BCS states and D-wave condensates in the 2D Hubbard model

2025/07/02 by Kazue Matsuyama, Jeff Greensite, Matsuyama, Kazue +1
Mathematics · Computer Science · #Spectral Theory in Mathematical Physics #Quantum Information and Cryptography #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2507.01280

Abstract

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_x²-y² 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.

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