Spin polarons in the t-J model in an unconstrained representation

TL;DR

This paper introduces a new fermion-boson representation for the t-J model, enabling more accurate analysis of spin polarons and holes in antiferromagnetic systems, with results validated against numerical data.

Contribution

It presents a novel unconstrained fermion-boson representation of the t-J model and demonstrates improved agreement with numerical data for single and two-hole problems.

Findings

Better agreement with numerical data than previous slave-fermion approaches

Effective model includes additional hole dispersion from quantum spin fluctuations

Successful numerical analysis of the two-hole problem using Bethe-Salpeter equation

Abstract

The report discusses the slave-fermion representations of the t-J model and describes another representation, in which fermions and bosons are completely commuting and in which the properties of fermions are directly related to the properties of physical holes. For a study of the system in the new representation at half-filling, interaction of fermions with two magnons is treated in mean-field theory. The obtained effective model, in comparison to that of the usual slave-fermion representation, has an additional bare hole dispersion due to the hole moving by using quantum spin fluctuations present in the undoped antiferromagnetic ground state. The single-hole Green's function at half-filling is then found numerically using the self-consistent Born approximation. For all studied quantities good or excellent agreement with numerical data is observed in the entire parameter range, noticeably better than in the studies with the slave-fermion representation. Using the same effective model, the two-hole problem is also studied by solving numerically the Bethe-Salpeter equation with noncrossing diagrams.