Planar p-String Condensation: Chiral Fracton Phases from Fractional Quantum Hall Layers and Beyond

Abstract

We present a coupled-wire construction of a model with chiral fracton topological order. The model combines the known construction of $\nu =1/m$ Laughlin fractional quantum Hall states with a planar p-string condensation mechanism. The bulk of the model supports gapped immobile fracton excitations that generate a hierarchy of mobile composite excitations. Open boundaries of the model are chiral and gapless, and can be used to demonstrate a fractional quantized Hall conductance where fracton composites act as charge carriers in the bulk. The planar p-string mechanism used to construct and analyze the model generalizes to a wide class of models including those based on layers supporting non-Abelian topological order. We describe this generalization and additionally provide concrete lattice-model realizations of the mechanism.

9+24 pages, 16 figures; v2 contains updated discussion of Gaussian fluctuations; v3 moves some materials from Appendices to main text and is the version accepted for publication

References in corpus (13)

• Local stabilizer codes in three dimensions without string logical operators
• Condensate induced transitions between topologically ordered phases
• Gauging quantum states: from global to local symmetries in many-body systems
• Fracton topological phases from strongly coupled spin chains
• Foliated Quantum Field Theory of Fracton Order
• Chiral Spin Liquids in Arrays of Spin Chains
• Layer construction of 3D topological states and string braiding statistics
• Isotropic Layer Construction and Phase Diagram for Fracton Topological Phases
• Fracton phases via exotic higher-form symmetry-breaking
• A Generalization of Non-Abelian Anyons in Three Dimensions
• Distilling Fractons from Layered Subsystem-Symmetry Protected Phases
• From coupled wires to coupled layers: Model with three-dimensional fractional excitations
• Fractalizing quantum codes

Cited by in corpus (14)

• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Interaction Enabled Fractonic Higher-Order Topological Phases
• Fractonic topological phases from coupled wires
• Topological defect network representations of fracton stabilizer codes
• Disentangling (2+1)d Topological States of Matter with the Entanglement Negativity
• No Strings Attached: Boundaries and Defects in the Cubic Code
• Three-dimensional fracton topological orders with boundary Toeplitz braiding
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Dihedral twist liquid models from emergent Majorana fermions
• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
• Topological Dipole Insulator
• Weak symmetry breaking and topological order in a 3D compressible quantum liquid
• Infinite-component $BF$ field theory: Connection of fracton order, Toeplitz braiding, and non-Hermitian amplification
• There and Back Again: A Gauging Nexus between Topological and Fracton Phases