Functional renormalization group approach to the BCS-BEC crossover

Abstract

The phase transition to superfluidity and the BCS-BEC crossover for an ultracold gas of fermionic atoms is discussed within a functional renormalization group approach. Non-perturbative flow equations, based on an exact renormalization group equation, describe the scale dependence of the flowing or average action. They interpolate continuously from the microphysics at atomic or molecular distance scales to the macroscopic physics at much larger length scales, as given by the interparticle distance, the correlation length, or the size of the experimental probe. We discuss the phase diagram as a function of the scattering length and the temperature and compute the gap, the correlation length and the scattering length for molecules. Close to the critical temperature, we find the expected universal behavior. Our approach allows for a description of the few-body physics (scattering and molecular binding) and the many-body physics within the same formalism.

30 pages, 13 figures

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• Imbalanced Fermi Gases at Unitarity
• Ultracold atoms and the Functional Renormalization Group
• Algorithmic derivation of functional renormalization group equations and Dyson-Schwinger equations
• Universal Aspects of QCD-like Theories
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• Fermionic two-loop functional renormalization group for correlated fermions: Method and application to the attractive Hubbard model
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• Modeling Finite-Volume Effects and Chiral Symmetry Breaking in Two-Flavor QCD Thermodynamics
• Critical temperature and superfluid gap of the Unitary Fermi Gas from Functional Renormalization
• Renormalization group study of Bose polarons
• Functional renormalization group at finite density and Bose condensation
• Many-flavor Phase Diagram of the (2+1)d Gross-Neveu Model at Finite Temperature
• Imaginary polarization as a way to surmount the sign problem in ab initio calculations of spin-imbalanced Fermi gases
• Mobile impurity in a Fermi sea from the functional renormalization group analytically continued to real time
• Pairing and the spin susceptibility of the polarized unitary Fermi gas in the normal phase
• Tan contact and universal high momentum behavior of the fermion propagator in the BCS-BEC crossover
• Sarma phase in relativistic and non-relativistic systems
• Finite-size and Particle-number Effects in an Ultracold Fermi Gas at Unitarity
• Fermi gases with imaginary mass imbalance and the sign problem in Monte Carlo calculations
• Fermionic Functional Renormalization Group Approach to Superfluid Phase Transition
• Collective excitations of superfluid Fermi gases near the transition temperature
• Phases of spin- and mass-imbalanced ultracold Fermi gases in harmonic traps
• Far-from-equilibrium dynamics of an ultracold Fermi gas
• Efimov physics from the functional renormalization group
• Error estimates and specification parameters for functional renormalization
• Universal behaviour of four-boson systems from a functional renormalisation group
• Dimensional crossover in ultracold Fermi gases from Functional Renormalisation
• Flowing bosonization in the nonperturbative functional renormalization-group approach
• Four-boson bound states from a functional renormalisation group
• Weakly-interacting Bose-Bose mixtures from the functional renormalisation group
• Spectral properties and observables in ultracold Fermi gases
• Flow equation of functional renormalization group for three-body scattering problems
• Fermionic Functional Renormalization Group Approach to Bose-Einstein Condensation of Dimers
• Deconfinement Phase Transition with External Magnetic Field in Friedberg-Lee Model
• Phase transitions in dipolar spin-1 Bose gases
• A lattice pairing-field approach to ultracold Fermi gases
• Superfluidity in multicomponent fermions via the functional renormalization group
• Fluctuation-induced first-order superfluid transition in unitary $\mathrm{SU}(N)$ Fermi gases