Journal
PHYSICAL REVIEW B
Volume 100, Issue 23, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.100.235150
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Funding
- US Department of Energy [DE-FG02-13ER41958]
- Simons Foundation
- Chicago MRSEC - NSF [DMR-1420709]
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We consider a (2 + 1)-dimensional Wilson-Fisher boson coupled to a (3 + 1)-dimensional U(1) gauge field. This theory possesses a strong-weak duality in terms of the coupling constant e and is self-dual at a particular value of e. We derive exact relations between transport coefficients for a v = 1 quantum Hall state at the self-dual point. Using boson-fermion duality, we map the v = 1 bosonic quantum Hall state to a Fermi sea of the dual fermion and observe that the exact relationships between transport coefficients at the bosonic self-dual point are reproduced by a simple random-phase approximation (RPA), coupled with a Drude formula, in the fermionic theory. We explain this success of the RPA by pointing out a cancellation of a parity-breaking term in the fermion theory which occurs only at the self-dual point, resulting in the fermion self-dual theory explored previously. In addition, we argue that the equivalence of the self-dual structure can be understood in terms of electromagnetic duality or modular invariance, and these features are not inherited by the nonrelativistic cousins of the present model.
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