Abstract
We study a one-dimensional lattice model of interacting spinless fermions. This model is integrable for both periodic and open boundary conditions; the latter case includes the presence of Grassmann valued non-diagonal boundary fields breaking the bulk U(1) symmetry of the model. Starting from the embedding of this model into a graded Yang–Baxter algebra, an infinite hierarchy of commuting transfer matrices is constructed by means of a fusion procedure. For certain values of the coupling constant related to anisotropies of the underlying vertex model taken at roots of unity, this hierarchy is shown to truncate giving a finite set of functional equations for the spectrum of the transfer matrices. For generic coupling constants, the spectral problem is formulated in terms of a functional (or TQ-)equation which can be solved by Bethe ansatz methods for periodic and diagonal open boundary conditions. Possible approaches for the solution of the model with generic non-diagonal boundary fields are discussed.
Highlights
We study a one-dimensional lattice model of interacting spinless fermions
In a previous publication [26] we have investigated the applicability of Bethe ansatz methods in the simpler case of a model of free fermions with similar open boundary conditions
Given an R-matrix as a solution to the Yang–Baxter equation (YBE) (2.4), the fusion procedure [29,30,31] allows for the construction of larger R-matrices as solutions to the corresponding YBEs, where larger refers to the dimensionality of the auxiliary space involved
Summary
Some materials exhibit a strong electron–phonon coupling that considerably reduces the mobility of electrons within the conduction band This interaction may be regarded as an increase of the electron’s effective mass, giving rise to quasi-particles called polarons. If the electron is essentially trapped at a single lattice site, the corresponding quasi-particle is said to be a small polaron. In this case, electron transport occurs either by thermally activated hopping (at high temperatures) or by tunneling (at low temperatures). It is convenient to define number operators nk ≡ ck†ck = 1 − nk In this context, the parameters t and V may be interpreted as hopping amplitude and density–density interaction strength, respectively
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