Non-relativistic interacting fermions in (1+1) dimension

Few-body physics plays a central role in many branches of physics, such as nuclear physics and atomic physics. Advances in controlling ultra-cold quantum gases provide an ideal testbed for few-body physics theory. In this work, we study a three-body system composed of two different species of particles in one spatial dimension using effective field theory in Refs.~[1, 2]. Particles of the same type do not interact with each other, but particles of different types can interact via pairwise contact $s$-wave and $p$-wave two-body interactions. We show that a three-body system can form bound states under $s$-wave interaction without a three-body force. The ratio between the three-body binding energy and the two-body subsystem binding energy is $7/4$, which is universal. For the $p$-wave interaction, a three-body force is required. We also observe a universal ratio between the three-body and two-body binding energy, which is $11/8$.

\noindent [1] S.Y. Young and D.T Son. \textit{Phys. Rev. A}, 97(4):043630, 2018

\noindent [2] Y. Sekino and Y. Nishida. \textit{Phys. Rev. A}, 97:011602, 2018