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Mirror symmetry and the half-filled Landau level by Kachru, Shamit; Mulligan, Michael; Torroba, Gonzalo; Wang, Huajia is a scholarly article available to read on EtoBox.

What is Mirror symmetry and the half-filled Landau level about?

We study the dynamics of the half-filled zeroth Landau level of Dirac fermions using mirror symmetry, a supersymmetric duality between certain pairs of $2+1$-dimensional theories. We show that the half-filled zeroth Landau level of a pair of Dirac fermions is dual to a pair of Fermi surfaces of electrically-neutral composite fermions, coupled to an emergent gauge field. Thus, we use supersymmetry to provide a derivation of flux attachment and the emergent Fermi liquid-like state for the lowest Landau level of Dirac fermions. We find that in the dual theory the Coulomb interaction induces a dynamical exponent $z=2$ for the emergent gauge field, making the interactions classically marginal. This enables us to map the problem of $2+1$-dimensional Dirac fermions in a finite transverse magnetic field, interacting via a strong Coulomb interaction, into a perturbatively controlled model. We analyze the resulting low-energy theory using the renormalization group and determine the nature of the BCS interaction in the emergent composite Fermi liquid.

Author

Kachru, Shamit; Mulligan, Michael; Torroba, Gonzalo; Wang, Huajia

Published

2015

Language

EN