Schwinger model on an interval: Analytic results and DMRG

Quantum electrodynamics in $1+1$ dimensions (Schwinger model) on an interval admits lattice discretization with a finite-dimensional Hilbert space, and is often used as testbed for quantum tensor network simulations. In this work we clarify the precise mapping between boundary conditions continuum theories. particular show that conventional Gauss law constraint commonly simulations induces strong effect charge density, reflecting appearance of fractionalized charges. Further, obtain by bosonization number exact analytic results local observables massless Schwinger model. We compare these simulation obtained density matrix renormalization group (DMRG) method find excellent agreements.