Bosonization based on Clifford algebras and its gauge theoretic interpretation

Abstract

We study the properties of a bosonization procedure based on Clifford algebra valued degrees of freedom, valid for spaces of any dimension. We present its interpretation in terms of fermions in presence of ${\mathbb{Z}}_2$ gauge fields satisfying a modified Gauss' law, resembling Chern-Simons-like theories. Our bosonization prescription involves constraints, which are interpreted as a flatness condition for the gauge field. Solution of the constraints is presented for toroidal geometries of dimension two. Duality between our model and $(d-1)$-form ${\mathbb{Z}}_2$ gauge theory is derived, which elucidates the relation between the approach taken here with another bosonization map proposed recently.

arXiv commentRevised version. 36 pages, 6 figures

References in corpus (24)

• Fault-tolerant quantum computation by anyons
• Generalized Global Symmetries
• Bosonization and Strongly Correlated Systems
• Fermionic quantum computation
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• Chern-Simons Theory with Finite Gauge Group
• Exactly solvable Kitaev model in three dimensions
• 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: ${\mathbf{Z}}_2$ Gauge Fields and Arf Invariants
• Twisted Gauge Theory Model of Topological Phases in Three Dimensions
• Duality between $(2+1)d$ Quantum Critical Points
• Bosonization in Higher Dimensions
• Topological phases and quantum computation
• Fermions without fermi fields
• 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
• Solving the sign problems of the massless lattice Schwinger model with a dual formulation
• Exact bosonization in arbitrary dimensions
• Potts Flux Tube Model at Nonzero Chemical Potential
• Constraints of kinematic bosonization in two and higher dimensions

Cited by in corpus (9)

• Equivalence between fermion-to-qubit mappings in two spatial dimensions
• Quantum phases of two-dimensional ${\mathbb{Z}}_2$ gauge theory coupled to single-component fermion matter
• Higher-dimensional Jordan-Wigner Transformation and Auxiliary Majorana Fermions
• Low-depth simulations of fermionic systems on square-grid quantum hardware
• Error-correcting codes for fermionic quantum simulation
• Bosonization of Majorana modes and edge states
• Dynamics of a lattice 2-group gauge theory model
• Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids
• Local fermion-to-qudit mappings: a practical recipe for four-level systems