Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2012-02-21
Physics
Condensed Matter
Statistical Mechanics
62 pages, 8 figures included
Scientific paper
We construct a family of integrable vertex model based on the typical four-dimensional representations of the quantum group deformation of the Lie superalgebra $sl(2|1)$. Upon alternation of such a representation with its dual this model gives rise to a mixed superspin Hamiltonian with local interactions depending on the representation parameter $\pm b$ and the deformation parameter ${\gamma}$. As a subsector this model contains integrable vertex models with ordinary symmetries for twisted boundary conditions. The thermodynamic limit and low energy properties of the mixed superspin chain are studied using a combination of analytical and numerical methods. Based on these results we identify the phases realized in this system as a function of the parameters $b$ and $\gamma$. The different phases are characterized by the operator content of the corresponding critical theory. Only part of the spectrum of this effective theory can be understood in terms of the $U(1)$ symmetries related to the physical degrees of freedom corresponding to spin and charge. The other modes lead to logarithmic finite-size corrections in the spectrum of the theory.
Frahm Holger
Martins Marcio J.
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