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Keywords
(8)
Correlation Function
Density Matrix
Ground State Energy
Operator Product Expansion
Pair Distribution Function
Thermodynamic Properties
Three Dimensional
Three Dimensions
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Tan relations in one dimension
Tan relations in one dimension,10.1016/j.aop.2011.05.010,Annals of Physics,Marcus Barth,Wilhelm Zwerger
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Tan relations in one dimension
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Marcus Barth
,
Wilhelm Zwerger
We derive exact relations that connect the universal C/k4decay of the momentum distribution at large k with both
thermodynamic properties
and correlation functions of twocomponent Fermi gases in one dimension with contact interactions. The relations are analogous to those obtained by Tan in the threedimensional case and are derived from an
operator product expansion
of the one and twoparticle density matrix. They extend earlier results by Olshanii and Dunjko (2003) [24] 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 threedimensional case. In both one and three dimensions, a Stoner instability to a saturated ferromagnet for repulsive fermions with zero range interactions is ruled out at any finite coupling.
Journal:
Annals of Physics  ANN PHYS N Y
, vol. 326, no. 10, pp. 25442565, 2011
DOI:
10.1016/j.aop.2011.05.010
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