Lattice calculations for two-component fermion systems with unequal masses: one dimension

Abstract

We consider systems of two-component fermions with unequal masses and interacting via a short-range attractive potential. We discuss the case where the two-component fermions form a shallow dimer with large scattering length. The three-fermion and four-fermion systems with such properties are universal and characterized by the twofermion scattering length aff and the ratio of the mass of spin-↑ fermion to the mass of spin-↓ fermion, m↑/m↓. In this study, using lattice effective field theory, we analyze fermion-dimer and dimer-dimer systems and calculate the universal fermion-dimer and dimer-dimer scattering lengths for various values of the mass ratio m↑/m↓. We find that these universal scattering lengths increase logarithmically with the mass ratio m↑/m↓.