Mirror symmetry and the half-filled Landau level

• Autores: Kachru, Shamit; Mulligan, Michael; Torroba, Gonzalo; Wang, Huajia
• Año de publicación: 2015
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Fractional Quantum Hall Effect; Supersymmetry; Duality; Mirror Symmetry
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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.
Fil: Kachru, Shamit. University of Stanford; Estados Unidos. Stanford Linear Accelerator Center; Estados Unidos
Fil: Mulligan, Michael. University of Stanford; Estados Unidos
Fil: Torroba, Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Fil: Wang, Huajia. University of Stanford; Estados Unidos