Quantum Computation of Phase Transition in the Massive Schwinger Model

As pointed out by Coleman, physical quantities in the Schwinger model depend on a parameter $\theta$ that determines the background electric field. There is a phase transition for $\theta =\pi$ only. We develop a momentum space formalism on a lattice and use it to perform a quantum computation of the critical point of this phase transition on the NISQ device IMB Q Lima. After error mitigation, our results give strong indication of the existence of a critical point at $m\mathrm{/}e\simeq 0.32$, where $m$ is the bare fermion mass and $e$ is the coupling strength, in good agreement with the classical numerical result $m\mathrm{/}e\simeq 0.3335$.