Fracton

One major open problem in quantum information theory is how to build a quantum hard drive, i.e. a quantum system that can store quantum information reliably for a long time without active error correction. No completely satisfying solution to this problem has been found, but in the search a whole new class of quantum many-body models have been discovered with exotic properties never seen before. This new class of models, dubbed the "fracton" models, have point excitations that cannot move freely, a robust ground state degeneracy that increases with system size, and slow dynamics even without any disorder. While fracton models exhibit a variety of exotic properties, it is not known which ones are universal and relatedly how to define a fracton phase. We realized that for a large class of fracton models -- the type I fracton models -- their properties depends on the foliation structure of the underlying manifold. In particular, the renormalization group transformation of these models involves adding / removing topological features in parallel planes. By allowing such sub-manifold changes of topological features, we obtain a useful definition of fracton phase which relates many seemingly different models and identify the direction of search for new phases.

Related Publications

1. "Fracton Models on General Three-Dimensional Manifolds",Wilbur Shirley, Kevin Slagle, Zhenghan Wang, Xie Chen, Phys. Rev. X 8, 031051 (2018).
   (Reveals the foliation structure of the X-cube model.)
2. "Fracton topological order via coupled layers", Han Ma, Ethan Lake, Xie Chen, Michael Hermele, Phys. Rev. B 95, 245126 (2017).
   (Coupled layer construction of the X-cube and the semionic X-cube model.)
3. "Fracton topological order from Higgs and partial confinement mechanisms of rank-two gauge theory", Han Ma, Michael Hermele, Xie Chen, Phys. Rev. B 98, 035111 (2018).
   (X-cube model from Higgsing the 'hollow' rank-two gauge theory.)
4. "Universal entanglement signatures of foliated fracton phases", Wilbur Shirley, Kevin Slagle, Xie Chen, SciPost Phys. 6, 015 (2019).
   (The universal entanglement measures in a foliated fracton phase.)
5. "Fractional excitations in foliated fracton phases", Wilbur Shirley, Kevin Slagle, Xie Chen, Annals of Physics, 410, 167922 (2019).
   (The universal fractional excitation properties in a foliated fracton phase.)
6. "Foliated fracton order in the checkerboard model", Wilbur Shirley, Kevin Slagle, Xie Chen, Phys. Rev. B 99, 115123 (2019).
   (Showing that the checkerboard model is equivalent to two copies of the Xcube model as a foliated fracton order.)
7. "Foliated fracton order from gauging subsystem symmetries", Wilbur Shirley, Kevin Slagle, Xie Chen, SciPost Phys. 6, 041 (2019).
   (Foliated fracton order obtained from gauging planar symmetries in 3D models.)
8. "Foliated fracton order in the Majorana checkerboard model", Taige Wang, Wilbur Shirley, Xie Chen, Phys. Rev. B 100, 085127 (2019).
   (The Majorana checkerboard model is equivalent to the Xcube model as a foliated fracton order.)
9. "Fracton Phases of Matter", Michael Pretko, Xie Chen, Yizhi You, International Journal of Modern Physics A, 35, 06, 2030003 (2020).
   (A review article on fracton.)
10. "Twisted foliated fracton phases", Wilbur Shirley, Kevin Slagle, Xie Chen, Phys. Rev. B 102, 115103 (2020).
    (Foliated fracton phases that are not equivalent to X-cube.)
11. "Screw dislocations in the X-cube fracton model", Nandagopal Manoj, Kevin Slagle, Wilbur Shirley, Xie Chen, SciPost Phys. 10, 094 (2021).
    (Zero modes on screw dislocations reveal nontrivial foliated fracton order.)
12. Xiuqi Ma, Wilbur Shirley, Meng Cheng, Michael Levin, John McGreevy, Xie Chen, "Fractonic order in infinite-component Chern-Simons gauge theories", Phys. Rev. B 105, 195124 (2022).
    (Foliated and beyond foliated fracton order in Chern-Simon theories with infinite component U(1) gauge fields.)
13. "Ground state degeneracy of the Ising cage-net model", Xiuqi Ma, Ananth Malladi, Zongyuan Wang, Zhenghan Wang, Xie Chen, Phys. Rev. B 107, 085123 (2023).
    (Explicit calculation of the ground state degeneracy of the Ising Cage-net model to show that it is not a foliated fracton order in the previously defined sense. An operator algebra method was developed to carry out this calculation.)
14. "Renormalization of Ising cage-net model and generalized foliation", Zongyuan Wang, Xiuqi Ma, David T. Stephen, Michael Hermele, Xie Chen, Phys. Rev. B 108, 035148 (2023).
    (A more generalized definition of foliated fracton order that incorporates Ising Cage-net like models.)