Develops a Mille-feuille SymTFT construction that generates foliated and exotic dual bulk theories realizing gapless boundary models with spontaneous continuous subsystem symmetry breaking, including duals of the XY plaquette and XYZ cube models.
Local stabilizer codes in three dimensions without string logical operators
5 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We suggest concrete models for self-correcting quantum memory by reporting examples of local stabilizer codes in 3D that have no string logical operators. Previously known local stabilizer codes in 3D all have string-like logical operators, which make the codes non-self-correcting. We introduce a notion of "logical string segments" to avoid difficulties in defining one dimensional objects in discrete lattices. We prove that every string-like logical operator of our code can be deformed to a disjoint union of short segments, and each segment is in the stabilizer group. The code has surface-like logical operators whose partial implementation has unsatisfied stabilizers along its boundary.
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The authors introduce fractonic solids via a new symmetry that ties fracton mobility to a material, enabling gauge-invariant momentum, boost compatibility, and gravitational coupling.
Decoherence on abelian topological order is modeled as a temporal defect in double TQFT driving boundary anyon condensation transitions classified by Lagrangian subgroups of the doubled order.
New analytic constructions yield quantum lattice models with continuous symmetry breaking and chiral topological order at arbitrarily high temperatures via entropic stabilization.
An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.
citing papers explorer
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SymTFT construction of gapless exotic-foliated dual models
Develops a Mille-feuille SymTFT construction that generates foliated and exotic dual bulk theories realizing gapless boundary models with spontaneous continuous subsystem symmetry breaking, including duals of the XY plaquette and XYZ cube models.
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Fractonic solids
The authors introduce fractonic solids via a new symmetry that ties fracton mobility to a material, enabling gauge-invariant momentum, boost compatibility, and gravitational coupling.
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Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions
Decoherence on abelian topological order is modeled as a temporal defect in double TQFT driving boundary anyon condensation transitions classified by Lagrangian subgroups of the doubled order.
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Exploring Entropic Orders: High Temperature Continuous Symmetry Breaking, Chiral Topological States and Local Commuting Projector Models
New analytic constructions yield quantum lattice models with continuous symmetry breaking and chiral topological order at arbitrarily high temperatures via entropic stabilization.
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Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.