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SUMMARY:Strong-coupling ansatz for the one-dimensional Fermi gas in a harm
 onic potential - Jesper F. Levinsen\, Aarhus Institute of Advanced Studies
 \, Aarhus University\, Denmark
DTSTART:20141023T131500Z
DTEND:20141023T141500Z
UID:TALK54148@talks.cam.ac.uk
CONTACT:Dr G Moller
DESCRIPTION:The one-dimensional (1D) Fermi gas with repulsive short-range 
 interactions provides an important model of strong correlations and is oft
 en amenable to exact methods. However\, in the presence of confinement\, n
 o exact solution is known for an arbitrary number of strongly interacting 
 fermions. Here\, we propose a novel ansatz for generating the lowest-energ
 y wavefunctions of the repulsive 1D Fermi gas in a harmonic potential near
  the Tonks-Girardeau (TG) limit of infinite interactions. We specialize to
  the case of a single impurity interacting with N majority particles\, whe
 re we may derive analytic forms of the approximate wavefunctions. Comparin
 g with exact numerics\, we show that the overlap between the wavefunctions
  from our ansatz and the exact ones in the ground-state manifold exceeds 0
 .9997 for N up to 8. Moreover\, the overlap for the ground-state wavefunct
 ion extrapolates to 0.9999 as N goes to infinity. Thus our ansatz is essen
 tially indistinguishable from numerically exact results in both the few- a
 nd many-body limits. We derive an effective Heisenberg spin-chain model fo
 r the regime near the TG limit\, within which our ansatz is exact. The ene
 rgy of states in excited manifolds is calculated using a dynamical SO(2\,1
 ) symmetry\, which provides an exact relation between states related by a 
 scaling transformation. We finally show how our results for the wavefuncti
 ons and the energy spectrum can be detected in cold atomic gases via colle
 ctive-mode\, tunneling\, and radio-frequency experiments.\n\nReference: J.
  Levinsen\, P. Massignan\, G. M. Bruun\, and M. M. Parish\, arXiv:1408.709
 6
LOCATION:TCM Seminar Room\, Cavendish Laboratory
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