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-rangeattractive potential. We discuss the case where the two-component fermions form a shallow dimer with large scatteringlength. 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 thisstudy, using lattice effective field theory, we analyze fermion-dimer and dimer-dimer systems and calculate the universalfermion-dimer and dimer-dimer scattering lengths for various values of the mass ratio m↑/m↓ . We find that theseuniversal scattering lengths increase logarithmically with the mass ratio m↑/m↓ .