Computing theta-dependent mass spectrum of the 2-flavor Schwinger model in the Hamiltonian formalism

TL;DR

This paper calculates the $ heta$-dependent mass spectrum of the 2-flavor Schwinger model using tensor network methods, identifying stable mesons, confirming results with bosonization, and exploring behavior at the critical point.

Contribution

It introduces a sign-problem-free tensor network approach to compute the $ heta$-dependent spectrum, improving accuracy over Monte Carlo methods and analyzing critical behavior.

Findings

Mesons are stable for nonzero $ heta$

Masses agree with bosonized model calculations

At $ heta=\pi$, mesons become nearly massless and exhibit CFT-like behavior

Abstract

We compute the $\theta$-dependent mass spectrum of the 2-flavor Schwingr model using the tensor network (DMRG) in the Hamiltonian formalism. The pion and the sigma meson are identified as stable particles of the model for nonzero $\theta$ whereas the eta meson becomes unstable. The meson masses are obtained from the one-point functions, using the meson operators defined by diagonalizing the correlation matrix to deal with the operator mixing. We also compute the dispersion relation directly by measuring the energy and momentum of the excited states, where the mesons are distinguished by the isospin quantum number. We confirmed that the meson masses computed by these methods agree with each other and are consistent with the calculation by the bosonized model. Our methods are free from the sign problem and show a significant improvement in accuracy compared to the conventional Monte Carlo methods. Furthermore, at the critical point $\theta = \pi$, the mesons become almost massless, and the one-point functions reproduce the expected CFT-like behavior.