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

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 two-fermion scattering length a_ff 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_↓.