Symmetry and Duality in Bosonization of Two-Dimensional Dirac Fermions

David F. Mross; Jason Alicea; Olexei I. Motrunich

doi:10.1103/PhysRevX.7.041016

Symmetry and Duality in Bosonization of Two-Dimensional Dirac Fermions

David F. Mross, Jason Alicea, Olexei I. Motrunich

Department of Condensed Matter Physics

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	041016
Number of pages	35
Journal	Physical Review X
Volume	7
Issue number	4
DOIs	https://doi.org/10.1103/PhysRevX.7.041016
State	Published - 23 Oct 2017

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

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https://arxiv.org/abs/1705.01106License: Other

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

author = "Mross, \{David F.\} and Jason Alicea and Motrunich, \{Olexei I.\}",

note = "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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doi = "10.1103/PhysRevX.7.041016",

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N2 - 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.

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Symmetry and Duality in Bosonization of Two-Dimensional Dirac Fermions

Abstract

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