BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Theory of Condensed Matter
SUMMARY:Strong-coupling ansatz for the one-dimensional Fer
mi gas in a harmonic potential - Jesper F. Levinse
n\, Aarhus Institute of Advanced Studies\, Aarhus
University\, Denmark
DTSTART;TZID=Europe/London:20141023T141500
DTEND;TZID=Europe/London:20141023T151500
UID:TALK54148AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/54148
DESCRIPTION:The one-dimensional (1D) Fermi gas with repulsive
short-range interactions provides an important mod
el of strong correlations and is often amenable to
exact methods. However\, in the presence of confi
nement\, no exact solution is known for an arbitra
ry number of strongly interacting fermions. Here\,
we propose a novel ansatz for generating the lowe
st-energy wavefunctions of the repulsive 1D Fermi
gas in a harmonic potential near the Tonks-Girarde
au (TG) limit of infinite interactions. We special
ize to the case of a single impurity interacting w
ith N majority particles\, where we may derive ana
lytic forms of the approximate wavefunctions. Comp
aring with exact numerics\, we show that the overl
ap between the wavefunctions from our ansatz and t
he exact ones in the ground-state manifold exceeds
0.9997 for N up to 8. Moreover\, the overlap for
the ground-state wavefunction extrapolates to 0.99
99 as N goes to infinity. Thus our ansatz is essen
tially indistinguishable from numerically exact re
sults in both the few- and many-body limits. We de
rive an effective Heisenberg spin-chain model for
the regime near the TG limit\, within which our an
satz is exact. The energy of states in excited man
ifolds is calculated using a dynamical SO(2\,1) sy
mmetry\, which provides an exact relation between
states related by a scaling transformation. We fin
ally show how our results for the wavefunctions an
d the energy spectrum can be detected in cold atom
ic gases via collective-mode\, tunneling\, and rad
io-frequency experiments.\n\nReference: J. Levinse
n\, P. Massignan\, G. M. Bruun\, and M. M. Parish\
, arXiv:1408.7096
LOCATION:TCM Seminar Room\, Cavendish Laboratory
CONTACT:Dr G Moller
END:VEVENT
END:VCALENDAR