Ising Anyons in Frustration-Free Majorana-Dimer Models

Abstract

Dimer models have long been a fruitful playground for understanding topological physics. Here we introduce a new class - termed Majorana-dimer models - wherein bosonic dimers are decorated with pairs of Majorana modes. We find that the simplest examples of such systems realize an intriguing, intrinsically fermionic phase of matter that can be viewed as the product of a chiral Ising theory, which hosts deconfined non-Abelian quasiparticles, and a topological $p_x-i{p}_y$ superconductor. While the bulk anyons are described by a single copy of the Ising theory, the edge remains fully gapped. Consequently, this phase can arise in exactly solvable, frustration-free models. We describe two parent Hamiltonians: one generalizes the well-known dimer model on the triangular lattice, while the other is most naturally understood as a model of decorated fluctuating loops on a honeycomb lattice. Using modular transformations, we show that the ground-state manifold of the latter model unambiguously exhibits all properties of the $\text{Ising}\times (p_x-i{p}_y)$ theory. We also discuss generalizations with more than one Majorana mode per site, which realize phases related to Kitaev's 16-fold way in a similar fashion.

References in corpus (15)

• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Condensate induced transitions between topologically ordered phases
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Characterizing topological order by studying the ground states of an infinite cylinder
• Explicit tensor network representation for the ground states of string-net models
• Strongly interacting Majorana fermions
• Chiral projected entangled-pair state with topological order
• Protection of topological order by symmetry and many-body localization
• Double Semion Phase in an Exactly Solvable Quantum Dimer Model on the Kagome Lattice
• General procedure for determining braiding and statistics of anyons using entanglement interferometry
• Semionic resonating valence bond states
• Tensor-product representations for string-net condensed states
• Measuring Modular Matrices by Shearing Lattices

Cited by in corpus (36)

• Fermionic SPT phases in higher dimensions and bosonization
• Gauging spatial symmetries and the classification of topological crystalline phases
• Gapless Symmetry Protected Topological Order
• Holographic tensor network models and quantum error correction: A topical review
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• Towards a complete classification of fermionic symmetry protected topological phases in 3D and a general group supercohomology theory
• Construction and classification of symmetry protected topological phases in interacting fermion systems
• Discrete spin structures and commuting projector models for 2d fermionic symmetry protected topological phases
• Interacting fermionic symmetry-protected topological phases in two dimensions
• Fermion condensation and super pivotal categories
• Anomaly Matching in the Symmetry Broken Phase: Domain Walls, CPT, and the Smith Isomorphism
• Fermionic projected entangled-pair states and topological phases
• Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions
• Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions
• Jordan-Wigner Dualities for Translation-Invariant Hamiltonians in Any Dimension: Emergent Fermions in Fracton Topological Order
• Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond
• Majorana-Hubbard model on the square lattice
• An Exactly Solvable Model for a $4+1D$ Beyond-Cohomology Symmetry Protected Topological Phase
• Fermion Condensation and Gapped Domain Walls in Topological Orders
• Majorana dimers and holographic quantum error-correcting codes
• Full Commuting Projector Hamiltonians of Interacting Symmetry-Protected Topological Phases of Fermions
• Ground state degeneracy of non-Abelian topological phases from coupled wires
• A UV perspective on mixed anomalies at critical points between bosonic symmetry-protected phases
• Disentangling interacting symmetry protected phases of fermions in two dimensions
• Simulating topological tensor networks with Majorana qubits
• Exactly Solvable Model for Two Dimensional Topological Superconductor
• Anomalous symmetry protected topological states in interacting fermion systems
• Phase diagrams of Majorana-Hubbard ladders
• Spin-one bilinear-biquadratic model on a star lattice
• Commuting-projector Hamiltonians for 2D topological insulators: edge physics and many-body invariants
• Majorana lattices from the quantized Hall limit of a proximitized spin-orbit coupled electron gas
• Commuting-projector Hamiltonians for chiral topological phases built from parafermions
• Unveiling Correlated Two-dimensional Topological Insulators through Fermionic Tensor Network States -- Classification, Edge Theories and Variational Wavefunctions
• Commuting projector models for (3+1)d topological superconductors via string net of (1+1)d topological superconductors
• Models of interacting bosons with exact ground states: a unified approach
• Variational Tensor Wavefunctions for the Interacting Quantum Spin Hall Phase