Symmetry and duality in bosonization of two-dimensional Dirac fermions

Creators: Mross, David F.; Alicea, Jason; Motrunich, Olexei I.

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. We generalize the latter to systems with long-range interactions and discover a continuous family of dualities embedding the previously studied cases.

Additional Information

© 2017 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Received 13 May 2017; published 23 October 2017. We gratefully acknowledge Chong Wang, Matthew Fisher, Yin-Chen He, and D. T. Son for valuable discussions. This work was supported by the NSF through Grants No. DMR-1341822 and DMR-1723367 (J. A.) and No. DMR-1619696 (O. I. M.). We also acknowledge support by the Institute for Quantum Information and Matter, a NSF Physics Frontiers Center, with support from the Gordon and Betty Moore Foundation.

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Published - PhysRevX.7.041016.pdf

Submitted - 1705.01106.pdf

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