CP-violating Dashen phase transition in the two-flavor Schwinger model: a study with matrix product states

TL;DR

This study uses matrix product states to explore a CP-violating phase transition in the two-flavor Schwinger model, revealing a second order transition characterized by fermion condensate formation and entanglement entropy changes.

Contribution

It introduces a numerical approach to investigate the CP-violating Dashen phase transition in the Schwinger model beyond Monte Carlo limitations.

Findings

Identifies a phase transition near equal flavor masses.

Observes fermion condensate formation at the transition.

Detects a peak in bipartite entanglement entropy.

Abstract

We numerically study the Hamiltonian lattice formulation of the two-flavor Schwinger model using matrix product states. Keeping the mass of the first flavor at a fixed positive value, we tune the mass of the second flavor through a range of negative values, thus exploring a regime where conventional Monte Carlo methods suffer from the sign problem and may run into instabilities due to zero modes. Our results indicate a phase transition at the point where the absolute value of the second flavor mass approaches the first flavor mass. The phase transition is accompanied by the formation of a fermion condensate, a steep drop of the average electric field, and a peak in the bipartite entanglement entropy. Our data hints at a second order transition, which is the 1+1D analog of the CP-violating Dashen phase transition in QCD.