Susceptibility of the one-dimensional, dimerized Hubbard model

TL;DR

This paper demonstrates that the zero-temperature susceptibility of the one-dimensional, dimerized Hubbard model at quarter-filling can be accurately computed using small cluster exact diagonalization, finite-size scaling, and quantum Monte Carlo simulations, providing reliable estimates for real materials.

Contribution

The study introduces a combined numerical approach using exact diagonalization, finite-size scaling, and quantum Monte Carlo to accurately determine susceptibility in the dimerized Hubbard model.

Findings

Finite-size scaling of spin velocity yields accurate susceptibility estimates.

Quantum Monte Carlo captures temperature dependence relevant to real materials.

Results agree with analytical solutions in weak and strong coupling limits.

Abstract

We show that the zero temperature susceptibility of the one-dimensional, dimerized Hubbard model at quarter-filling can be accurately determined on the basis of exact diagonalization of small clusters. The best procedure is to perform a finite-size scaling of the spin velocity $u_\sigma$, and to calculate the susceptibility from the Luttinger liquid relation $\chi=2/\pi u_\sigma$. We show that these results are reliable by comparing them with the analytical results that can be obtained in the weak and strong coupling limits. We have also used quantum Monte Carlo simulations to calculate the temperature dependence of the susceptibility for parameters that should be relevant to the Bechgaard salts. This shows that, used together, these numerical techniques are able to give precise estimates of the low temperature susceptibility of realistic one-dimensional models of correlated electrons.