Vanishing and non-vanishing persistent currents of various conserved quantities

TL;DR

This paper investigates the scaling behavior of persistent currents in quantum many-body systems, distinguishing between those associated with conserved quantities and accidental conservation, with implications for understanding spontaneous flows.

Contribution

It provides a theoretical framework for bounding persistent currents linked to conserved quantities and demonstrates that accidental conserved currents can remain nonzero in the thermodynamic limit.

Findings

Persistent currents for conserved quantities decay algebraically with system size.

Accidental conserved quantities can sustain nonzero persistent currents even at infinite size.

Analytic expression derived for energy current in the $S=1/2$ XXZ spin chain.

Abstract

For every conserved quantity written as a sum of local terms, there exists a corresponding current operator that satisfies the continuity equation. The expectation values of current operators at equilibrium define the persistent currents that characterize spontaneous flows in the system. In this work, we consider quantum many-body systems on a finite one-dimensional lattice and discuss the scaling of the persistent currents as a function of the system size. We show that, when the conserved quantities are given as the Noether charges associated with internal symmetries or the Hamiltonian itself, the corresponding persistent currents can be bounded by a correlation function of two operators at a distance proportional to the system size, implying that they decay at least algebraically as the system size increases. In contrast, the persistent currents of accidentally conserved quantities can be nonzero even in the thermodynamic limit and even in the presence of the time-reversal symmetry. We discuss `the current of energy current' in $S=1/2$ XXZ spin chain as an example and obtain an analytic expression of the persistent current.