Yang–Baxter equation-based potential model for a one-dimensional fermion system

Abstract

We propose a velocity-dependent δ-function potential model for a one-dimensional fermion system, under which the two-particle interchange operators in the Bethe hypothesis satisfy the Yang–Baxter equation. This model, proportional to the product of the momenta of two interacting particles, is not translation invariant. It is found that the ground-state particle distribution densities become negative in the low momentum region. To resolve the controversy, we apply an overall momentum shift to the system, and obtain reasonable solutions. The dependence of the ground-state distributions on the momentum shift is discussed.