The mass spectrum of the Schwinger model with Matrix Product States

TL;DR

This paper demonstrates the effectiveness of matrix product states in studying the Schwinger model, achieving high precision in calculating mass spectra and excitations, thus advancing tensor network methods for lattice gauge theories.

Contribution

The authors introduce new tensor network techniques for excitation computation and state identification in lattice gauge theories, showing their effectiveness in the Schwinger model.

Findings

MPS techniques achieve high precision for ground state and mass gaps.

New methods enable excitation calculations with open boundary conditions.

Results are comparable to the best existing techniques.

Abstract

We show the feasibility of tensor network solutions for lattice gauge theories in Hamiltonian formulation by applying matrix product states algorithms to the Schwinger model with zero and non-vanishing fermion mass. We introduce new techniques to compute excitations in a system with open boundary conditions, and to identify the states corresponding to low momentum and different quantum numbers in the continuum. For the ground state and both the vector and scalar mass gaps in the massive case, the MPS technique attains precisions comparable to the best results available from other techniques.