- Open Access
Fractonic solids
Phys. Rev. D 113, 105015 – Published 21 May, 2026
DOI: https://doi.org/10.1103/jdnr-cwpy
Abstract
Fractons are exotic quasiparticles whose mobility in space is restricted by symmetries. In potential real-world realizations, fractons are likely lodged to a physical material rather than absolute space. Motivated by this, we propose and explore a new symmetry principle that restricts the motion of fractons relative to a physical solid. Unlike models with restricted mobility in absolute space, these fractonic solids admit gauge-invariant momentum density, are compatible with boost symmetry, and can consistently be coupled to gravity. We also propose a holographic model for fractonic solids.
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References (64)
- C. Chamon, Quantum glassiness, Phys. Rev. Lett. 94, 040402 (2005).
- S. Bravyi, B. Leemhuis, and B. M. Terhal, Topological order in an exactly solvable 3D spin model, Ann. Phys. (Amsterdam) 326, 839 (2011).
- J. Haah, Local stabilizer codes in three dimensions without string logical operators, Phys. Rev. A 83, 042330 (2011).
- S. Vijay, J. Haah, and L. Fu, A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations, Phys. Rev. B 92, 235136 (2015).
- R. M. Nandkishore and M. Hermele, Fractons, Annu. Rev. Condens. Matter Phys. 10, 295 (2019).
- M. Pretko, X. Chen, and Y. You, Fracton phases of matter, Int. J. Mod. Phys. A 35, 2030003 (2020).
- S. Vijay, J. Haah, and L. Fu, Fracton topological order, generalized lattice gauge theory and duality, Phys. Rev. B 94, 235157 (2016).
- Y. You, T. Devakul, F. J. Burnell, and S. L. Sondhi, Subsystem symmetry protected topological order, Phys. Rev. B 98, 035112 (2018).
- N. Seiberg and S.-H. Shao, Exotic symmetries, duality, and fractons in -dimensional quantum field theory, SciPost Phys. 10, 027 (2021).
- N. Seiberg and S.-H. Shao, Exotic symmetries, duality, and fractons in -dimensional quantum field theory, SciPost Phys. 9, 046 (2020).
- M. Pretko, Subdimensional particle structure of higher rank U(1) spin liquids, Phys. Rev. B 95, 115139 (2017).
- A. Gromov, Towards classification of Fracton phases: The multipole algebra, Phys. Rev. X 9, 031035 (2019).
- K. Slagle, A. Prem, and M. Pretko, Symmetric tensor gauge theories on curved spaces, Ann. Phys. (Amsterdam) 410, 167910 (2019).
- A. Jain and K. Jensen, Fractons in curved space, SciPost Phys. 12, 142 (2022).
- F. Peña Benitez, Fractons, symmetric gauge fields and geometry, Phys. Rev. Res. 5, 013101 (2023).
- L. Bidussi, J. Hartong, E. Have, J. Musaeus, and S. Prohazka, Fractons, dipole symmetries and curved spacetime, SciPost Phys. 12, 205 (2022).
- P. Glorioso, X. Huang, J. Guo, J. F. Rodriguez-Nieva, and A. Lucas, Goldstone bosons and fluctuating hydrodynamics with dipole and momentum conservation, J. High Energy Phys. 05 (2023) 022.
- K. Jensen and A. Raz, Large N fractons, Phys. Rev. Lett. 132, 071603 (2024).
- A. Gromov, A. Lucas, and R. M. Nandkishore, Fracton hydrodynamics, Phys. Rev. Res. 2, 033124 (2020).
- A. Osborne and A. Lucas, Infinite families of fracton fluids with momentum conservation, Phys. Rev. B 105, 024311 (2022).
- K. T. Grosvenor, C. Hoyos, F. Peña Benitez, and P. Surówka, Hydrodynamics of ideal fracton fluids, Phys. Rev. Res. 3, 043186 (2021).
- A. Jain, K. Jensen, R. Liu, and E. Mefford, Dipole superfluid hydrodynamics, J. High Energy Phys. 09 (2023) 184.
- J. Armas and E. Have, Ideal fracton superfluids, SciPost Phys. 16, 039 (2024).
- A. Jain, K. Jensen, R. Liu, and E. Mefford, Dipole superfluid hydrodynamics. Part II., J. High Energy Phys. 07 (2024) 197.
- M. Pretko and L. Radzihovsky, Fracton-elasticity duality, Phys. Rev. Lett. 120, 195301 (2018).
- D. X. Nguyen, A. Gromov, and S. Moroz, Fracton-elasticity duality of two-dimensional superfluid vortex crystals: Defect interactions and quantum melting, SciPost Phys. 9, 076 (2020).
- A. Gromov, Chiral topological elasticity and fracton order, Phys. Rev. Lett. 122, 076403 (2019).
- A. Caddeo, C. Hoyos, and D. Musso, Emergent dipole gauge fields and fractons, Phys. Rev. D 106, L111903 (2022).
- D. Doshi and A. Gromov, Vortices and fractons, arXiv:2005.03015.
- Y. You and F. von Oppen, Majorana quantum lego, a route towards fracton matter, Phys. Rev. Res. 1, 013011 (2019).
- Y. You, Z. Bi, and M. Pretko, Emergent fractons and algebraic quantum liquid from plaquette melting transitions, Phys. Rev. Res. 2, 013162 (2020).
- J. Sous and M. Pretko, Fractons from polarons, Phys. Rev. B 102, 214437 (2020).
- E. Guardado-Sanchez, A. Morningstar, B. M. Spar, P. T. Brown, D. A. Huse, and W. S. Bakr, Subdiffusion and heat transport in a tilted two-dimensional Fermi-Hubbard system, Phys. Rev. X 10, 011042 (2020).
- H. Leutwyler, Phonons as Goldstone bosons, Helv. Phys. Acta 70, 275 (1997).
- A. Nicolis, R. Penco, F. Piazza, and R. Rattazzi, Zoology of condensed matter: Framids, ordinary stuff, extra-ordinary stuff, J. High Energy Phys. 06 (2015) 155.
- J. Armas and A. Jain, Viscoelastic hydrodynamics and holography, J. High Energy Phys. 01 (2020) 126.
- J. Armas and A. Jain, Hydrodynamics for charge density waves and their holographic duals, Phys. Rev. D 101, 121901 (2020).
- J. Armas, A. Jain, and R. Lier, Approximate symmetries, pseudo-Goldstones, and the second law of thermodynamics, Phys. Rev. D 108, 086011 (2023).
- J. Armas, E. van Heumen, A. Jain, and R. Lier, Hydrodynamics of plastic deformations in electronic crystals, Phys. Rev. B 107, 155108 (2023).
- M. Fukuma and Y. Sakatani, Relativistic viscoelastic fluid mechanics, Phys. Rev. E 84, 026316 (2011).
- M. Pretko, The fracton gauge principle, Phys. Rev. B 98, 115134 (2018).
- M. Boninsegni and N. V. Prokof’ev, Colloquium: Supersolids: What and where are they?, Rev. Mod. Phys. 84, 759 (2012).
- C. Stahl, M. Qi, P. Glorioso, A. Lucas, and R. Nandkishore, Fracton superfluid hydrodynamics, Phys. Rev. B 108, 144509 (2023).
One may also approach hydrodynamics using Schwinger-Keldysh effective actions [45, 46, 47, 48, 49, 50, 51], useful for including stochastic fluctuations in hydrodynamic models.
- S. Grozdanov and J. Polonyi, Viscosity and dissipative hydrodynamics from effective field theory, Phys. Rev. D 91, 105031 (2015).
- M. Harder, P. Kovtun, and A. Ritz, On thermal fluctuations and the generating functional in relativistic hydrodynamics, J. High Energy Phys. 07 (2015) 025.
- M. Crossley, P. Glorioso, and H. Liu, Effective field theory of dissipative fluids, J. High Energy Phys. 09 (2017) 095.
- F. M. Haehl, R. Loganayagam, and M. Rangamani, Topological sigma models & dissipative hydrodynamics, J. High Energy Phys. 04 (2016) 039.
- F. M. Haehl, R. Loganayagam, and M. Rangamani, Effective action for relativistic hydrodynamics: Fluctuations, dissipation, and entropy inflow, J. High Energy Phys. 10 (2018) 194.
- K. Jensen, N. Pinzani-Fokeeva, and A. Yarom, Dissipative hydrodynamics in superspace, J. High Energy Phys. 09 (2018) 127.
- H. Liu and P. Glorioso, Lectures on non-equilibrium effective field theories and fluctuating hydrodynamics, Proc. Sci. TASI2017 (2018) 008 [arXiv:1805.09331].
- See the Mathematica notebook, https://github.com/ajainphysics/Mathematica-Notebooks/tree/main/%5BarXiv%3A2406.07334%5D%20Fractonic%20Solids/FractonicSolids_Modes.nb (2024), for details of the mode spectrum of various phases of crystal-dipole-invariant relativistic hydrodynamics.
There will still be finite wavevector instabilities that usually appear in relativistic hydrodynamics and may be treated using similar techniques.
- P. Gorantla, H. T. Lam, N. Seiberg, and S.-H. Shao, Low-energy limit of some exotic lattice theories and UV/IR mixing, Phys. Rev. B 104, 235116 (2021).
- K. Ganesan and A. Lucas, Holographic subdiffusion, J. High Energy Phys. 12 (2020) 149.
- M. Baggioli and O. Pujolas, Electron-phonon interactions, metal-insulator transitions, and holographic massive gravity, Phys. Rev. Lett. 114, 251602 (2015).
- L. Alberte, M. Baggioli, A. Khmelnitsky, and O. Pujolas, Solid holography and massive gravity, J. High Energy Phys. 02 (2016) 114.
- M. Baggioli and B. Goutéraux, Colloquium: Hydrodynamics and holography of charge density wave phases, Rev. Mod. Phys. 95, 011001 (2023).
- T. Andrade and B. Withers, A simple holographic model of momentum relaxation, J. High Energy Phys. 05 (2014) 101.
- J. Bhattacharya, S. Bhattacharyya, and S. Minwalla, Dissipative superfluid dynamics from gravity, J. High Energy Phys. 04 (2011) 125.
- M. Baggioli and G. Frangi, Holographic supersolids, J. High Energy Phys. 06 (2022) 152.
- J. C. Baez and J. Huerta, An invitation to higher gauge theory, Gen. Relativ. Gravit. 43, 2335 (2011).
- D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, Generalized global symmetries, J. High Energy Phys. 02 (2015) 172.
- See the Mathematica notebook, https://github.com/ajainphysics/Mathematica-Notebooks/tree/main/%5BarXiv%3A2406.07334%5D%20Fractonic%20Solids/FractonicSolids_Holography.nb (2024), for details of the quasi-normal modes of a charged black brane in the holographic model for fractonic solids.