Quantum antiferromagnetism and high $T_C$ superconductivity: a close connection between the t-J model and the projected BCS Hamiltonian

TL;DR

This paper establishes a strong theoretical and numerical connection between the t-J model and the Gutzwiller-projected BCS Hamiltonian, supporting the idea that the t-J model can exhibit high-temperature superconductivity.

Contribution

It analytically and numerically demonstrates the equivalence of ground states of the t-J model and the projected BCS Hamiltonian, providing evidence for superconductivity in the t-J model.

Findings

Ground state of the t-J model at half filling is equivalent to the projected BCS Hamiltonian ground state.

High wavefunction overlap at moderate doping supports superconductivity in the t-J model.

The relationship between the projected BCS ground state and the resonating valence bond state is discussed.

Abstract

A connection between quantum antiferromagnetism and high $T_C$ superconductivity is theoretically investigated by analyzing the t-J model and its relationships to the Gutzwiller-projected BCS Hamiltonian. After numerical corroboration via exact diagonalization, it is analytically shown that the ground state of the t-J model at half filling (i.e., the 2D antiferromagnetic Heisenberg model) is entirely equivalent to the ground state of the Gutzwiller-projected BCS Hamiltonian with strong pairing. Combined with the high wavefunction overlap between the ground states of the t-J model and the projected BCS Hamiltonian at moderate doping, this equivalence provides strong support for the existence of superconductivity in the t-J model. The relationship between the ground state of the projected BCS Hamiltonian and Anderson's resonating valence bond state (i.e., the projected BCS ground state) is discussed.