Lattice calculations for two-component fermion systems

In this study, we investigate systems of two-component fermions characterized by unequal masses and subjected to a short-range attractive potential. Specifically, we explore scenarios where these fermions form shallow dimers with a considerable scattering length. The universality of three-fermion and four-fermion systems in this context is determined by the two-fermion scattering length and the ratio of the mass of spin-$\uparrow$ fermions to spin-$\downarrow$ fermions, denoted as $m_{\uparrow}/m_{\downarrow}$. Utilizing Nuclear Lattice Effective Field Theory (NLEFT), we conduct a comprehensive analysis of fermion-dimer system in one-dimension and three-dimension, and dimer-dimer systems in one-dimension. Our focus lies in the calculation of universal fermion-dimer and dimer-dimer scattering lengths across a range of mass ratio values, $m_{\uparrow}/m_{\downarrow}$. Intriguingly, our findings reveal a logarithmic increase in these universal scattering lengths as the mass ratio $m_{\uparrow}/m_{\downarrow}$ varies.