Critical drag as a mechanism for resistivity

TL;DR

This paper investigates the conditions under which quantum many-body systems exhibit zero or nonzero resistivity, introducing the concept of 'critical drag' as a novel mechanism for resistivity unrelated to symmetry breaking.

Contribution

It identifies critical fluctuations as a new mechanism for resistivity and links emergent symmetries with mixed anomalies to the presence of nonzero resistivity in lattice systems.

Findings

Zero resistivity requires specific symmetries or anomalies.

Critical fluctuations can induce nonzero resistivity without symmetry breaking.

The Quantum Lifshitz Model exemplifies the critical drag mechanism.

Abstract

A quantum many-body system with a conserved electric charge can have a DC resistivity that is either exactly zero (implying it supports dissipationless current) or nonzero. Exactly zero resistivity is related to conservation laws that prevent the current from degrading. In this paper, we carefully examine the situations in which such a circumstance can occur. We find that exactly zero resistivity requires either continuous translation symmetry, or an internal symmetry that has a certain kind of "mixed anomaly" with the electric charge. (The symmetry could be a generalized global symmetry associated with the emergence of unbreakable loop or higher dimensional excitations.) However, even if one of these is satisfied, we show that there is still a mechanism to get nonzero resistivity, through critical fluctuations that drive the susceptibility of the conserved quantity to infinity; we call this mechanism "critical drag". Critical drag is thus a mechanism for resistivity that, unlike conventional mechanisms, is unrelated to broken symmetries. We furthermore argue that an emergent symmetry that has the appropriate mixed anomaly with electric charge is in fact an inevitable consequence of compressibility in systems with lattice translation symmetry. Critical drag therefore seems to be the only way (other than through irrelevant perturbations breaking the emergent symmetry, that disappear at the renormalization group fixed point) to get nonzero resistivity in such systems. Finally, we present a very simple and concrete model -- the "Quantum Lifshitz Model" -- that illustrates the critical drag mechanism as well as the other considerations of the paper.