aqora

The sl2 Loop Algebra Symmetry of the Six-Vertex Model at Roots of Unity

Tetsuo Deguchi, K. Fabricius, Barry M. McCoy

arXiv:cond-mat/9912141Journal of Statistical PhysicsFeb 1, 2001135 citations

The sl_2 loop algebra symmetry of the six-vertex model at roots of unity I: Jordan-Wigner techniques

Tetsuo Deguchi, K. Fabricius, Barry M. McCoy

Dec 8, 19991 citation

22aTE-13 The sl_2 loop algebra symmetry of the XXZ model at roots of unity

哲生出口, K. Fabricius, B M McCoyB

日本物理学会講演概要集Sep 10, 20000 citations

QUANTUM GROUP IN ROOTS OF UNITY AND THE RESTRICTION OF XXZ MODEL

Alexander A. Belavin

International Workshop on Lie Theory and Its Applications in Physics (LT)Jul 1, 20040 citations

THE 8V CSOS MODEL AND THE sl2 LOOP ALGEBRA SYMMETRY OF THE SIX-VERTEX MODEL AT ROOTS OF UNITY

Tetsuo Deguchi

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 Eτ,η(sl2) at the discrete coupling constants: 2N η = m1 + im2τ, where N, m1 and m2 are integers. Then we show that degenerate eigenvectors of the transfer matrix of the six-vertex model at roots of unity in the sector SZ ≡ 0 ( mod N) are derived from those of the 8V CSOS model, through the trigonometric limit. They are associated with the complete N strings. From the result we see that the dimension of a given degenerate eigenspace in the sector SZ ≡ 0 ( mod N) of the six-vertex model at Nth roots of unity is given by [Formula: see text], where [Formula: see text] is the maximal value of the total spin operator SZ in the degenerate eigenspace.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 Eτ,η(sl2) at the discrete coupling constants: 2N η = m1 + im2τ, where N, m1 and m2 are integers. Then we show that degenerate eigenvectors of the transfer matrix of the six-vertex model at roots of unity in the sector SZ ≡ 0 ( mod N) are derived from those of the 8V CSOS model, through the trigonometric limit. They are associated with the complete N strings. From the result we see that the dimension of a given degenerate eigenspace in the sector SZ ≡ 0 ( mod N) of the six-vertex model at Nth roots of unity is given by [Formula: see text], where [Formula: see text] is the maximal value of the total spin operator SZ in the degenerate eigenspace.

arXiv:cond-mat/0110121International Journal of Modern Physics BJun 20, 200219 citations

CENTRAL ELEMENTS OF THE ELLIPTIC YANG–BAXTER ALGEBRA IN ROOTS OF UNITY

Alexander Belavin, M. Jimbo

We describe the center of the algebra of monodromy matrices connected with the R-matrix of the eight-vertex model in the case where the crossing parameter has rational values.

International Journal of Modern Physics AMay 1, 20047 citations

THE 8V CSOS MODEL AND THE sl2 LOOP ALGEBRA SYMMETRY OF THE SIX-VERTEX MODEL AT ROOTS OF UNITY

Related papers

THE 8V CSOS MODEL AND THE sl2 LOOP ALGEBRA SYMMETRY OF THE SIX-VERTEX MODEL AT ROOTS OF UNITY

Related papers