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.
Anomaly-free symmetries with obstructions to gauging and onsiteability
9 Pith papers cite this work. Polarity classification is still indexing.
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UNVERDICTED 9representative 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.
Lattice CPT symmetry upgrades the Onsager chiral symmetry anomaly from order two to infinite order, better matching the continuum chiral anomaly, with discussion of associated 2+1d SPT phases.
Sequential circuit invariants detect non-invertible symmetry anomalies and characterize non-Abelian fermionic loops plus a new mixed topological order in (3+1)D.
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.
The paper shows phase equivalence for two 1D mixed-state phases connected by a phase transition by constructing low-depth channel circuits from parent Lindbladians, generalizing the analysis to intrinsically nontrivial cases beyond fixed points.
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.
Anomaly inflow on monodromy defects in anomalous symmetry theories defines them as domain walls inducing topological order, yielding protected chiral edge modes and adiabatic pumping of gapless degrees of freedom, verified in chiral symmetry examples on continuum and lattice.
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
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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.
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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.
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Infinite-Order Lattice Chiral Anomalies and CPT
Lattice CPT symmetry upgrades the Onsager chiral symmetry anomaly from order two to infinite order, better matching the continuum chiral anomaly, with discussion of associated 2+1d SPT phases.
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Invariants of Sequential Circuits and Generalized Non-Abelian Statistics
Sequential circuit invariants detect non-invertible symmetry anomalies and characterize non-Abelian fermionic loops plus a new mixed topological order in (3+1)D.
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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.
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Establishing Mixed-State Phase Equivalence beyond Renormalization Fixed Points
The paper shows phase equivalence for two 1D mixed-state phases connected by a phase transition by constructing low-depth channel circuits from parent Lindbladians, generalizing the analysis to intrinsically nontrivial cases beyond fixed points.
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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.
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When Symmetries Twist: Anomaly Inflow on Monodromy Defects
Anomaly inflow on monodromy defects in anomalous symmetry theories defines them as domain walls inducing topological order, yielding protected chiral edge modes and adiabatic pumping of gapless degrees of freedom, verified in chiral symmetry examples on continuum and lattice.
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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.