-K Zhou

Published Aug 19, 1996• 4 citations

Abstract

The formulation of integrable models with open boundary conditions and the functional relations of fused transfer matrices are discussed. It is shown that finite-size corrections to the transfer matrices and unitarity relations of free energies can be obtained from the functional relations. Unitarity relations of surface free energies presented in previous papers are also reviewed.

DOI: 10.48550/arxiv.solv-int/9608005

Related papers

FUSION HIERARCHY AND FINITE-SIZE CORRECTIONS OF Uq[sl(2)] INVARIANT VERTEX MODELS WITH OPEN BOUNDARIES

The fused six-vertex models with open boundary conditions are studied. The Bethe ansatz solution given by Sklyanin has been generalized to the transfer matrices of the fused models. We have shown that the eigenvalues of transfer matrices satisfy a group of functional relations, which are the su(2) fusion rule held by the transfer matrices of the fused models. The fused transfer matrices form a commuting family and also commute with the quantum group Uq[sl(2)]. In the case of the parameter qh = −1 (h = 4,5, · · ·) the functional relations in the limit of spectral parameter u → i ∞ are truncated. This shows that the su(2) fusion rule with finite level appears for the six vertex model with the open boundary conditions. We have solved the functional relations to obtain the finite-size corrections of the fused transfer matrices for low-lying excitations. From the corrections the central charges and conformal weights of underlying conformal field theory are extracted. To see different boundary conditions we also have studied the six-vertex model with a twisted boundary condition. hep-th/9502053; to appear in NPB. 1

Jan 1, 19950 citations

Exact solution and surface critical behaviour of open cyclic SOS lattice models

Yu‐Kui Zhou, Murray T. Batchelor

We consider the L-state cyclic solid-on-solid lattice models under a class of open boundary conditions. The integrable boundary face weights are obtained by solving the reflection equations. Functional relations for the fused transfer matrices are presented for both periodic and open boundary conditions. The eigenspectra of the unfused transfer matrix is obtained from the functional relations using the analytic Bethe ansatz. For a special case of crossing parameter , the finite-size corrections to the eigenspectra of the critical models are obtained, from which the corresponding conformal dimensions follow. The calculation of the surface free energy away from criticality yields two surface specific heat exponents, and , where coprime to L. These results are in agreement with the scaling relations and .

arXiv:cond-mat/9602078Journal of Physics A Mathematical and GeneralMay 7, 19969 citations

Fusion procedure for the Belavin model with open boundary conditions

Heng Fan, Kangjie Shi, Bo-Yu Hou

We have recently used unitarity and cross-unitarity properties of an symmetric R-matrix to construct the transfer matrix t(u) for an N-site open spin chain. Here we give a fusion procedure for such a chain, and we prove that the fused transfer matrix is commutative with the original transfer matrix t(u).

Journal of Physics A Mathematical and GeneralSep 21, 19960 citations

SU(2) FUSION HIERARCHIES OF DILUTE MODELS

YU-KUI ZHOU

The dilute AL models have been studied by analyzing their adjacency conditions, face weights and transfer matrices. The new results including two su(2) fusion rules and Bethe ansatz solutions of the fused transfer matrices are presented. Some relevant physics aspects such as the finite-size corrections to transfer matrices are also discussed.

arXiv:hep-th/9506107International Journal of Modern Physics BNov 15, 19969 citations

Surface free energy for systems with integrable boundary conditions

Frank Göhmann, Michael Bortz, Holger Frahm

The surface free energy is the difference between the free energies for a system with open boundary conditions and the same system with periodic boundary conditions. We use the quantum transfer matrix formalism to express the surface free energy in the thermodynamic limit of systems with integrable boundary conditions as a matrix element of certain projection operators. Specializing to the XXZ spin 1/2 chain we introduce a novel `finite temperature boundary operator' which characterizes the thermodynamical properties of surfaces related to integrable boundary conditions.

arXiv:cond-mat/0508377Journal of Physics A Mathematical and GeneralNov 30, 200519 citations

Integrable quenches in nested spin chains II: fusion of boundary transfer matrices

Lorenzo Piroli, Eric Vernier, Pasquale Calabrese +1 more

Abstract We consider quantum quenches in the integrable -invariant spin chain (Lai–Sutherland model), and focus on the family of integrable initial states. By means of a quantum transfer matrix approach, these can be related to ‘soliton-non-preserving’ boundary transfer matrices in an appropriate transverse direction. In this work, we provide a technical analysis of such integrable transfer matrices. In particular, we address the computation of their spectrum: this is achieved by deriving a set of functional relations between the eigenvalues of certain ‘fused operators’ that are constructed starting from the soliton-non-preserving boundary transfer matrices (namely the T - and Y -systems). As a direct physical application of our analysis, we compute the Loschmidt echo for imaginary and real times after a quench from the integrable states. Our results are also relevant for the study of the spectrum of -invariant Hamiltonians with open boundary conditions.

arXiv:1812.05330Journal of Statistical Mechanics Theory and ExperimentJun 1, 201924 citations