Projected BCS Theory for the Unification of Antiferromagnetism and Strongly Correlated Superconductivity

TL;DR

This paper introduces a projected BCS theory that unifies antiferromagnetism and strongly correlated superconductivity, providing accurate trial states for the $t$-$J$ model and a continuous phase diagram across doping levels.

Contribution

The paper presents a novel projected BCS approach that effectively captures both antiferromagnetism and superconductivity in strongly correlated systems, improving upon previous models.

Findings

Accurately models the ground state of the $t$-$J$ model on a square lattice.

Generates a continuous phase diagram as a function of hole doping.

Outperforms the resonating valence bond state in trial accuracy.

Abstract

The intimate connection between antiferromagnetism and superconductivity is at the core of high-temperature superconductivity. Here, we put forward the projected BCS theory for the unification of antiferromagnetism at half filling and strongly correlated superconductivity at moderate doping. Specifically, it is shown that the projected BCS theory provides excellent trial states for the exact ground states of the $t$-$J$ model in the square lattice, generating the unified phase diagram as a continuous function of hole concentration. Precisely capturing antiferromagnetism at half filling, which is ultimately a consequence of the strong correlation between Cooper pairs, the projected BCS theory is able to produce better trial states for strongly correlated superconductivity at moderate doping than the resonating valence bond state. Finally, we discuss various ramifications of the projected BCS theory.