One-band Hubbard model with hopping asymmetry and the effective theory at finite U: Phase diagram and metal-insulator transition

TL;DR

This paper investigates the phase diagram and metal-insulator transition in the one-band Hubbard model with hopping asymmetry at finite U, using variational Monte Carlo methods and effective theory up to second order.

Contribution

It introduces a detailed analysis of the phase diagram and metal-insulator transition in the asymmetric Hubbard model at finite U, incorporating an effective model and variational wave functions.

Findings

Metal-insulator transition occurs when hopping parameter tmix vanishes.

Effective model shows a clear metal-insulator transition at finite tmix.

Large U favors AF-RVB wave function; small U favors RVB wave function.

Abstract

We study the one-band Hubbard model at half filling with hopping asymmetry and its effective model at finite but large U up to the second order of tmix/U. Two variational wave functions, the resonating valence bond (RVB) wave function and antiferromagnetic (AF) RVB coexisted wave function, are studied by variational Monte Carlo method on L*L square lattices up to L=12. Based on these two wave functions, the phase diagrams for both models are presented. For the Hubbard model, we find that there is a metal-insulator transition when the hopping parameter tmix which changes the local double occupant vanishes while only a metal-insulator crossover is explored for any finite tmix. For the effective model in which the perturbation expansion is up to the second order of tmix/U, a clear metal-insulator transition can be identified for both variational wave functions and the phase diagram can be drawn accordingly. In both models, we find that the systems are dominated by AF-RVB wave function when U is large while the RVB wave function is favored when U is small.