181 research outputs found
On the Degenerate Multiplicity of the Loop Algebra for the 6V Transfer Matrix at Roots of Unity
We review the main result of cond-mat/0503564. The Hamiltonian of the XXZ
spin chain and the transfer matrix of the six-vertex model has the loop
algebra symmetry if the parameter is given by a root of unity,
, for an integer . We discuss the dimensions of the degenerate
eigenspace generated by a regular Bethe state in some sectors, rigorously as
follows: We show that every regular Bethe ansatz eigenvector in the sectors is
a highest weight vector and derive the highest weight , which
leads to evaluation parameters . If the evaluation parameters are
distinct, we obtain the dimensions of the highest weight representation
generated by the regular Bethe state.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
The 8V CSOS model and the loop algebra symmetry of the six-vertex model at roots of unity
We review an algebraic method for constructing degenerate eigenvectors of the
transfer matrix of the eight-vertex Cyclic Solid-on-Solid lattice model (8V
CSOS model), where the degeneracy increases exponentially with respect to the
system size.
We consider the elliptic quantum group at the discrete
coupling constants: , where and are
integers. Then we show that degenerate eigenvectors of the transfer matrix of
the six-vertex model at roots of unity in the sector (mod )
are derived from those of the 8V CSOS model, through the trigonometric limit.
They are associated with the complete strings. From the result we see that
the dimension of a given degenerate eigenspace in the sector
(mod ) of the six-vertex model at th roots of unity is given by
, where is the maximal value of the total spin
operator in the degenerate eigenspace.Comment: 7 pages, no figure, conference proceeding
- …