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• W1978580947 abstract "We study the two-dimensional attractive Hubbard model using the mapping onto the half-filled repulsive Hubbard model in a uniform magnetic field coupled to the fermion spins. The low-energy effective action for charge and pairing fluctuations is obtained in the hydrodynamic regime. We recover the action of a Bose superfluid where half the fermion density is identified as the conjugate variable of the phase of the superconducting order parameter. By integrating out charge fluctuations, we obtain a phase-only action. In the zero-temperature superconducting state, this action describes a collective phase mode smoothly evolving from the Anderson-Bogoliubov mode at weak coupling to the Bogoliubov mode of a Bose superfluid at strong coupling. At finite temperature, the phase-only action can be used to extract an effective $XY$ model and thus obtain the Berezinskii-Kosterlitz-Thouless (BKT) phase transition temperature. We also identify a renormalized classical regime of superconducting fluctuations above the BKT phase transition, and a regime of incoherent pairs at higher temperature. Special care is devoted to the nearly half-filled case where the symmetry of the order parameter is enlarged to SO(3) due to strong $mathbf{q}=(ensuremath{pi},ensuremath{pi})$ charge fluctuations. The low-energy effective action is then an SO(3) nonlinear $ensuremath{sigma}$ model with a (symmetry breaking) magnetic field proportional to the doping. In the strong-coupling limit, the attractive Hubbard model can be mapped onto the Heisenberg model in a magnetic field, which reduces to the quantum $XY$ model (except for a weak magnetic field, i.e., in the low-density limit of the attractive model). In the low-density limit, the Heisenberg model allows one to recover the action of a Bose superfluid, including the ${(mathbf{ensuremath{nabla}}ensuremath{rho})}^{2}$ term (with $ensuremath{rho}$ the density), and in turn the Gross-Pitaevskii equation." @default.
• W1978580947 created "2016-06-24" @default.
• W1978580947 creator A5078731679 @default.
• W1978580947 date "2004-10-13" @default.
• W1978580947 modified "2023-09-24" @default.
• W1978580947 title "Berezinskii-Kosterlitz-Thouless transition and BCS-Bose crossover in the two-dimensional attractive Hubbard model" @default.
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• W1978580947 doi "https://doi.org/10.1103/physrevb.70.134502" @default.
• W1978580947 hasPublicationYear "2004" @default.
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