Zero sound and higher-form symmetries in compressible holographic phases
Zero sound and higher-form symmetries in compressible holographic phases
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. We comment on the relation between our results and the application of the Luttinger theorem to compressible holographic states of matter.
- HERIOT-WATT UNIVERSITY United Kingdom
- Department of Physics and Astronomy University of Western Ontario Canada
- École Polytechnique France
- University of Toronto Canada
- University of Victoria Canada
conductivity: electric, density, Strongly Correlated Electrons (cond-mat.str-el), FOS: Physical sciences, spontaneous symmetry breaking, gap, anomaly, symmetry: U(1), black hole: horizon, High Energy Physics - Theory (hep-th), temperature: low, Fermi surface, infrared, temperature: 0, holography, [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th], symmetry: Lorentz, excited state: collective, [PHYS.COND] Physics [physics]/Condensed Matter [cond-mat]
conductivity: electric, density, Strongly Correlated Electrons (cond-mat.str-el), FOS: Physical sciences, spontaneous symmetry breaking, gap, anomaly, symmetry: U(1), black hole: horizon, High Energy Physics - Theory (hep-th), temperature: low, Fermi surface, infrared, temperature: 0, holography, [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th], symmetry: Lorentz, excited state: collective, [PHYS.COND] Physics [physics]/Condensed Matter [cond-mat]
1512
1■0-23 10-1 10-21 100 1021 101 102 3 k/T
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