Thermodynamics, spin-charge separation and correlation functions of spin-1/2 fermions with repulsive interaction

TL;DR

This paper analyzes the thermodynamics and correlation functions of one-dimensional spin-1/2 fermions with strong repulsive interactions, revealing spin-charge separation and critical behavior using exact methods.

Contribution

It provides the first detailed derivation of low-temperature thermodynamics and correlation functions for this model in a magnetic field, including explicit formulas near critical points.

Findings

Exact thermodynamics in weak magnetic fields derived

Correlation functions' asymptotics and critical exponents obtained

Conformal dimensions calculated for specific correlation functions

Abstract

We investigate the low temperature thermodynamics and correlation functions of one-dimensional spin-1/2 fermions with strong repulsion in an external magnetic field via the thermodynamic Bethe ansatz method. The exact thermodynamics of the model in a weak magnetic field is derived with the help of Wiener-Hopf techniques. It turns out that the low energy physics can be described by spin-charge separated conformal field theories of an effective Tomonaga-Luttinger liquid and an antiferromagnetic SU(2) Heisenberg spin chain. However, these two types of conformally invariant low-lying excitations may break down as excitations take place far away from the Fermi points. The long distance asymptotics of the correlation functions and the critical exponents for the model in the presence of a magnetic field at zero temperature are derived in detail by solving dressed charge equations and by conformal mapping. Furthermore, we calculate the conformal dimensions for particular cases of correlation functions. The leading terms of these correlation functions are given explicitly for a weak magnetic field $H\ll 1$ and for a magnetic field close to the critical field $H\rightarrow H_{c}$. Our analytical results provide insights into universal thermodynamics and criticality in one-dimensional many-body physics.