Critical behavior of the Schwinger model via gauge-invariant VUMPS

TL;DR

This paper employs a gauge-invariant VUMPS approach to accurately analyze the critical behavior of the Schwinger model, confirming its Ising universality class and precisely locating the critical endpoint.

Contribution

The study introduces a gauge-invariant VUMPS algorithm that enforces Gauss law constraints, enabling precise analysis of phase transitions in the Schwinger model.

Findings

Identifies the critical endpoint in the continuum Schwinger model.

Confirms the Ising universality class for the phase transition.

Provides high-precision data collapse in the critical and continuum limits.

Abstract

We study the lattice Schwinger model by combining the variational uniform matrix product state (VUMPS) algorithm with a gauge-invariant matrix product ansatz that locally enforces the Gauss law constraint. Both the continuum and lattice versions of the Schwinger model with $\theta=\pi$ are known to exhibit first-order phase transitions for the values of the fermion mass above a critical value, where a second-order phase transition occurs. Our algorithm enables a precise determination of the critical endpoint in the continuum theory. We further analyze the scaling in the simultaneous critical and continuum limits and confirm that the data collapse aligns with the Ising universality class to remarkable precision.