Tan relations in one dimension

Marcus Barth; Wilhelm Zwerger

doi:10.1016/j.aop.2011.05.010

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arXiv · 1101.5594

Tan relations in one dimension

Marcus Barth·Wilhelm Zwerger

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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, a Stoner instability to a saturated ferromagnet for repulsive fermions with zero range interactions is ruled out at any finite coupling.

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Marcus Barth, Wilhelm Zwerger. 2011-01-28. Tan relations in one dimension. https://doi.org/10.1016/j.aop.2011.05.010

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