# Quantum antiferromagnetism and high $T\_C$ superconductivity: a close connection between the t-J model and the projected BCS Hamiltonian

Source: [Quantum antiferromagnetism and high $T\_C$ superconductivity: a close connection between the t-J model and the projected BCS Hamiltonian](<https://www.sota2.com/research/paper/68fa20397a2b558e2932f867>)

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Data updated: 2025-10-23T21:16:51.469Z

Authors: K. Park

Published: 2005-08-15T20:04:26.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0508357>)

[PDF](<https://arxiv.org/pdf/cond-mat/0508357.pdf>)