Renormalization of Ising cage-net model and generalized foliation

Abstract

A large class of type-I fracton models, including the X-cube model, have been found to be fixed points of the foliated renormalization group (RG). The system size of such foliated models can be changed by adding or removing decoupled layers of $2$D topological states and continuous deformation of the Hamiltonian. In this paper, we study a closely related model -- the Ising cage-net model -- and find that this model is not foliated in the same sense. In fact, we point out certain unnatural restrictions in the foliated RG, and find that removing these restrictions leads to a generalized foliated RG under which the Ising cage-net model is a fixed point, and which includes the original foliated RG as a special case. The Ising cage-net model thus gives a prototypical example of the generalized foliated RG, and its system size can be changed either by condensing / uncondensing bosonic planon excitations near a 2D plane or through a linear depth quantum circuit in the same plane. We show that these two apparently different RG procedures are closely related, as they lead to the same gapped boundary when implemented in part of a plane. Finally, we briefly discuss the implications for foliated fracton phases, whose universal properties will need to be reexamined in light of the generalized foliated RG.

References in corpus (7)

• Generalized Global Symmetries
• Local stabilizer codes in three dimensions without string logical operators
• Condensate induced transitions between topologically ordered phases
• Topological boundary conditions in abelian Chern-Simons theory
• Entanglement renormalization and topological order
• Tensor-product representations for string-net condensed states
• Ground state degeneracy of the Ising cage-net model

Cited by in corpus (7)

• Sequential Quantum Circuits as Maps between Gapped Phases
• Fracton Self-Statistics
• Multipole groups and fracton phenomena on arbitrary crystalline lattices
• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
• Composite subsystem symmetries and decoration of sub-dimensional excitations
• Entanglement renormalization of fractonic anisotropic ${\mathbb{Z}}_N$ Laplacian models
• Planon-modular fracton orders