Boundary correlations for the six-vertex model with reflecting end boundary condition

Abstract

We consider the six-vertex model with reflecting end boundary condition. We compute analytically boundary correlation functions, such as the boundary polarization and the emptiness formation probability. In order to do that, we use the Sklyanin's reflection algebra to derive recursion relations for the partition function of the model as well as for the boundary correlations in terms of the partition function. Thanks to the Tsuchiya determinant formula, these recursion relations allow the boundary correlations to be also efficiently written in determinant form. *

Arctic curve of the free-fermion six-vertex model with reflecting end boundary condition

“…Using the reflection algebra one can find recurrence relations between the correlations G N and the partition function of 2(N −1) ×(N −1) rectangular sublattices [24]. Then, using Tsuchiya formula (15), these correlations can also be written in terms of determinants of N × N matrices.…”

“…In this section, we review two types of boundary correlations necessary to the determination of the arctic curve and its contact points. For the six-vertex model with reflecting end boundary condition, these correlations were first introduced in [24].…”

“…Note that h N (1) = 1 thanks to (24). From Cauchy integral formula, we can invert this relation in order to obtain H (r)…”

“…More recently, the six-vertex model with reflecting end boundary condition [22] was also considered. In this case, the evaluation of thermodynamic properties [23] and the boundary correlations [24] were analytically done. This was made possible thanks to the fact that the partition function of the six-vertex model with reflecting end boundary can be built from the Bethe state defined in Sklyanin construction for open spin chains [25].…”

Construction of determinants for the six-vertex model with domain wall boundary conditions

“…It is useful to mention that for the trigonometric case of the model with pDWBC in the limit where the lattice domain become a semi-infinite strip shape, the partition function can be given in terms of a Pfaffian [16]. Other directions to be explored concern more general fixed boundary conditions and calculation of correlation functions in these models [17][18][19][20][21].…”