Integrability of the spin-1/2 fermions with charge pairing and Hubbard interaction

TL;DR

This paper presents an exact solution for a one-dimensional spin-1/2 electron model with triplet pairing and Hubbard interaction, revealing integrability and detailed spectral properties through Bethe ansatz and classical statistical mechanics connections.

Contribution

It introduces a Bethe ansatz solution for a novel spin-1/2 fermion model with charge pairing and Hubbard interaction, including a mapping to an imaginary hopping Hubbard chain.

Findings

Spectrum analyzed via exact diagonalization and Bethe equations

Charge gap converges for even and odd lattice sizes

Finite-size spin excitation corrections match the Heisenberg model

Abstract

In this paper we study the exact solution of a one-dimensional model of spin-$\frac{1}{2}$ electrons composed by a nearest-neighbor triplet pairing term and the on-site Hubbard interaction. We argue that this model admits a Bethe ansatz solution through a mapping to a Hubbard chain with imaginary kinetic hopping terms. The Bethe equations are similar to that found by Lieb and Wu \cite{LW} but with additional twist phases which are dependent on the ring size. We have studied the spectrum of the model with repulsive interaction by exact diagonalization and through the Bethe equations for large lattice sizes. One feature of the model is that it is possible to define the charge gap for even and odd lattice sites and both converge to the same value in the infinite size limit. We analyze the finite-size corrections to the low-lying spin excitations and argue that they are equivalent to that of the spin-$\frac{1}{2}$ isotropic Heisenberg model with a boundary twist depending on the lattice parity. We present the classical statistical mechanics model whose transfer matrix commutes with the model Hamiltonian. To this end we have used the construction employed by Shastry \cite{SHA1,SHA2} for the Hubbard model. In our case, however, the building block is a free-fermion eight-vertex model with a particular null weight.