Collective dynamics in holographic fractonic solids

TL;DR

Problem: understanding collective dynamics in fractonic solids with constrained mobility. Approach: a (3+1)D holographic model combining axion-induced translation breaking and crystal-dipole symmetry, analyzed via quasinormal modes to obtain hydrodynamic excitations. Key findings: two acoustic phonons, a longitudinal diffusive mode, and a robust subdiffusive mode with dispersion ω ∼ -i k^4; the subdiffusive mode remains gapless under explicit translation breaking and influences dissipative sectors. Significance: provides a holographic realization of fracton hydrodynamics, showing the crystal-dipole mode protection and suggesting extensions to fracton superfluids and higher multipole conservations.

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 $ω\sim-ik^4$. 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.

Figures (9)

• Figure 1: Dispersion relations of transverse hydrodynamic modes, where the dots are the numerical data points and the solid line represents the hydrodynamic prediction \ref{['trsound']}. Left: Real part. Right: Imaginary part. Here, we have fixed $\mu/T=1,\ m/T=1.2$. We only plot the branch with positive real part of frequency ($\text{Re}[\omega]>0$). The corresponding negative branch ($\text{Re}[\omega]<0$) is symmetric and has been omitted for clarity. This omission applies to all figures in the following.
• Figure 2: Dispersion relations of longitudinal hydrodynamic modes for $\mu/T=1,\ m/T=1.2$. Left: Real part. Right: Imaginary part. The plotting conventions are the same as in FIG. \ref{['transback']}.
• Figure 3: The coefficients in the transverse sound modes as the function of $m/T$ for $\mu/T =\{0, 1, 3, 5\}$ (black, red, blue, green). Left: Transverse sound velocity $v_T$. Right: Dimensionless transverse sound attenuation $\Gamma_TT$. The solid and dashed lines represent the phase with and without $\delta A_a^I$, respectively. The same convention is used for all subsequent plots.
• Figure 4: The coefficients in the longitudinal sound modes as the function of $m/T$ for $\mu/T =\{0,1,3,5\}$ (black, red, blue, green). Left: Longitudinal sound velocity $v_L$. Right: Dimensionless longitudinal sound attenuation $\Gamma_LT$.
• Figure 5: The dimensionless longitudinal diffusivity $D_L T$ as the function of $m/T$ for $\mu/T =\{0,1,3,5\}$ (black, red, blue, green).