The Bloch theorem in the presence of an additional conserved charge

TL;DR

This paper revisits the Bloch theorem's restrictions on persistent currents in systems with an additional conserved charge, providing a canonical ensemble derivation and discussing conditions under which the current vanishes.

Contribution

It offers a canonical ensemble derivation of the Bloch theorem with an extra conserved charge and analyzes the conditions for current suppression when coupled to an external reservoir.

Findings

Derivation based on the canonical ensemble confirms the theorem's predictions.

Persistent current tends to vanish with an external momentum reservoir.

The approach complements previous generalized Gibbs ensemble results.

Abstract

The Bloch theorem is a general theorem restricting the persistent current associated with a conserved U(1) charge in a ground state or in a thermal equilibrium. It gives an upper bound of the magnitude of the current density, which is inversely proportional to the system size. In a recent paper, Else and Senthil applied the argument for the Bloch theorem to a generalized Gibbs ensemble, assuming the presence of an additional conserved charge, and predicted a nonzero current density in the nonthermal steady state [D. V. Else and T. Senthil, Phys. Rev. B 104, 205132 (2021)]. In this work, we provide a complementary derivation based on the canonical ensemble, given that the additional charge is strictly conserved within the system by itself. Furthermore, using the example where the additional conserved charge is the momentum operator, we discuss that the persistent current tends to vanish when the system is in contact with an external momentum reservoir in the co-moving frame of the reservoir.