Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms

Abstract

Abstract:The Izergin-Korepin model with general non-diagonal boundary terms, a typical integrable model beyond A-type and without U(1)-symmetry, is studied via the offdiagonal Bethe ansatz method. Based on some intrinsic properties of the R-matrix and the K-matrices, certain operator product identities of the transfer matrix are obtained at some special points of the spectral parameter. These identities and the asymptotic behaviors of the transfer matrix together allow us to construct the inhomogeneous T − Q relation and the associated Bethe ansatz equations. In the diagonal boundary limit, the reduced results coincide exactly with those obtained via other methods.

Exact spectrum of the spin-s Heisenberg chain with generic non-diagonal boundaries

“…Keeping the very properties (2.13)-(2.15) in mind and following the method developed in [62,63], after a tedious calculation, we find that the spin-(s, s) transfer matrix satisfies the following operator identities, 4…”

“…Subsequently, the nested-version of ODBA for the models associated with su(n) algebra [62], the application to the integrable models beyond A-type [63] and the thermodynamic analysis based on the ODBA solutions [64] were developed. We remark that two other promising methods, namely, the q-Onsager algebra method [65] and the separation of variables (SoV) method [47][48][49][50]66] were also used to approach the spin-1 2 chains with generic integrable boundaries.…”

Exact solution of the alternating XXZ spin chain with generic non-diagonal boundaries

“…Keeping the very property (2.13) and (2.14) in mind and following the method developed in [50,48], we can derive the following relations with the help of QYBE (2.1),…”

“…Recently, a method for solving the eigenvalue problem of integrable models with generic boundary conditions, i.e., the off-diagonal Bethe Ansatz (ODBA) method was proposed in [44] ( [45] for the details) and then several long-standing models [44,46,47] were solved. Subsequently, its applications to integrable models beyond A-type [48] and to the high spin XXX open chain [49] were performed, and the nested-version of ODBA for the models associated with su(n) algebra [50] was developed. In addition, the method for thermodynamic analysis based on the ODBA solutions [51] was also proposed.…”

A representation basis for the quantum integrable spin chain associated with the su(3) algebra

“…Several long-standing models [29,[31][32][33][34][35][36] have since been solved. It should be noted that besides ODBA [37,38] some other methods such as the q-Onsager algebra method [39][40][41][42], the separation of variables (SoV) method [43][44][45][46][47][48][49] and the modified algebraic Bethe ansatz method [50][51][52][53] were also used to obtain the eigenstates of the XXZ spin chains with generic boundary conditions.…”