We consider states of BCS form in the 2D Hubbard model which, starting from some arbitrary point in state space in the neighborhood of a Hartree-Fock ground state, are relaxed within that BCS ansatz to local minima of the energy. As in the Hartree-Fock approximation there are a vast number of local minima, nearly degenerate in energy. What is new, and unlike the conventional Hartree-Fock states, is that there is a region in parameter space where these local minima are clearly associated with d-wave condensates of the form $d_{x^2-y^2}$ in the underdoped region. There are also indications of $d_{xy}$ condensation in the overdoped region, at least in this approximation to the 2D Hubbard model, as well as condensates over a range of parameters on triangular lattices.We consider states of BCS form in the 2D Hubbard model which, starting from some arbitrary point in state space in the neighborhood of a Hartree-Fock ground state, are relaxed within that BCS ansatz to local minima of the energy. As in the Hartree-Fock approximation there are a vast number of local minima, nearly degenerate in energy. What is new, and unlike the conventional Hartree-Fock states, is that there is a region in parameter space where these local minima are clearly associated with d-wave condensates of the form $d_{x^2-y^2}$ in the underdoped region. There are also indications of $d_{xy}$ condensation in the overdoped region, at least in this approximation to the 2D Hubbard model, as well as condensates over a range of parameters on triangular lattices.

arXiv:2507.01280Jul 2, 20250 citations

d_{x^2-y^2}

in the underdoped region. There are also indications of

d_{xy}

condensation in the overdoped region, at least in this approximation to the 2D Hubbard model, as well as condensates over a range of parameters on triangular lattices.