One-dimensional Spin-polarized Fermi Gas near resonances

We study a quantum field theory for resonantly interacting spinless fermions in one dimension. This fermions are known to correspond to one-dimensional bosons with delta-function interaction [1]. We perform the renormalization group analysis and clarify that three-body coupling, which is zero in the ultraviolet theory, emergently appears in the infrared limit [2]. This running coupling allows us to rederive the energy relaiton, i.e., the expresson of energy in terms of a momentum distribution and contact parameters characterizing local corretions of the system. The obtained energy relation is consistent with that previously derived in the first quantization formalism [3].

[1] T. Cheon and T. Shigehara, Phys. Rev. Lett. 82, 2536 (1999)
[2] Y. Sekino and Y. Nishida, in preparation
[3] Y. Sekino, S. Tan, and Y. Nishida, Phys. Rev. A 97, 013621 (2018)