On Non-Relativistic Conformal Field Theory and Trapped Atoms: Virial Theorems and the State-Operator Correspondence in Three Dimensions
arXiv:0712.0867 · doi:10.1103/PhysRevA.78.013614
Abstract
The field theory of nonrelativistic fermions interacting via contact interactions can be used to calculate the properties of few-body systems of cold atoms confined in harmonic traps. The state-operator correspondence of Non-Relativistic Conformal Field Theory (NRCFT) shows that the energy eigenvalues (in oscillator units) of N harmonically trapped fermions can be calculated from the scaling dimensions of N-fermion operators in the NRCFT. They are also in one-to-one correspondence with zero-energy, scale-invariant solutions to the N-body problem in free space. We show that these two mappings of the trapped fermion problem to free space problems are related by an automorphism of the SL(2,R) algebra of the conformal symmetry of fermions at the unitary limit. This automorphism exchanges the internal Hamiltonian of the gas with the trapping potential and hence provides a novel method for deriving virial theorems for trapped Fermi gases at the unitary limit. We also show that the state-operator correspondence can be applied directly in three spatial dimensions by calculating the scaling dimensions of two- and three-fermion operators and finding agreement with known exact results for energy levels of two and three trapped fermions at the unitary limit.
arXiv comment23 pages, 3 .ps figures
References in corpus (30)
- Quantum computation with trapped polar molecules
- Observation of a Strongly-Interacting Degenerate Fermi Gas of Atoms
- Entanglement of atoms via cold controlled collisions
- Creation of ultracold molecules from a Fermi gas of atoms
- A New Expansion for Nucleon-Nucleon Interactions
- Quantum Logic Gates in Optical Lattices
- Renormalization of the Three-Body System with Short-Range Interactions
- Nonrelativistic conformal field theories
- Measurement of interaction energy near a Feshbach resonance in a 6Li Fermi gas
- Ultracold heteronuclear molecules in a 3D optical lattice
- Molecules of Fermionic Atoms in an Optical Lattice
- The unitary gas in an isotropic harmonic trap: symmetry properties and applications
- Nucleon-Deuteron Scattering from an Effective Field Theory
- Epsilon expansion for a Fermi gas at infinite scattering length
- Self-consistent model of ultracold atomic collisions and Feshbach resonances in tight harmonic traps
- Virial Theorem and Universality in a Unitary Fermi Gas
- Long-lived Feshbach molecules in a 3D optical lattice
- Rearranging Pionless Effective Field Theory
- Conformal Invariance for Non-Relativistic Field Theory
- Analytical solutions for the dynamics of two trapped interacting ultracold atoms
- Preparation of a quantum state with one molecule at each site of an optical lattice
- Fermi gas near unitarity around four and two spatial dimensions
- Pseudopotential method for higher partial wave scattering
- Effective Theory for Trapped Few-Fermion Systems
- Higher Partial Waves in an Effective Field Theory Approach to nd Scattering
- The few-body problem for trapped bosons with large scattering length
- Generalized Pseudopotentials for Higher Partial Wave Scattering
- Density-functional theory for fermions in the unitary regime
- Quantum Logic for Trapped Atoms via Molecular Hyperfine Interactions
- Density functional theory for fermions close to the unitary regime
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- Gravity duals for non-relativistic CFTs
- On the spectrum of nonrelativistic AdS/CFT
- Quantum anomaly, universal relations, and breathing mode of a two-dimensional Fermi gas
- Lattice methods for strongly interacting many-body systems
- An effective field theory approach to two trapped particles
- Nucleon-Nucleon Scattering in a Harmonic Potential
- Three and Four Harmonically Trapped Particles in an Effective Field Theory Framework
- Induced p-wave superfluidity in two dimensions: Brane world in cold atoms and nonrelativistic defect CFTs
- Remark on quantum mechanics with conformal Galilean symmetry
- Two and Three Nucleons in a Trap and the Continuum Limit
- Illustration of universal relations for trapped four-fermion system with arbitrary s-wave scattering length
- Remark on quantum mechanics with N=2 Schrodinger supersymmetry
- OPE convergence in non-relativistic conformal field theories
- Ground-state energy of the unitary Fermi gas from the epsilon expansion
- Effective interactions and operators in no-core shell model
- Three-body contact for fermions. I. General relations
- Numerical study of unitary fermions in one spatial dimension
- Conformal Symmetry in nuclear structure
- Contact interactions, self-adjoint extensions, and low-energy scattering