In:
Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, Vol. 2021, No. 2 ( 2021-02-01), p. 023102-
Abstract:
The eight-vertex model on the square lattice with vertex weights a , b , c , d obeying the relation ( a 2 + ab )( b 2 + ab ) = ( c 2 + ab )( d 2 + ab ) is considered. Its transfer matrix with L = 2 n + 1, n ⩾ 0, vertical lines and periodic boundary conditions along the horizontal direction has the doubly-degenerate eigenvalue Θ n = ( a + b ) 2 n +1 . A basis of the corresponding eigenspace is investigated. Several scalar products involving the basis vectors are computed in terms of a family of polynomials introduced by Rosengren and Zinn-Justin. These scalar products are used to find explicit expressions for particular entries of the vectors. The proofs of these results are based on the generalisation of the eigenvalue problem for Θ n to the inhomogeneous eight-vertex model.
Type of Medium:
Online Resource
ISSN:
1742-5468
DOI:
10.1088/1742-5468/abda28
Language:
Unknown
Publisher:
IOP Publishing
Publication Date:
2021
detail.hit.zdb_id:
2138944-5
Bookmarklink