Negative string tension of higher-charge Schwinger model via digital quantum simulation

TL;DR

This paper uses digital quantum simulation to study the charge-$q$ Schwinger model, revealing negative string tension behavior indicative of charge repulsion, and confirms the findings with classical simulation methods.

Contribution

It introduces a quantum simulation approach to observe negative string tension in the higher-charge Schwinger model, a novel application in lattice gauge theories.

Findings

Observation of negative string tension indicating charge repulsion.

Measurement of local energy density differences inside and outside probe charges.

Confirmation of negative string tension behavior through classical simulation.

Abstract

We study some properties of generalized global symmetry for the charge-$q$ Schwinger model in the Hamiltonian formalism, which is the $(1+1)$-dimensional quantum electrodynamics with a charge-$q$ Dirac fermion. This model has the $\mathbb{Z}_q$ $1$-form symmetry, which is a remnant of the electric $U(1)$ $1$-form symmetry in the pure Maxwell theory. It is known that if we put the theory on closed space, then the Hilbert space is decomposed into $q$ distinct sectors, called universes and some states with higher energy density do not decay to the ground state due to the selection rule of the $1$-form symmetry. Even with open boundaries, we can observe the stability of such states by seeing a negative string tension behavior, meaning that opposite charges repel with each other. We develop a method based on the adiabatic state preparation to see this feature with digital quantum simulation and confirm it using a classical simulator of quantum devices. Especially, we measure local energy density and see how it jumps between inside and outside of insertion of the probe charges. We explicitly see that the energy density inside is lower than the outside one. This is a clear signature of the negative string tension.