Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
By S. Vijay, Jeongwan Haah, Liang Fu. 2016
447 citations recorded by the source corpus.
We introduce a generalization of conventional lattice gauge theory to describe fracton topological phases, which are characterized by immobile, pointlike topological excitations, and subextensive topological degeneracy. We demonstrate a duality between fracton topological order and interacting spin systems with symmetries along extensive, lower-dimensional subsystems, which may be used to systematically search for and characterize fracton topological phases. Commutative algebra and elementary algebraic geometry provide an effective mathematical tool set for our results. Our work paves the way for identifying possible material realizations of fracton topological phases.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/fe4127d5d276793c5d3386ef27c49779fc2c23ce
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Localization in Fractonic Random Circuits (2018, background): “Parallel to the developments in quantum dynamics, recent years have also witnessed an explosion of interest in fracton phases of quantum matter [26–45] - for a review, see [46].”
- Fractons (2018, methodology): “[12] started from subsystem-symmetric spin models as a means to discover new fracton models, including the X-cube model.”
- Fracton hydrodynamics (2020, background): “Other fracton models are understood by duality to systems with subsystem symmetries [68].”
- Generalized Symmetries in Condensed Matter (2022, unknown): “Foliated fracton phases (68) like the X-cube model (69) spontaneously break a ‘foliated 1-form symmetry’ acting independently on each plane of a lattice (65).”
- Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians (2019, background): “[50] Sagar Vijay, Jeongwan Haah, and Liang Fu, “Fracton topological order, generalized lattice gauge theory, and duality,” Phys.”
- Fracton phases of matter (2020, methodology): “It was not until the seminal work of Vijay, Haah, and Fu that it became clear that these models were only two examples of a much larger class of fracton systems, representing a fundamentally new type of phase of matter [3, 4].”
- Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases (2021, methodology): “Fourth, we achieve a new perspective on Kramers-Wannier (KW) [18, 70–78] and Jordan-Wigner (JW) [79– 87] transformations.”
- Localization from Hilbert space shattering: From theory to physical realizations (2020, background): “[31] Sagar Vijay, Jeongwan Haah, and Liang Fu, “Fracton”