Collective dynamics in holographic fractonic solids

TL;DR

This paper explores the collective low-energy excitations of holographic fractonic solids, revealing unique hydrodynamic modes including a protected subdiffusive mode, through analysis of black hole quasinormal modes.

Contribution

It introduces a (3+1)-dimensional holographic model for fractonic solids and systematically characterizes their hydrodynamic excitations, highlighting the robustness of the subdiffusive mode.

Findings

Identified two acoustic phonons and a diffusive mode.

Discovered a gapless subdiffusive mode with $\, ext{omega} \, ext{ extasciitilde}-i k^4$ dispersion.

Subdiffusive mode remains gapless even when translational symmetry is broken.

Abstract

Fractonic phases of matter, a class of states in which collective excitations with constrained mobility exist, were originally discovered in the study of quantum error-correcting codes in solvable lattice spin models such as Haah's code and the X-cube model. Recently, they have also drawn the attention of the high-energy physics community due to the UV/IR mixing that arises when coarse-graining these lattice models. In this work, we consider a (3+1)-dimensional holographic model of fractonic solids and investigate the low-energy collective dynamics systematically. By computing the quasinormal modes of black holes, we obtain all the hydrodynamic excitations on the boundary, including two acoustic phonons, a longitudinal diffusive mode, and a subdiffusive collective mode with the dispersion $\omega \sim-ik^4$. In addition, it is found that the latter remains gapless when translational symmetry is explicitly broken. These results suggest that the subdiffusive mode is inherently protected by the crystal-dipole symmetry in solids and is qualitatively unaffected by broken spacetime symmetries.