FCC, Checkerboards, Fractons, and QFT

Abstract

We consider XY-spin degrees of freedom on an FCC lattice, such that the system respects some subsystem global symmetry. We then gauge this global symmetry and study the corresponding $U(1)$ gauge theory on the FCC lattice. Surprisingly, this $U(1)$ gauge theory is dual to the original spin system. We also analyze a similar ${\mathbb{Z}}_N$ gauge theory on that lattice. All these systems are fractonic. The $U(1)$ theories are gapless and the ${\mathbb{Z}}_N$ theories are gapped. We analyze the continuum limits of all these systems and present free continuum Lagrangians for their low-energy physics. Our ${\mathbb{Z}}_2$ FCC gauge theory is the continuum limit of the well known checkerboard model of fractons. Our continuum analysis leads to a straightforward proof of the known fact that this theory is dual to two copies of the ${\mathbb{Z}}_2$ X-cube model. We find new models and new relations between known models. The ${\mathbb{Z}}_N$ FCC gauge theory can be realized by coupling three copies of an anisotropic model of lineons and planons to a certain exotic ${\mathbb{Z}}_2$ gauge theory. Also, although for $N=2$ this model is dual to two copies of the ${\mathbb{Z}}_2$ X-cube model, a similar statement is not true for higher $N$.

88 pages, 3 figures

References in corpus (4)

• Local stabilizer codes in three dimensions without string logical operators
• Foliated Quantum Field Theory of Fracton Order
• Quantum mechanical and information theoretic view on classical glass transitions
• More Exotic Field Theories in 3+1 Dimensions

Cited by in corpus (26)

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• A Modified Villain Formulation of Fractons and Other Exotic Theories
• The low-energy limit of some exotic lattice theories and UV/IR mixing
• Anomaly Inflow for Subsystem Symmetries
• Subsystem Non-Invertible Symmetry Operators and Defects
• Fractons with Twisted Boundary Conditions and Their Symmetries
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• 2+1d Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• Hybrid Fracton Phases: Parent Orders for Liquid and Non-Liquid Quantum Phases
• Quantum effects on unconventional pinch point singularities
• Lattice Quantum Villain Hamiltonians: Compact scalars, $U(1)$ gauge theories, fracton models and Quantum Ising model dualities
• Foliated BF theories and Multipole symmetries
• Generating Lattice Non-invertible Symmetries
• Fractons and exotic symmetries from branes
• Boson-fermion duality with subsystem symmetry
• Gapped Lineon and Fracton Models on Graphs
• Fractons on Graphs and Complexity
• Scalar, fermionic and supersymmetric field theories with subsystem symmetries in d+1 dimensions
• Spectroscopic fingerprints of gapless type-II fracton phases
• ${\mathbb{Z}}_2$ phases and Majorana spectroscopy in paired Bose-Hubbard chains
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions
• Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory
• Entanglement renormalization of fractonic anisotropic ${\mathbb{Z}}_N$ Laplacian models
• Exotic theta terms in 2+1d fractonic field theory
• Planon-modular fracton orders