Thermodynamics of Non-Relativistic Scattering Theory

TL;DR

This paper applies thermodynamic Bethe ansatz to analyze the low-energy excitations of the 1D Hubbard model, revealing how holons and spinons contribute to the model's thermodynamics and conformal properties.

Contribution

It provides a detailed thermodynamic analysis of the Hubbard model's excitations using $S$-matrices, clarifying the IR and UV limits and the role of massless and massive modes.

Findings

Central charge c=1 in IR limit due to massless holons

Central charge vanishes in UV limit, massive modes decouple

Results align with lattice Bethe ansatz computations

Abstract

We use thermodynamic Bethe ansatz to study nonrelativistic scattering theory of low energy excitations of 1D Hubbard model, using the $S$-matrices proposed by E\ss ler and Korepin. This model can be described by two types of excitation states, holons and spinons, as asymptotic states. In the attractive regime, the spinon is massive while the holon is massless. The situation is reversed with a repulsive coupling. We derive that the central charge of the Hubbard model in the IR limit is $c=1$ while it vanishes in the UV limit. The contribution is due to the massless degree of freedom, i.e. the holon for the attractive regime, 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.