Implementing a Lattice Formulation of the Schwinger Modelwith Periodic Boundary Conditions Using Tensor Networks

Abstract

I attempt to develop a simple tensor network formulation of the Schwinger model with periodic boundary conditions. The primary challenge is to enforce the local constraints imposed by Gauss's Law. I do this by combining global conservation of a specially defined quantum number with the local optimization steps used in the density matrix renormalization group (DMRG) algorithm for finding the ground state of a quantum system. However, due to practical constraints, I still use matrix product states and matrix product operators with open boundary conditions. I demonstrate the efficacy of the model in computing the bulk limit (the limit as the number of lattice sites goes to infinity) for the energy density, chiral condensate, and electric field energy density of the ground state. Future investigation should begin with recreating the model using periodic matrix product states and matrix product operators and using a version of DMRG that has been optimized for periodic boundary conditions.