2019/10/14 by Djordje Radicevic, Radicevic, Djordje · 1 citation
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.str-el #hep-lat #hep-th
paper · pdf · doi:10.48550/arxiv.1910.06336
41 pages, 8 figures. v2: minor clarifications and references added. v3: expanded discussion of models on BCC lattices and with nonabelian symmetries, further minor clarifications and reference additions
arxiv created 2020/03/07 · arxiv updated 2020/03/10
Fracton theories possess exponentially degenerate ground states, excitations with restricted mobility, and nontopological higher-form symmetries. This paper shows that such theories can be defined on arbitrary spatial lattices in three dimensions. The key element of this construction is a generalization of higher-form gauge theories to so-called \mathfrakFp gauge theories, in which gauge transformations of rank-k fields are specified by rank-(k - p) gauge parameters. The ℤ2 rank-two theory of type \mathfrakF2, placed on a cubic lattice and coupled to scalar matter, is shown to have a topological phase exactly dual to the well-known X-cube model. Generalizations of this example yield novel fracton theories. In the continuum, the U(1) rank-two theory of type \mathfrakF2 is shown to have a perturbatively gapless fracton regime that cannot be consistently interpreted as a tensor gauge theory of any kind. The compact scalar fields that naturally couple to this \mathfrakF2 theory also show gapless fracton behavior; on a cubic lattice they have a conserved U(1) charge and dipole moment, but these particular charges are not necessarily conserved on more general lattices. The construction straightforwardly generalizes to \mathfrakF2 theories of nonabelian rank-two gauge fields, giving first examples of pure nonabelian higher-rank theories.