Correlation length of the 1D Hubbard Model at half-filling : equal-time one-particle Green's function

TL;DR

This paper computes the correlation length of the equal-time one-particle Green's function in the half-filled 1D Hubbard model at finite temperature using a fermionic quantum transfer matrix approach, confirming a conjecture at zero temperature.

Contribution

It introduces a fermionic formulation of the quantum transfer matrix for the Hubbard model and provides accurate numerical data for the correlation length at low temperatures.

Findings

Correlation length remains finite at T=0 due to charge gap.

Numerical data confirms the conjectured analytic expression for T=0.

Oscillations in Green's function reflect Fermi momentum at half-filling.

Abstract

The asymptotics of the equal-time one-particle Green's function for the half-filled one-dimensional Hubbard model is studied at finite temperature. We calculate its correlation length by evaluating the largest and the second largest eigenvalues of the Quantum Transfer Matrix (QTM). In order to allow for the genuinely fermionic nature of the one-particle Green's function, we employ the fermionic formulation of the QTM based on the fermionic R-operator of the Hubbard model. The purely imaginary value of the second largest eigenvalue reflects the k_F (= pi/2) oscillations of the one-particle Green's function at half-filling. By solving numerically the Bethe Ansatz equations with Trotter numbers up to N=10240, we obtain accurate data for the correlation length at finite temperatures down into the very low temperature region. The correlation length remains finite even at T=0 due to the existence of the charge gap. Our numerical data confirm Stafford and Millis' conjecture regarding an analytic expression for the correlation length at T=0.