The authors equip CSS codes with cup product structures to generate logical operators in the Λ-th Clifford hierarchy level on Λ code copies via constant-depth unitaries, and construct code families supporting this for any Λ.
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The paper classifies one-dimensional Abelian translationally covariant modulated symmetries via Jordan normal forms and derives their Goldstone actions, which modify the conventional theorem by type of symmetry.
Decoherence of the color code produces a mixed state with topological entanglement negativity ln 2 that corresponds to an emergent single toric code.
A covariant Maxwell-like fracton theory is constructed in 6D with a symmetric tensor gauge field whose scalar gauge symmetry enforces charge and dipole conservation, restricting isolated charges to immobility.
Relativistic continuous matrix product states yield competitive variational approximations to ground state energies and observables in the phi^4, Sine-Gordon, and Sinh-Gordon models, including strongly coupled regimes.
Non-invertible symmetry-breaking phases are characterized by long-range order parameters obeying generalized algebra, with certain transitions dual to beyond-Landau points of invertible symmetries under precise conditions established via generalized gauging.
The paper gives examples of gauging Z2 symmetries in Dijkgraaf-Witten Z2 theory and Tambara-Yamagami categories via equivariantisation, G-crossed braided zesting, and generalised orbifolds, while introducing zested orbifold data that are Morita-equivalent.
Ensemble averaging in holography is reframed as averaging over topological completions of a relative theory via SymTFT boundary conditions, reproducing known moments in Marolf-Maxfield and Narain models.
Refines charge quantization via homotopy type A whose homotopy groups classify brane charges and homology groups classify higher-form symmetries, deriving swampland-like constraints that rule out noncompact gauge groups and non-nilpotent Lie algebras for field strengths.
The continuum limit of gauged tensor networks is well defined and produces a new class of states for non-perturbative continuum gauge theories.
Inserting a symmetry defect along the orientation-reversing cycle on a Klein bottle in a 2D Z2 SPT phase induces an extra ground state charge that persists at the transition to the trivial phase, causing exact two-fold degeneracy independent of system size.
A rank-4 tensor gauge theory yields emergent fracton strings with a new generalised dipole conservation law for closed strings and reduces to linearised area-metric gravity in a suitable limit.
Decohered non-Abelian Kitaev quantum double states exhibit strong-to-weak spontaneous symmetry breaking of non-invertible higher-form symmetries and form an information convex set whose dimension equals the pure-state ground-state degeneracy.
The paper reviews how the ZSR equation's chaotic solutions may produce gluon condensation that appears as broken-power-law spectra in cosmic gamma rays, potentially bridging QCD and astrophysics.
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Cups and Gates I: Cohomology invariants and logical quantum operations
The authors equip CSS codes with cup product structures to generate logical operators in the Λ-th Clifford hierarchy level on Λ code copies via constant-depth unitaries, and construct code families supporting this for any Λ.
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Translationally Covariant Modulated Symmetries: Classification and Goldstone
The paper classifies one-dimensional Abelian translationally covariant modulated symmetries via Jordan normal forms and derives their Goldstone actions, which modify the conventional theorem by type of symmetry.
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Decohered color code and emerging mixed toric code by anyon proliferation: Topological entanglement negativity perspective
Decoherence of the color code produces a mixed state with topological entanglement negativity ln 2 that corresponds to an emergent single toric code.
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Covariant Fracton Electrodynamics in Six Dimensions
A covariant Maxwell-like fracton theory is constructed in 6D with a symmetric tensor gauge field whose scalar gauge symmetry enforces charge and dipole conservation, restricting isolated charges to immobility.
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Some progress on the use of the variational method in quantum field theory
Relativistic continuous matrix product states yield competitive variational approximations to ground state energies and observables in the phi^4, Sine-Gordon, and Sinh-Gordon models, including strongly coupled regimes.
-
Spontaneous breaking of non-invertible symmetries and duality to beyond-Landau transitions
Non-invertible symmetry-breaking phases are characterized by long-range order parameters obeying generalized algebra, with certain transitions dual to beyond-Landau points of invertible symmetries under precise conditions established via generalized gauging.
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Examples of Invertible Gauging via Orbifold Data, Zesting, and Equivariantisation
The paper gives examples of gauging Z2 symmetries in Dijkgraaf-Witten Z2 theory and Tambara-Yamagami categories via equivariantisation, G-crossed braided zesting, and generalised orbifolds, while introducing zested orbifold data that are Morita-equivalent.
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From Baby Universes to Narain Moduli: Topological Boundary Averaging in SymTFTs
Ensemble averaging in holography is reframed as averaging over topological completions of a relative theory via SymTFT boundary conditions, reproducing known moments in Marolf-Maxfield and Narain models.
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Generalised Symmetries and Swampland-Type Constraints from Charge Quantisation via Rational Homotopy Theory
Refines charge quantization via homotopy type A whose homotopy groups classify brane charges and homology groups classify higher-form symmetries, deriving swampland-like constraints that rule out noncompact gauge groups and non-nilpotent Lie algebras for field strengths.
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Continuum limit of gauged tensor network states
The continuum limit of gauged tensor networks is well defined and produces a new class of states for non-perturbative continuum gauge theories.
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Transition between 2D Symmetry Protected Topological Phases on a Klein Bottle
Inserting a symmetry defect along the orientation-reversing cycle on a Klein bottle in a 2D Z2 SPT phase induces an extra ground state charge that persists at the transition to the trivial phase, causing exact two-fold degeneracy independent of system size.
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Emergent fracton strings from covariant bi-form gauge field theory
A rank-4 tensor gauge theory yields emergent fracton strings with a new generalised dipole conservation law for closed strings and reduces to linearised area-metric gravity in a suitable limit.
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Strong-to-weak spontaneous symmetry breaking of higher-form non-invertible symmetries in Kitaev's quantum double model
Decohered non-Abelian Kitaev quantum double states exhibit strong-to-weak spontaneous symmetry breaking of non-invertible higher-form symmetries and form an information convex set whose dimension equals the pure-state ground-state degeneracy.
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Looking for Condensed Gluons: A Cross-Scale Journey from the Deep Structure of Protons to High-Energy Cosmic Rays -- A Mini-Review
The paper reviews how the ZSR equation's chaotic solutions may produce gluon condensation that appears as broken-power-law spectra in cosmic gamma rays, potentially bridging QCD and astrophysics.
- Lattice Gauging Interfaces and Noninvertible Defects in Higher Dimensions