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Physica C Superconductivity

Phase diagram and BCS–Bose condensation crossover in 1D and 2D Hubbard models

ARMEN N. KOCHARIAN, Chia‐Wei Yang, Y. L. Chiang

Published Nov 1, 2001• 3 citations
Publisher
DOI
10.1016/s0921-4534(01)00730-4

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[[abstract]]The ground-state energy, the concentration of double occupied sites and the density of bound electron pairs in low-dimensional attractive Hubbard model are calculated by means of the generalized self-consistent field (GSCF) approach. This approach gives an excellent agreement with the corresponding Bethe-ansatz solution and the quantum Monte-Carlo calculations in a wide range of interaction strength U < 0 and electron concentration n. A simple relationship is found between the order parameter and the density of bound electron pairs, valid for any dimension and in entire parameter space U, n and magnetic field h. The electron pairing and the crossover from the itinerant BCS regime into the Bose condensation regime of local pairs are studied in dependence of both U and n. The GSCF theory correctly displays the separation of the energy gap from the BCS order parameter at n not equal 1 as \U \ increases. (C) 2001 Elsevier Science B.V. All rights reserved.
We predict the existence of self-trapping, stable, moving solitons and breathers of Fermi wave packets along the Bose-Einstein condensation (BEC)-BCS crossover in one dimension (1D), 2D, and 3D optical lattices. The dynamical phase diagrams for self-trapping, solitons, and breathers of the Fermi matter waves along the BEC-BCS crossover are presented analytically and verified numerically by directly solving a discrete nonlinear Schrödinger equation. We find that the phase diagrams vary greatly along the BEC-BCS crossover; the dynamics of Fermi wave packet are different from that of Bose wave packet.