Heisenberg Symmetry and Collective Modes of One Dimensional Unitary Correlated Fermions

Abstract

The correlated fermionic many-particle system, near infinite scattering length, reveals an underlying Heisenberg symmetry in one dimension, as compared to an $SO(2,1)$ symmetry in two dimensions. This facilitates an exact map from the interacting to the non-interacting system, both with and without a harmonic trap, and explains the short-distance scaling behavior of the wave-function. Taking advantage of the phenomenological Calogero-Sutherland-type interaction, motivated by the density functional approach, we connect the ground-state energy shift, to many-body correlation effect. For the excited states, modes at integral values of the harmonic frequency $\omega$, are predicted in one dimension, in contrast to the breathing modes with frequency $2\omega$ in two dimensions.

5 pages, revamped version for clarity

References in corpus (25)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• Realization of an Excited, Strongly-Correlated Quantum Gas Phase
• Fermi gases in one dimension: From Bethe Ansatz to experiments
• Spin-Imbalance in a One-Dimensional Fermi Gas
• A one-dimensional liquid of fermions with tunable spin
• Nonrelativistic conformal field theories
• From Few to Many: Observing the Formation of a Fermi Sea One Atom at a Time
• The unitary gas in an isotropic harmonic trap: symmetry properties and applications
• Antiferromagnetic Heisenberg Spin Chain of a Few Cold Atoms in a One-Dimensional Trap
• Epsilon expansion for a Fermi gas at infinite scattering length
• Universal properties of a trapped two-component Fermi gas at unitarity
• Density-functional theory for fermions in the unitary regime
• Universality in a 2-component Fermi System at Finite Temperature
• Universal Two-Body Spectra of Ultracold Harmonically Trapped Atoms in Two and Three Dimensions
• Pair condensation in a Finite Trapped Fermi Gas
• Fermionic ground state at unitarity and Haldane Exclusion Statistics
• Universal behavior of a trapped Fermi superfluid in the BCS-unitarity crossover
• Cold Fermi-gas with long range interaction in a harmonic trap
• An explicit realization of fractional statistics in one dimension
• A new effective interaction for the trapped fermi gas: the BEC-BCS crossover