Green's Function Monte Carlo for Lattice Fermions: Application to the t-J Model

TL;DR

This paper introduces a Green's Function Monte Carlo method for studying the zero-temperature properties of strongly correlated electron models on large lattices, specifically applied to the two-dimensional t-J model, revealing persistent phase separation across interaction strengths.

Contribution

The paper develops a novel numerical approach resembling Green's Function Monte Carlo that accurately determines phase diagrams and minimizes finite-size effects in lattice fermion models.

Findings

Finite-size effects are small with fixed electron numbers at closed-shells.

A phase-separated state exists above a certain electron density for all interaction strengths.

Results support phase separation in the t-J model across all tested interaction parameters.

Abstract

We develop a general numerical method to study the zero temperature properties of strongly correlated electron models on large lattices. The technique, which resembles Green's Function Monte Carlo, projects the ground state component from a trial wave function with no approximations. We use this method to determine the phase diagram of the two-dimensional t-J model, using the Maxwell construction to investigate electronic phase separation. The shell effects of fermions on finite-sized periodic lattices are minimized by keeping the number of electrons fixed at a closed-shell configuration and varying the size of the lattice. Results obtained for various electron numbers corresponding to different closed-shells indicate that the finite-size effects in our calculation are small. For any value of interaction strength, we find that there is always a value of the electron density above which the system can lower its energy by forming a two-component phase separated state. Our results are compared with other calculations on the t-J model. We find that the most accurate results are consistent with phase separation at all interaction strengths.