Large physical spin approach for strongly correlated electrons

TL;DR

This paper introduces a large-spin expansion method for the $t$-$J$ model that avoids the no-double-occupancy constraint, enabling accurate analysis of strongly correlated electrons and their excitations.

Contribution

The authors develop a systematic large-spin expansion approach for the $t$-$J$ Hamiltonian that maintains exact correspondence with physical excitations, improving analysis of strongly correlated systems.

Findings

Quasiparticle weight varies with momentum as $t/J$ increases.

Method agrees well with exact diagonalization results.

Smooth dependence of physical quantities on $1/s$ expansion parameter.

Abstract

We present a novel approach for a systematic large--spin expansion of the $t$-$J$ Hamiltonian which enables us to work without the constraint of no double occupancy. In our scheme we can perform the large--spin limit ensuring that the low energy spin excitations are in {\em exact} correspondence with the physical excitations of the $s={1\over2}$ Hilbert space. As a consequence, we expect a smooth dependence of the physical quantities on the expansion parameter $1/ s$. As a first application of the method we study the case of a single hole in a N\'eel background. A systematic expansion in fluctuations about this stable solution indicates that by increasing $t/J$ the quasiparticle weight strongly depends on the momentum carried by the hole. Results, obtained on small lattice sizes, are found in excellent agreement with exact diagonalization data.