Collective dynamics in holographic fractonic solids

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 $ω\sim-ik^4$. 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.

💡 Research Summary

This paper presents a comprehensive holographic study of fractonic solids, focusing on their low‑energy collective excitations. The authors construct a (3+1)‑dimensional AdS bulk model that incorporates two massless scalar “axion” fields Φ I (I = 1,2) to break spatial translations, a standard U(1) gauge field Aμ for charge conservation, and an additional set of gauge fields A I μ that encode the crystal‑dipole symmetry characteristic of fracton systems. The bulk action reads

S = ∫d⁴x √−g