Zero sound and higher-form symmetries in compressible holographic phases

TL;DR

This paper explores zero sound modes in holographic states of matter, revealing their origin in higher-form symmetries and anomalies, and analyzing their behavior at different temperatures and densities.

Contribution

It uncovers the role of mixed 't Hooft anomalies and higher-form symmetries in generating zero sound modes in holographic quantum critical states.

Findings

Zero sound modes are linked to mixed 't Hooft anomalies.

Finite temperature gaps lead to Drude-like peaks in conductivity.

Zero temperature modes dissolve into branch cuts due to IR backreaction.

Abstract

Certain holographic states of matter with a global U(1) symmetry support a sound mode at zero temperature, caused neither by spontaneous symmetry breaking of the global U(1) nor by the emergence of a Fermi surface in the infrared. In this work, we show that such a mode is also found in zero density holographic quantum critical states. We demonstrate that in these states, the appearance of a zero temperature sound mode is the consequence of a mixed `t Hooft anomaly between the global U(1) symmetry and an emergent higher-form symmetry. At non-zero temperatures, the presence of a black hole horizon weakly breaks the emergent symmetry and gaps the collective mode, giving rise to a sharp Drude-like peak in the electric conductivity. A similar gapped mode arises at low temperatures for non-zero densities when the state has an emergent Lorentz symmetry, also originating from an approximate anomalous higher-form symmetry. However, in this case the collective excitation does not survive at zero temperature where, instead, it dissolves into a branch cut due to strong backreaction from the infrared, critical degrees of freedom. We comment on the relation between our results and the application of the Luttinger theorem to compressible holographic states of matter.