Bethe ansatz solution of the small polaron with nondiagonal boundary terms

Abstract

The small polaron with generic, nondiagonal boundary terms is investigated within the framework of quantum integrability. The fusion hierarchy of the transfer matrices and its

Off-diagonal Bethe ansatz solutions of the anisotropic spin- chains with arbitrary boundary fields

“…3 Some deformed T − Q ansatz for the eigenvalues of the graded XXZ open chain was introduced in [58]. 17) where the functions Q 1 (u) and Q 2 (u) are some trigonometric polynomials parameterized by N Bethe roots {µ j |j = 1, .…”

Modified algebraic Bethe ansatz for XXZ chain on the segment – I: Triangular cases

“…Another recent result is the off-diagonal Bethe ansatz (ODBA), introduced by Cao et al [14], that extends the analytical BA to all models without U (1) symmetry in term of "quite" conventional BE. The main feature consists in adding a new term in the eigenvalues and the BE 5 , see also [30] for 3 the completeness of the spectrum follows from the representation theory of the q-Onsager algebra [5] 4 The Hamiltonian (1.1) is constructed from the homogeneous transfer matrix, thus the SoV does not characterize directly its spectrum. 5 The ODBA allows one to consider different parametrization for the eigenvalues.…”

Small polaron with generic open boundary conditions: Exact solution via the off-diagonal Bethe ansatz

“…We remark that the roots {µ (±) j |j = 1, · · · , N} to the BAEs (4.22) are Grassmann number valued, which implies that the corresponding Q-functions in (4.17) can be expressed as 1 · · · , N}, which resembles those in [13,14].…”

“…Following [5,6], for a given R-matrix, we introduce a pair of K-matrices K − (u) and K + (u). The former satisfies the graded reflection equation 14) and the latter satisfies the dual graded reflection equation…”