Phase Diagram of an Integrable Alternating $U_q[sl(2|1)]$ Superspin Chain    [PDF]

Holger Frahm, MĂĄrcio J. Martins
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.
View original: http://arxiv.org/abs/1202.4676