Low-energy effective representation of the Gutzwiller-projected BCS Hamiltonian close to half filling

TL;DR

This paper analytically explores the connection between the Gutzwiller-projected BCS Hamiltonian and the t-J model, showing that near half filling it exhibits antiferromagnetic order and at moderate doping resembles the resonating valence bond state, capturing key low-energy physics.

Contribution

It demonstrates that the Gutzwiller-projected BCS Hamiltonian naturally reproduces antiferromagnetism near half filling and the RVB state at moderate doping, linking these phenomena to the t-J model.

Findings

Near half filling, the model develops antiferromagnetic order.

At moderate doping, the ground state resembles the RVB state.

The projected BCS Hamiltonian captures the low-energy physics of the t-J model.

Abstract

We investigate analytically a connection between the t-J model and the strongly correlated Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, with the effect of strong electron correlations accounted by the Gutzwiller projection. We show that in the immediate vicinity of half filling the projected 2D BCS Hamiltonian with strong pairing develops an antiferromagnetically (AF) ordered ground state. This result explicitly demonstrates that antiferromagnetism in this model appears as a natural consequence of the strong Coulomb repulsion in a low doped regime. At moderate doping the ground state of the Gutzwiller-projected BCS Hamiltonian becomes qualitatively similar to Anderson's resonating valence bond state which is known to fit nicely the properties of the t-J model in this regime. These two properties taken together indicate that the projected BCS Hamiltonian captures the essential low-energy physics of the t-J model in the whole underdoped region.