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Tan relations in one dimension | | Marcus Barth
; Wilhelm Zwerger
; | | Date: |
28 Jan 2011 | | Abstract: | We derive exact relations that connect the universal C/k^4-decay of the
momentum distribution at large k with both thermodynamic properties and
correlation functions of two-component Fermi gases in one dimension with
contact interactions. The relations are analogous to those obtained by Tan in
the three-dimensional case and are derived from an operator product expansion
of the one- and two-particle density matrix. They extend earlier results by
Olshanii and Dunjko [Phys. Rev. Lett. 91, 090401 (2003)] for the bosonic
Lieb-Liniger gas. As an application, we calculate the pair distribution
function at short distances and the dimensionless contact in the limit of
infinite repulsion. The ground state energy approaches a universal constant in
this limit, a behavior that also holds in the three-dimensional case. In both
one and three dimensions, the Tan relations rule out a Stoner instability to a
saturated ferromagnet for repulsive Femions with zero range interactions. | | Source: | arXiv, 1101.5594 | | Services: | Forum | Review | PDF | Favorites | |
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