Symmetry and duality in bosonization of two-dimensional Dirac fermions

Abstract

Recent work on a family of boson-fermion mappings has emphasized the interplay of symmetry and duality: Phases related by a particle-vortex duality of bosons (fermions) are related by time-reversal symmetry in their fermionic (bosonic) formulation. We present exact mappings for a number of concrete models that make this property explicit on the operator level. We illustrate the approach with one- and two-dimensional quantum Ising models, and then similarly explore the duality web of complex bosons and Dirac fermions in (2+1) dimensions.

31 pages, 9 figures

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• Conformality loss and quantum criticality in topological Higgs electrodynamics in 2+1 dimensions
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• Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays