Thermodynamics of non-relativistic scattering theory

We use the thermodynamic Bethe ansatz to study the nonrelativistic scattering theory of low-energy excitations of the 1D Hubbard model using the S-matrices proposed by EBler and Korepin. This model can be described by two types of excitation states, holons and spinons, as asymptotic states. In the attractive region, the spinon is massive while the holon is massless. The situation is reversed with a repulsive coupling. We show that the central charge of the Hubbard model in the IR limit is c = 1 due to the massless degree of freedom, i.e., the holon for the attractive region, and the massive mode decouples completely. This result is consistent with various known results based on lattice Bethe ansatz computations. Our results make it possible to use the S-matrices of the excitations to compute more interesting quantities like correlation functions.