Mirror symmetry and the half-filled Landau level

Abstract

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.

36 pages including appendices, v.2 slightly clarified review, fixed typos, and added references

References in corpus (17)

• The electronic properties of graphene
• Non-Abelian Anyons and Topological Quantum Computation
• Topological Insulators with Inversion Symmetry
• Topological Field Theory of Time-Reversal Invariant Insulators
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Particle-hole symmetry and the Pfaffian state
• Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Is the Composite Fermion a Dirac Particle?
• Are non-Fermi-liquids stable to Cooper pairing?
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Dual Dirac liquid on the surface of the electron topological insulator
• Particle-Hole Symmetry and the Composite Fermi Liquid
• Composite Dirac liquids: parent states for symmetric surface topological order
• A controlled expansion for certain non-Fermi liquid metals
• Aspects of Renormalization in Finite Density Field Theory
• Enhanced Pairing of Quantum Critical Metals Near d=3+1

Cited by in corpus (55)

• Level/rank Duality and Chern-Simons-Matter Theories
• Particle-Vortex Duality from 3d Bosonization
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
• Particle-vortex duality in topological insulators and superconductors
• Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids
• Bosonization and Mirror Symmetry
• Nonsupersymmetric dualities from mirror symmetry
• Self-dual Quantum Electrodynamics as Boundary State of the three dimensional Bosonic Topological Insulator
• Emergence of supersymmetric quantum electrodynamics
• The nature of composite fermions and the role of particle hole symmetry: A microscopic account
• Composite fermi liquids in the lowest Landau level
• Exact Boson-Fermion Duality on a 3D Euclidean Lattice
• Composite fermion duality for half-filled multicomponent Landau Levels
• Composite fermions and the field-tuned superconductor-insulator transition
• The $\nu =\frac{1}{2}$ Landau level: Half-full or half-empty?
• Emergent particle-hole symmetry in the half-filled Landau level
• Nematic quantum phase transition of composite Fermi liquids in half-filled Landau levels and their geometric response
• Landau-Level Mixing and Particle-Hole Symmetry Breaking for Spin Transitions in the Fractional Quantum Hall Effect
• Paired states at 5/2: PH Pfaffian and particle-hole symmetry breaking
• Fractional $S$-duality, Classification of Fractional Topological Insulators and Surface Topological Order
• The Quantum Hall Effect in Supersymmetric Chern-Simons Theories
• Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions
• Geometric Resonance of Composite Fermions near Bilayer Quantum Hall States
• Emergent particle-hole symmetry in spinful bosonic quantum Hall systems
• Non-Abelian bosonization and modular transformation approach to superuniversality
• Loop Models, Modular Invariance, and Three Dimensional Bosonization
• Strong-Weak Chern-Simons-Matter Dualities from a Lattice Construction
• Bosonic Analogue of Dirac Composite Fermi Liquid
• Weiss oscillations and particle-hole symmetry at the half-filled Landau level
• Parity Anomaly and Duality Web
• Particle-hole symmetry for composite fermions: An emergent symmetry in the fractional quantum Hall effect
• Particle-vortex symmetric liquid
• Entanglement entropy of composite Fermi liquid states on the lattice: In support of the Widom formula
• Quantum phase transition in many-flavor supersymmetric QED${}_3$
• Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System
• Geometric Resonance of Four-Flux Composite Fermions
• Nematic fluctuations balancing the zoo of phases in half-filled quantum Hall systems
• Non-Abelian Fermionization and Fractional Quantum Hall Transitions
• Fluctuations and magnetoresistance oscillations near the half-filled Landau level
• Duality Web on a 3D Euclidean Lattice and Manifestation of Hidden Symmetries
• Pairing of particle-hole symmetric composite fermions in half-filled Landau level
• Partial filled Landau Level at even denominator, a vortex metal with Berry phase
• Fermionic Response in Finite-Density ABJM Theory with Broken Symmetry
• Pairing instabilities of Dirac composite fermions
• Scaling and Diffusion of Dirac Composite Fermions
• Thermal Hall response of an abelian chiral spin liquid at finite temperatures
• Universal conductivity at a 2d superconductor-insulator transition: the effects of quenched disorder and Coulomb interaction
• Discussion of the Duality in Three Dimensional Quantum Field Theory
• A Duality Web in Condensed Matter Systems
• Random Magnetic Field and the Dirac Fermi Surface
• Current Algebra Approach to 2d Chiral Metals
• Specific heat and pairing of Dirac composite fermions in the half-filled Landau level
• Nonperturbative emergence of Dirac fermion in strongly correlated composite fermions of fractional quantum Hall effects
• "Self-Dual" Quantum Critical Point on the surface of $3d$ Topological Insulator