Non-relativistic interacting fermions in (1 + 1) dimensions

One-dimensional systems of interacting fermions are not only theoretically rich but also experimentally relevant in cold atom setups. In this poster, I will present a lattice regularization scheme for two species of non-relativistic fermions with general contact interactions, consistent with fundamental symmetries such as Galilean invariance and parity, in one dimension. This includes a special type of interaction that depends on the relative velocity of particles. We particularly study the lattice spacing dependence of local lattice interactions as we take the continuum limit of the lattice theory. We then explore the impact of these interactions on the binding energy of few-body systems using the exact diagonalization method, given that our system is small. We also compare different renormalization schemes with ours. These discussions can help extend our methods to a more complex four- or five-body system.