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arXiv:hep-th/0303205 · Nuclear Physics B

Fused integrable lattice models with quantum impurities and open boundaries

Anastasia Doikou

Published Aug 8, 2003• 47 citations
arXivHTMLPDF
DOI
10.1016/j.nuclphysb.2003.07.001

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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 .
We present a general method for constructing integrable stochastic processes, with two-step discrete time Floquet dynamics, from the transfer matrix formalism. The models can be interpreted as a discrete time parallel update. The method can be applied for both periodic and open boundary conditions. We also show how the stationary distribution can be built as a matrix product state. As an illustration we construct parallel discrete time dynamics associated with the R-matrix of the SSEP and of the ASEP, and provide the associated stationary distributions in a matrix product form. We use this general framework to introduce new integrable generalized exclusion processes, where a fixed number of particles is allowed on each lattice site in opposition to the (single particle) exclusion process models. They are constructed using the fusion procedure of R-matrices (and K-matrices for open boundary conditions) for the SSEP and ASEP. We develop a new method, that we named “fused” matrix ansatz, to build explicitly the stationary distribution in a matrix product form. We use this algebraic structure to compute physical observables such as the correlation functions and the mean particle current.