2019/10/07 by Vijay B. Shenoy, Roderich Moessner · 1 citation
Mathematics · Physics and Astronomy · #Antisymmetric relation #Black Holes and Theoretical Physics #Combinatorics #Dimension (graph theory) #Fracton #Geology #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Order (exchange) #Physics #Quantum many-body systems #Rank (graph theory) #Type (biology) #cond-mat.other #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.101.085106
published as Phys. Rev. B 101, 085106 (2020) · 6 pages, 1 figure
arxiv created 2019/10/07 · openalex publication_date 2020/02/06 · arxiv updated 2020/02/12 · openalex created_date 2020/02/14 · openalex updated_date 2026/08/06
Fractons emerge as charges with reduced mobility in a class of gauge theories. Here, we generalize fractonic theories of U(1) type to what we call (k,n)-fractonic Maxwell theory, which employs symmetric rank-n tensors of k forms (rank-k antisymmetric tensors) as ``vector potentials.'' The generalization, valid in any spatial dimension d, has two key manifestations. First, the objects with mobility restrictions extend beyond simple charges to higher-order multipoles (dipoles, quadrupoles, etc.) all the way to (n\ensuremath-1)th-order multipoles, which we call the order-n fracton condition. Second, these fractonic charges themselves are characterized by tensorial densities of (k\ensuremath-1)-dimensional extended objects. For any (k,n), the theory can be constructed to have a gapless ``photon modes'' with dispersion \ensuremathω\ensuremath∼|q|z, where the integer z can range from 1 to n.