Lax pair formulation for a small-polaron chain with integrable boundaries

Recently, there has been renewed interest in integrable boundary systems [1, 2] due to their connection to the Kondo problem [3] and boundary conformal field theory [4] in low-dimensional quantum many-body systems. Sklyanin [5] proposed a systematic approach to construct and solve integrable quantum spin systems with open boundary conditions (BC). Central to his method is the introduction of the so-called reflection equations (RE), which are the boundary analogues of the Yang-Baxter equations (YBE) [6]. For integrable fermion systems, in particular models of strongly correlated electrons, graded versions of the YBE and the RE [7] have been applied. However, solutions to the graded RE have so far been found only for certain models due to the mathematical complexity of the graded RE. An alternative method to Sklyanin’s approach is the Lax pair formulation for integrable quantum systems with open BC [8]. In this article, we use the Lax pair formulation to construct an integrable model of correlated fermions with general BC. The Lax pair and the boundary supermatrices K± are given explicitly.