Berezinskii-Kosterlitz-Thouless transition and BCS-Bose crossover in the two-dimensional attractive Hubbard model

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 $\mathbf{q}=(\pi ,\pi )$ charge fluctuations. The low-energy effective action is then an SO(3) non-linear 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, from which we recover the Gross-Pitaevskii equation in the low-density limit.

31 pages, 12 figures, RevTex4; (v2) changes following referees' comments, references added

References in corpus (26)

• Observation of resonance condensation of fermionic atom pairs
• Observation of Bose-Einstein Condensation of Molecules
• Evidence for Superfluidity in a Resonantly Interacting Fermi Gas
• Non-perturbative many-body approach to the Hubbard model and single-particle pseudogap
• Phase Fluctuations and Pseudogap Phenomena
• From the Bogoliubov-de Gennes equations for superfluid fermions to the Gross-Pitaevskii equation for condensed bosons
• Effective Actions and Phase Fluctuations in d-wave Superconductors
• Effective Lagrangians for BCS Superconductors at T=0
• Nonperturbative XY-model approach to strong coupling superconductivity in two and three dimensions
• Ginzburg-Landau theory of superconductors with short coherence length
• Effective action for Superconductors and BCS-Bose crossover
• Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: a non-linear sigma model approach
• Quantum Phase Transitions and Conserved Charges
• The low-energy phase-only action in a superconductor: a comparison with the XY model
• From Cooper Pairs to Composite Bosons: A Generalized RPA Analysis of Collective Excitations
• Pairing fluctuations and pseudogaps in the attractive Hubbard model
• Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: Slater vs Mott-Heisenberg
• Finite Temperature Time-Dependent Effective Theory for the Phase Field in two-dimensional d-wave Neutral Superconductor
• Coherence length in superconductors from weak to strong coupling
• Role of symmetry and dimension on pseudogap phenomena
• Finite Temperature Time-Dependent Effective Theory For The Goldstone Field In A BCS-Type Superfluid
• Dynamics of T=0 BCS condensates
• Nonlinear Schrödinger Equation for Superconductors
• Phase Fluctuations and Single Fermion Spectral Density in 2D Systems with Attraction
• Quantum Phase Fluctuations Responsible for Pseudogap
• Time-dependent Gross-Pitaevskii equation for composite bosons as the strong-coupling limit of the fermionic BCS-RPA approximation

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• Quantum Geometric Contributions to the BKT Transition: Beyond Mean Field Theory
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• Strong coupling s-wave superconductors in the extreme Pauli limit: I.The breached pair and metastable FFLO phases
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• Hidden fermionic excitation in the superconductivity of the strongly attractive Hubbard model
• A real space auxiliary field approach to the BCS-BEC crossover
• The effect of amplitude fluctuations on the BKT transition
• Fermionic Superfluid from a Bilayer Band Insulator in an Optical Lattice
• Pair condensation in the BCS-BEC crossover of ultracold atoms loaded onto a 2D square lattice
• Thermal transitions, pseudogap behavior and BCS-BEC crossover in Fermi-Fermi mixtures
• Evolution of pairing from weak to strong coupling on a honeycomb lattice
• Effective action for superfluid Fermi systems in the strong-coupling limit
• Effective Hamiltonian based Monte Carlo for the BCS to BEC crossover in the attractive Hubbard model
• Electron-hole superfluidity controlled by a periodic potential
• Probing phase coherence via density of states for strongly correlated excitons
• Strongly fluctuating fermionic superfluid in attractive π-flux Hubbard model
• Comment on ``Universal Spin-Flip Transition in Itinerant Antiferromagnets"
• The attractive Hubbard model as an $SO(3)$ system of competing phases: supersolid order and its thermal melting