Bosonization of Majorana modes and edge states
arXiv:2107.06335 · doi:10.1103/PhysRevB.105.155105
Abstract
We present a bosonization procedure which replaces fermions with generalized spin variables subject to local constraints. It requires that the number of Majorana modes per lattice site matches the coordination number modulo two. If this condition is not obeyed, then bosonization introduces additional fermionic excitations not present in the original model. In the case of one Majorana mode per site on a honeycomb lattice, we recover a sector of Kitaev's model. We discuss also decagonal and rectangular geometries and present bosonization of the Hubbard model. For geometries with a boundary we find that certain fermionic edge modes naturally emerge. They are of different nature than edge modes encountered in topological phases of matter. Euclidean representation for the unconstrained version of a spin system of the type arising in our construction is derived and briefly studied by computing some exact averages for small volumes.
arXiv comment15 pages, 12 figures
References in corpus (40)
- Fault-tolerant quantum computation by anyons
- Anyons in an exactly solved model and beyond
- Unpaired Majorana fermions in quantum wires
- Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
- Majorana Zero Modes and Topological Quantum Computation
- Fermionic quantum computation
- A Duality Web in 2+1 Dimensions and Condensed Matter Physics
- Is the Composite Fermion a Dirac Particle?
- Particle-Vortex Duality from 3d Bosonization
- Mapping local Hamiltonians of fermions to local Hamiltonians of spins
- Fermionic SPT phases in higher dimensions and bosonization
- Spin TQFTs and fermionic phases of matter
- A Web of 2d Dualities: Gauge Fields and Arf Invariants
- Algebraic spin liquid in an exactly solvable spin model
- Duality between Quantum Critical Points
- The Bond-Algebraic Approach to Dualities
- Bosonization in Higher Dimensions
- Microscopic models for Kitaev's sixteenfold way of anyon theories
- Bond Algebras and Exact Solvability of Hamiltonians: Spin S=1/2 Multilayer Systems and Other Curiosities
- Fermions without fermi fields
- A -matrix generalization of the Kitaev model
- Exact bosonization in two spatial dimensions and a new class of lattice gauge theories
- Eliminating fermionic matter fields in lattice gauge theories
- Bosonization in three spatial dimensions and a 2-form gauge theory
- Three-dimensional topological phase on the diamond lattice
- Exact Boson-Fermion Duality on a 3D Euclidean Lattice
- Emulating quantum teleportation of a Majorana zero mode qubit
- Solving the sign problems of the massless lattice Schwinger model with a dual formulation
- Exact bosonization in arbitrary dimensions
- Thermodynamic classification of three-dimensional Kitaev spin liquids
- Three-dimensional topological phases in a layered honeycomb spin-orbital model
- Zero modes, Bosonization and Topological Quantum Order: The Laughlin State in Second Quantization
- Bosonization based on Clifford algebras and its gauge theoretic interpretation
- Constraints of kinematic bosonization in two and higher dimensions
- Three-dimensional Topological Insulators and Bosonization
- Statistical interactions and boson-anyon duality in fractional quantum Hall fluids
- Anatomy of Z2 fluxes in anyon Fermi liquids and Bose condensates
- Partial flux ordering and thermal Majorana metals in (higher-order) spin liquids
- Quantum phase diagram of Shiba impurities from bosonization
- From Luttinger liquids to Luttinger droplets via higher-order bosonization identities