Fusion Hierarchy Research Articles

From fusion hierarchy to excited state TBA

Functional relations among the fusion hierarchy of quantum transfer matrices give a novel derivation of the TBA equations, namely without string hypothesis. This is demonstrated for two important models of 1D highly correlated electron systems, the supersymmetric t- J model and the supersymmetric extended Hubbard model. As a consequence, “the excited state TBA” equations, which characterize correlation lengths, are explicitly derived for the t- J model. To the authors' knowledge, this is the first explicit derivation of excited state TBA equations for ]D lattice electron systems. © 1998 Elsevier Science B.V

A construction of solutions to reflection equations for interaction-round-a-face models

We present a procedure in which known solutions to reflection equations for interaction-round-a-face lattice models are used to construct new solutions. The procedure is particularly well suited to models which have a known fusion hierarchy and which are based on graphs containing a node of valency 1. Among such models are the Andrews - Baxter - Forrester models, for which we construct reflection equation solutions for fixed and free boundary conditions.

Fusion of dilute AL lattice models

The fusion procedure is implemented for the dilute A L lattice models and a fusion hierarchy of functional equations with an su(3) structure is derived for the fused transfer matrices. We also present the Bethe ansatz equations for the dilute A L lattice models and discuss their connection with the fusion hierarchy. The solution of the fusion hierarchy for the eigenvalue spectra of the dilute A L lattice models will be presented in a subsequent paper.

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 the transfer matrices satisfy a group of functional relations, which is 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 U q [ sl(2)]. In the case of the parameter q h = −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 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 the underlying conformal field theory are extracted. To see the effect of different boundary conditions we also have studied the six-vertex model with a twisted boundary condition.

Interaction-round-a-face models with fixed boundary conditions: The ABF fusion hierarchy

We use boundary weights and reflection equations to obtain families of commuting double-row transfer matrices for interaction-round-a-face models with fixed boundary conditions. In particular, we consider the fusion hierarchy of the Andrews-Baxter-Forrester models, for which we find that the double-row transfer matrices satisfy functional equations with an su(2) structure.

A General Formula for Colored ZnGradedBraid Matrices and the Fusion Braid Matrices

We present formulae for matrix elements of a new hierarchy of multivariable colored braid matrices with Z n graded symmetry. We point out that a condition of roots of unity is necessary for the colored matrices to satisfy the colored braid relation (the colored Yang-Baxter relation). We give a general formula for the colored braid matrix elements which generalizes the colored Z n graded hirearchy and the fusion hierarchy.

Investigation of temporal integration by video sampling.

The results from the preliminary set of experiments in which a new video sampling apparatus was used are reported. With the aid of this apparatus experiments were carried out to measure the maximum visual temporal integration time (critical duration) at various background intensities (0·034–34 cd m−2). The aim was to determine to what extent this phenomenon is attributable to either ‘central’ or ‘peripheral’ events. The extended integration period found for the number recognition task is interpreted as evidence of a ‘central’ process; to follow the argument further, an attempt was made to demonstrate information integration using a rotating form in a similar identification–discrimination situation. Monocular, binocular, and dichoptic arrangements were employed, and the amount of dichoptic summation of form information, achieved by both normal and strabismic subjects without stereoscopic depth perception, was used to test two theoretical models of binocular fusion. In addition, stereoscopic depth was generated with uncorrected sampling of the left and right images, which may be due to the action of a ‘fusion hierarchy’. Signal detection theory is suggested as a possible solution to the problem of expectation effects in identification-threshold experiments.