# Generalization of Lieb-Wu wave function inspired by one-dimensional ionic Hubbard model

## TL;DR

This paper generalizes the Lieb-Wu wave function inspired by the ionic Hubbard model, providing a new analytical approach that is valid in certain regimes and useful for cold atom experiments.

## Contribution

It introduces a generalized Bethe ansatz wave function incorporating an ionic parameter, extending the Lieb-Wu solution to the ionic Hubbard model.

## Key findings

- The generalized wave function reduces to Lieb-Wu in the limit of zero ionic parameter.
- The two-particle scattering matrix satisfies the Yang-Baxter equation.
- Numerical solutions of the generalized Bethe equations yield ground state energies in the thermodynamic limit.

## Abstract

With the ionic Hubbard model (IHM) in mind, we construct a non-trivial generalization of the Bethe ansatz (BA) wave function which naturally generalizes the Lieb-Wu wave function with an ionic parameter $\Delta$, and reduces to Lieb-Wu solution in the limit $\Delta\to 0$. The resulting two-particle scattering matrix satisfies the Yang-Baxter equation. To the extent that the unit cells with more than two electrons (Choy-Haldane issue) are avoided on average, our wave function represents an effective soluiton for the one-dimensional IHM. The Choy-Haldane issue restricts the validity of our solution to low-filling and large $U\gtrsim 4$. This regime is attainable in cold atom realizations of the IHM. For this regime, we numerically solve the generalized Bethe equations and compute the ground state energy in the thermodynamic limit.