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Universal properties of hard-core bosons confined on one-dimensional lattices
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Universal properties of hard-core bosons confined on one-dimensional lattices
Marcos Rigol and Alejandro Muramatsu
Institut fu?r Theoretische Physik III, Universita?t Stuttgart,
Pfaffenwaldring 57, D-70550 Stuttgart, Germany.
Based on an exact treatment of hard-core bosons confined on one-dimensional lattices, we obtain
the large distance behavior of the one-particle density matrix, and show how it determines the
occupation of the lowest natural orbital in the thermodynamic limit. We also study the occupation
λη of the natural orbitals for large-η at low densities. Both quantities show universal behavior
independently of the confining potential. Finite-size corrections and the momentum distribution
function for finite systems are also analyzed.
PACS numbers: 03.75.Hh, 05.30.Jp
Trapped atomic gases at very low temperatures be-
came in the past years a center of attention in atomic and
condensed matter physics. Particularly interesting is the
case where the dynamics of the system is restricted to
one-dimension (1D) due to a strong transversal confine-
ment. It has been shown recently [1] that in regimes of
large positive scattering length, low densities, and low
temperatures, a quasi-1D gas of bosons behaves as a
gas of impenetrable particles, i.e., as hard-core bosons
(HCB). Ultracold Bose gases in 1D have been realized
experimentally [2], so that it is expected that soon it will
be possible to make the 1D HCB gas a physical reality.
The 1D gas of HCB was first introduced theoretically
by Girardeau [3], who also established its exact mapping
to a gas of noninteracting spinless fermions. Since then, it
remained a subject of recurring attention, and a number
of exact results were obtained for the momentum distri-
bution function (MDF) n(k) and the one-particle density
matrix (OPDM) ρ(x) in the homogeneous [4, 5] and the
periodic [6] case. It was shown that n
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