Determinant formula for the partition function of the six-vertex model with a non-diagonal reflecting end

Abstract

With the help of the F-basis provided by the Drinfeld twist or factorizing F-matrix for the open XXZ spin chain with non-diagonal boundary terms, we obtain the determinant representation of the partition function of the six-vertex model with a nondiagonal reflecting end under domain wall boundary condition.

Determinant representations of scalar products for the open XXZ chain with non-diagonal boundary terms

“…is closely related to the partition function computed in [44]. Solving the recursive relations (5.19), we find that if the parameters {v…”

“…It was shown [44] that the scalar product S I,II ({u α }; {v (2) i }) (resp. S II,I ({u α }; {v (1) i })) can be expressed in terms of some determinant no matter the parameters {v (2) i } (resp.…”

“…Note that these functions Z N ({ū J }) correspond to the partition functions of the six-vertex model with domain wall boundary conditions and one reflecting end [43] specified by the non-diagonal K-matrices (2.8) and (2.10) respectively [44].…”

“…The polarization free representations (4.20) and (4.21) of the pseudo-particle creation/annihilation operators allowed ones [44] to express the above functions in terms of the determinants representations of some N × N matrices as follows:…”

Correlation functions of the XXZ spin chain with the twisted boundary condition

“…The thermodynamical limit of the determinant is considered for XXZ model with a diagonal open boundary condition [23]. Recently, The determinant representations of the scalar products and correlation functions are extensively studied for models related to various boundary conditions especially those with non-diagonal boundary terms [7,24,25,26,27,28,29,30]. Among them, the seperation of variables(SOV) method [7,32,33] gives an attractive approach to obtain the determinant representations of the scalar product between an eigenstate and an arbitrary state with the open boundary conditions.…”