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arXiv:cond-mat/9908421

An integrable model for the integer quantum Hall transition I: The vertex model

R. M. Gade

Published Aug 28, 1999• 0 citations
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Abstract

In this study, an integrable vertex model based on the quantum affine superalgebra $U_q\bigl(\hat{gl}(2|2)\bigr)$ is constructed. The model is characterized by a particular assignment of spectral parameters and lowest as well as highest weight $U_q\bigl(gl(2|2) \bigr)$ modules to its lattice links. Solutions of the corresponding intertwining conditions yield the Boltzmann weights. The set of mutually commuting charges contains a quantity equivalent to the super spin chain Hamiltonian proposed for the description of the integer quantum Hall transition.

DOI
10.48550/arxiv.cond-mat/9908421

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Boundary state of Uq(gl^(N∣N))U_q(\hat{gl}(N|N))Uq​(gl^​(N∣N)) analog of half-infinite t−Jt-Jt−J model
The Uq(gl^(N∣N))U_q(\hat{gl}(N|N))Uq​(gl^​(N∣N))-analog of the half-infinite t−Jt-Jt−J model with a boundary is considered by using the vertex operator approach. We find explicit bosonic formula of the boundary state in the integrable highest-weight module over the quantum superalgebra Uq(gl^(N∣N))U_q(\hat{gl}(N|N))Uq​(gl^​(N∣N)).
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We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains.The graphical forms of the unitarity and various crossing relations are introduced.Their explicit analytical forms for the case of integrable systems associated with the quantum loop algebra U q (L(sl l+1 )) are given.The commutativity conditions for the transfer operators of lattices with a boundary are derived by the graphical method.Our consideration reveals useful advantages of the graphical approach for certain problems in the theory of quantum integrable systems.