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arXiv · 1705.05841

Exact Boson-Fermion Duality on a 3D Euclidean Lattice

Jing-Yuan Chen·Jun Ho Son·Chao Wang·S. Raghu
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Abstract

The idea of statistical transmutation plays a crucial role in descriptions of the fractional quantum Hall effect. However, a recently conjectured duality between a critical boson and a massless 2-component Dirac fermion extends this notion to gapless systems. This duality sheds light on highly non-trivial problems such as the half-filled Landau level, the superconductor-insulator transition, and surface states of strongly coupled topological insulators. Although this boson-fermion duality has undergone many consistency checks, it has remained unproven. We describe the duality in a non-perturbative fashion using an exact UV mapping of partition functions on a 3D Euclidean lattice.

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Jing-Yuan Chen, Jun Ho Son, Chao Wang, S. Raghu. 2017-12-22. Exact Boson-Fermion Duality on a 3D Euclidean Lattice. https://doi.org/10.1103/physrevlett.120.016602

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