Formation of clusters in the two dimensional t-J model: The mechanism for phase separation

TL;DR

This paper investigates phase separation in the 2D t-J model using a variational cluster approach, revealing how hole clusters form and evolve with coupling strength, contributing to understanding the mechanism behind phase separation.

Contribution

It introduces a variational product ansatz with two cluster types to analyze phase separation in the 2D t-J model, highlighting the role of hole clusters and their charge properties.

Findings

Hole clusters carry even charge and zero total spin for moderate coupling.

Increasing coupling reduces the charge of hole clusters.

The approach provides insights into the boundary of phase separation in parameter space.

Abstract

The emergence of phase separation is investigated in the framework of a 2D t-J model by means of a variational product ansatz, which covers the infinite lattice by two types of L x L clusters. Clusters of the first type are completely occupied with electrons, i.e. they carry maximal charge Q_e=L^2 and total spin 0, and thereby form the antiferromagnetic background. Holes occur in the second type of clusters -- called ``hole clusters''. They carry a charge Q_h<L^2. The charge Q_h and the number N(Q_h) of hole clusters is fixed by minimizing the total energy at given hole density and spin exchange coupling \alpha=J/t. For \alpha not too small (\alpha>0.5) it turns out that hole clusters are occupied with an even number Q_h<L^2 of electrons and carry a total spin 0. For increasing \alpha the charge Q_h(\alpha) of the hole clusters decreases.Some points on the boundary curve can be extracted from Q_h(\alpha).