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-up arrow fermion to the mass of spin-down arrow, fermion, m(up arrow)-/m(down arrow). 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(up arrow)-/m(down arrow). We find that these universal scattering lengths increase logarithmically with the mass ratio m(up arrow)-/m(down arrow).