Theoretical Evidence for Equivalence between the Ground States of the Strong-Coupling BCS Hamiltonian and the Antiferromagnetic Heisenberg Model

TL;DR

This paper provides theoretical evidence that, in the strong-coupling limit, the ground state of the Gutzwiller-projected BCS Hamiltonian is equivalent to that of the 2D antiferromagnetic Heisenberg model, linking superconductivity and magnetism.

Contribution

It demonstrates the equivalence of ground states between the Gutzwiller-projected BCS Hamiltonian and the Heisenberg model in the strong-coupling limit through exact diagonalization.

Findings

High wavefunction overlap in the strong-coupling limit

Adiabatic connection to the t-J model at moderate doping

Ground state equivalence in the strong-coupling regime

Abstract

By explicitly computing wavefunction overlap via exact diagonalization in finite systems, we provide evidence indicating that, in the limit of strong coupling, i.e., $\Delta/t \to \infty$, the ground state of the Gutzwiller-projected BCS Hamiltonian (accompanied by proper particle-number projection) is identical to the exact ground state of the 2D antiferromagnetic Heisenberg model on the square lattice. This identity is adiabatically connected to a very high overlap between the ground states of the projected BCS Hamiltonian and the t-J model at moderate doping.