A layered gauging method constructs (k+1)-dimensional topological orders, including fracton models like the X-cube, from k-dimensional symmetries such as subsystem, anomalous, or noninvertible ones.
2025.arXiv e-prints
7 Pith papers cite this work. Polarity classification is still indexing.
7
Pith papers citing it
citation-role summary
background 3
method 1
citation-polarity summary
representative citing papers
Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
Parameterized families of toric code Hamiltonians realize em-duality pumping and higher-order anyon pumping, diagnosed by topological pumping into tensor-network bond spaces and corner modes.
For finite 1-form symmetries in (2+1)D, onsiteability holds exactly when the 't Hooft anomaly meets an algebraic condition allowing 1-gauging; the symmetry can then be realized as transversal Pauli operators via ancillas and circuits.
The review summarizes Lieb-Schultz-Mattis anomalies and anomaly matching, starting from spin chains and extending to higher dimensions, disordered systems, fermionic systems, and symmetry-protected topological phases.
citing papers explorer
-
Constructing Bulk Topological Orders via Layered Gauging
A layered gauging method constructs (k+1)-dimensional topological orders, including fracton models like the X-cube, from k-dimensional symmetries such as subsystem, anomalous, or noninvertible ones.
-
Symmetry Spans and Enforced Gaplessness
Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
-
Parameterized Families of Toric Code Phase: $em$-duality family and higher-order anyon pumping
Parameterized families of toric code Hamiltonians realize em-duality pumping and higher-order anyon pumping, diagnosed by topological pumping into tensor-network bond spaces and corner modes.
-
Onsiteability of Higher-Form Symmetries
For finite 1-form symmetries in (2+1)D, onsiteability holds exactly when the 't Hooft anomaly meets an algebraic condition allowing 1-gauging; the symmetry can then be realized as transversal Pauli operators via ancillas and circuits.
-
Lieb-Schultz-Mattis Anomalies and Anomaly Matching
The review summarizes Lieb-Schultz-Mattis anomalies and anomaly matching, starting from spin chains and extending to higher dimensions, disordered systems, fermionic systems, and symmetry-protected topological phases.
- When Symmetries Twist: Anomaly Inflow on Monodromy Defects
- Establishing Mixed-State Phase Equivalence beyond Renormalization Fixed Points