Determinant formula for the six-vertex model with reflecting end

Abstract

Using the Quantum Inverse Scattering Method for the XXZ model with open boundary conditions, we obtained the determinant formula for the six vertex model with reflecting end.Comment: 10 page

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

“…Moreover after the same similarity transformation and taking the limit the resulting K-matrix becomes the diagonal matrix solution of the reflection equation (2.3). Hence the partition function in the limit reduces to that of the six-vertex model [21].…”

“…Moreover, one may check that the R-matrix satisfies weight conservation condition, 21) and crossing relation…”

“…This problem is closely related to that of open spin chain [22]. The DW partition function of the sixvertex model with a diagonal reflection end was exactly calculated and expressed in terms some determinant [21]. Then such an explicit determinant representation was re-derived [23,24] by using F-basis of the closed XXZ chain.…”

“…For a two-dimensional statistical model with a reflection end [21], in addition to the local interaction vertex, a reflecting matrix or K-matrix which describes the boundary interactions needs to be introduced at the reflection end of the lattice (see figure 4 below). This problem is closely related to that of open spin chain [22].…”

Recursive formulas for the overlaps between Bethe states and product states in XXZ Heisenberg chains

“…[43] using Boundary Bethe Ansatz techniques [73]. Denoting generically with |ψ the two-site shift invariant state, we want to prove the following determinant formula [43] …”