Unitary Fermi gas, epsilon expansion, and nonrelativistic conformal field theories

Abstract

We review theoretical aspects of unitary Fermi gas (UFG), which has been realized in ultracold atom experiments. We first introduce the epsilon expansion technique based on a systematic expansion in terms of the dimensionality of space. We apply this technique to compute the thermodynamic quantities, the quasiparticle spectrum, and the critical temperature of UFG. We then discuss consequences of the scale and conformal invariance of UFG. We prove a correspondence between primary operators in nonrelativistic conformal field theories and energy eigenstates in a harmonic potential. We use this correspondence to compute energies of fermions at unitarity in a harmonic potential. The scale and conformal invariance together with the general coordinate invariance constrains the properties of UFG. We show the vanishing bulk viscosities of UFG and derive the low-energy effective Lagrangian for the superfluid UFG. Finally we propose other systems exhibiting the nonrelativistic scaling and conformal symmetries that can be in principle realized in ultracold atom experiments.

44 pages, 15 figures, contribution to Lecture Notes in Physics "BCS-BEC crossover and the Unitary Fermi Gas" edited by W. Zwerger

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• Nonrelativistic conformal field theories
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• Epsilon expansion for a Fermi gas at infinite scattering length
• Scattering in Mixed Dimensions with Ultracold Gases
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• Universal properties of a trapped two-component Fermi gas at unitarity
• Fermi gas near unitarity around four and two spatial dimensions
• Universal Fermi Gas with Two- and Three-Body Resonances
• Causality and universality in low-energy quantum scattering
• Next-to-next-to-leading-order epsilon expansion for a Fermi gas at infinite scattering length
• Induced p-wave superfluidity in two dimensions: Brane world in cold atoms and nonrelativistic defect CFTs
• Confinement-induced Efimov resonances in Fermi-Fermi mixtures
• Universal four-component Fermi gas in one dimension
• Phases of a bilayer Fermi gas

Cited by in corpus (29)

• BCS-BEC Crossover and the Unitary Fermi Gas
• Liberating Efimov physics from three dimensions
• OPE convergence in non-relativistic conformal field theories
• Spontaneously broken boosts and the Goldstone continuum
• Aspects of Non-Relativistic Quantum Field Theories
• Nonrelativistic Conformal Field Theories in the Large Charge Sector
• The Spinful Large Charge Sector of Non-Relativistic CFTs: From Phonons to Vortex Crystals
• Renormalization properties of a Galilean Wess-Zumino model
• On Superconformal Anyons
• Spin Matrix Theory in near $\frac{1}{8}$-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• Universal dimer-dimer scattering in lattice effective field theory
• Nonrelativistic CFTs at Large Charge: Casimir Energy and Logarithmic Enhancements
• Equations of fluid dynamics with the l-conformal Galilei symmetry
• The Operator Product Expansion Beyond Leading Order for Two-Component Fermions
• Supersymmetric Galilean Electrodynamics
• General Freeze-in and Freeze-out
• Hamiltonian formulation for perfect fluid equations with the l-conformal Galilei symmetry
• The Conformal Spectrum of Non-Abelian Anyons
• Triviality of Entanglement Entropy in the Galilean Vacuum
• Viscosity spectral function of a scale invariant non-relativistic fluid from holography
• Three-body contact for fermions. I. General relations
• Perfect fluid dynamics with conformal Newton-Hooke symmetries
• Gapped dilatons in scale invariant superfluids
• Perfect fluid coupled to a solenoidal field which enjoys the l-conformal Galilei symmetry
• N=1,2,3 l-conformal Galilei superalgebras
• The Quantum Origins of Non-Topological Vortices
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory
• Short-distance production of three particles with large scattering length
• Remarks on Galilean electromagnetism