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 charazteried by the two-fermion scattering length $a_{\text{ff}}$ and the ratio of the mass of spin-$\uparrow$ fermion to the mass of spin-$\downarrow$ fermion, $m_{\uparrow}/m_{\downarrow}$. 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 $m_{\uparrow}/m_{\downarrow}$. We find that these universal scattering lengths increase logarithmically with the mass ratio $m_{\uparrow}/m_{\downarrow}$.