# 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

- "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.) - "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.) - "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.) - "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.) - "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.) - "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.) - "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.) - "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.) - "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.) - "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.) - "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.) - 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.) - "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.) - "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.)