Field-theoretical aspects of one-dimensional Bose and Fermi gases with contact interactions

• URL: http://arxiv.org/abs/2011.11971v2
• Date: Wed, 7 Apr 2021 11:03:43 GMT
• Title: Field-theoretical aspects of one-dimensional Bose and Fermi gases with contact interactions
• Authors: Yuta Sekino, Yusuke Nishida
• Abstract summary: We investigate local quantum field theories for 1D Bose and Fermi gases with contact interactions. Because of this three-body coupling, the three-body contact characterizing a local correlation appears in the energy relation for fermions. The triads for the Tonks-Girardeau gas, which is a Bose gas with a hardcore repulsion, as well as the Bose-Fermi correspondence in the presence of three-body attractions are also discussed.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate local quantum field theories for one-dimensional (1D) Bose and Fermi gases with contact interactions, which are closely connected with each other by Girardeau's Bose-Fermi mapping. While the Lagrangian for bosons includes only a two-body interaction, a marginally relevant three-body interaction term is found to be necessary for fermions. Because of this three-body coupling, the three-body contact characterizing a local triad correlation appears in the energy relation for fermions, which is one of the sum rules for a momentum distribution. In addition, we apply in both systems the operator product expansion to derive large-energy and momentum asymptotics of a dynamic structure factor and a single-particle spectral density. These behaviors are universal in the sense that they hold for any 1D scattering length at any temperature. The asymptotics for the Tonks-Girardeau gas, which is a Bose gas with a hardcore repulsion, as well as the Bose-Fermi correspondence in the presence of three-body attractions are also discussed.

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