Self-dual $\nu =1$ bosonic quantum Hall state in mixed-dimensional QED

Journal Article · 30 December 2019 · Physical Review B

DOI: https://doi.org/10.1103/physrevb.100.235150 · OSTI ID:1801933

Hsiao, Wei-Han  ^[1]; Son, Dam Thanh ^[2]

---

1. Univ. of Chicago, IL (United States); OSTI
2. Univ. of Chicago, IL (United States)

Here, 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 $$\mathcal{e}$$. We derive exact relations between transport coefficients for a $$\mathcal{ν}$$ = 1 quantum Hall state at the self-dual point. Using boson-fermion duality, we map the $$\mathcal{ν}$$ = 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.

• Research Organization: Univ. of Chicago, IL (United States)
• Sponsoring Organization: National Science Foundation (NSF); Simons Foundation; USDOE Office of Science (SC)
• Grant/Contract Number: SC0009924
• OSTI ID: 1801933
• Journal Information: Physical Review B, Journal Name: Physical Review B Journal Issue: 23 Vol. 100; ISSN 2469-9950
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English