Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-12-08
Nucl.Phys.B847:220-246,2011
Physics
Condensed Matter
Statistical Mechanics
32 pages, 7 figures included; Nucl. Phys. B [FS] (2011) in press
Scientific paper
10.1016/j.nuclphysb.2011.01.026
Based on the exact solution of the eigenvalue problem for the $U_q[sl(2|1)]$ vertex model built from alternating 3-dimensional fundamental and dual representations by means of the algebraic Bethe ansatz we investigate the ground state and low energy excitations of the corresponding mixed superspin chain for deformation parameter $q=\exp(-i\gamma/2)$. The model has a line of critical points with central charge $c=0$ and continua of conformal dimensions grouped into sectors with $\gamma$-dependent lower edges for $0\le\gamma<\pi/2$. The finite size scaling behaviour is consistent with a low energy effective theory consisting of one compact and one non-compact bosonic degree of freedom. In the 'ferromagnetic' regime $\pi<\gamma\le2\pi$ the critical theory has $c=-1$ with exponents varying continuously with the deformation parameter. Spin and charge degrees of freedom are separated in the finite size spectrum which coincides with that of the $U_q[osp(2|2)]$ spin chain. In the intermediate regime $\pi/2<\gamma<\pi$ the finite size scaling of the ground state energy depends on the deformation parameter.
Frahm Holger
Martins Marcio J.
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