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

We study some properties of generalized global symmetry for the charge-q Schwinger model in the Hamiltonian formalism, which is the (1 + 1)D quantum electrodynamics with a charge-q Dirac fermion. This model has the $Z_{q}1$-form symmetry, which is a remnant of the electric $U\left(1\right)1$-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 each other. In order to see negative string tensions, the vacuum angle θ has to be large enough and the standard path-integral Monte Carlo method suffers from the sign problem. 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. In particular, we measure the local energy density and see how it jumps between the inside and outside of the insertion of the probe charges. We explicitly see that the energy density inside is lower than that outside. This is a clear signature of the negative string tension.