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Renormalization of Ising cage-net model and generalized foliation

Journal Article · · Physical Review. B
 [1];  [2];  [3];  [4];  [2]
  1. California Institute of Technology (CalTech), Pasadena, CA (United States); OSTI
  2. California Institute of Technology (CalTech), Pasadena, CA (United States)
  3. California Institute of Technology (CalTech), Pasadena, CA (United States); University of Colorado, Boulder, CO (United States)
  4. University of Colorado, Boulder, CO (United States)
+ Show Author Affiliations

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 2D 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. Additionally, 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.

Research Organization:
University of Colorado, Boulder, CO (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF); Simons Foundation
Grant/Contract Number:
SC0014415
OSTI ID:
2420360
Journal Information:
Physical Review. B, Journal Name: Physical Review. B Journal Issue: 3 Vol. 108; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

2-dimensional systems
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Fractons
Materials Science
Physics
Renormalization group
Topological order