Numerical Study of a Dual Representation of the Integer Quantum Hall Transition

Abstract

We study the critical properties of the non-interacting integer quantum Hall to insulator transition (IQHIT) in a "dual" composite-fermion (CF) representation. A key advantage of the CF representation over electron coordinates is that at criticality, $\text{CF states are delocalized at all}$ energies. The CF approach thus enables us to study the transition from a new vantage point. Using a lattice representation of CF mean-field theory, we compute the critical and multifractal exponents of the IQHIT. We obtain $\nu =2.56\pm 0.02$ and $\eta =0.51\pm 0.01$, both of which are consistent with the predictions of the Chalker-Coddington network model formulated in the electron representation.

arXiv comment8 pages, 7 figures; v2: published version

References in corpus (36)

• Anderson Transitions
• Continuous Quantum Phase Transitions
• Scaling Theory of the Integer Quantum Hall Effect
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Is the Composite Fermion a Dirac Particle?
• Corrections to scaling at the Anderson transition
• Gauge-invariant response functions of fermions coupled to a gauge field
• Exact relations between multifractal exponents at the Anderson transition
• Lowest-Landau-level theory of the quantum Hall effect: the Fermi-liquid-like state
• Critical exponent for the quantum Hall transition
• A dipole interpretation of the $\nu =1/2$ state
• Evidence for charge-flux duality near the quantum Hall liquid to insulator transition
• Multifractality at the quantum Hall transition: Beyond the parabolic paradigm
• Towards a Field Theory of the Plateau Transition
• Finite Size Effects and Irrelevant Corrections to Scaling near the Integer Quantum Hall Transition
• Conformal invariance, multifractality, and finite-size scaling at Anderson localization transitions in two dimensions
• Numerical study of the localization length critical index in a network model of plateau-plateau transitions in the quantum Hall effect
• Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level
• The integer quantum Hall plateau transition is a current algebra after all
• Conformal field theory of the integer quantum Hall plateau transition
• Short-Range Interactions and Scaling Near Integer Quantum Hall Transitions
• Geometrically disordered network models, quenched quantum gravity, and critical behavior at quantum Hall plateau transitions
• Integer quantum Hall effect of interacting electrons: dynamical scaling and critical conductivity
• Topological quantum number and critical exponent from conductance fluctuations at the quantum Hall plateau transition
• Integer quantum Hall transition on a tight-binding lattice
• Finite Size Scaling of the Chalker-Coddington Model
• Localization length exponent in two models of quantum Hall plateau transitions
• Evidence for the PSL(2$|$2) Wess-Zumino-Novikov-Witten model as a model for the plateau transition in Quantum Hall effect: Evaluation of numerical simulations
• Gaussian free fields at the integer quantum Hall plateau transition
• Random network models with variable disorder of geometry
• Localization length index in a Chalker-Coddington model: a numerical study
• Integer quantum Hall transition in a $\text{fraction}$ of a Landau level
• Why is the HLR theory particle-hole symmetric?
• Universality at integer quantum Hall transitions
• Self-duality of the integer quantum Hall to insulator transition: composite fermion description
• Critical behavior at the integer quantum Hall transition in a network model on the Kagome lattice

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• Localization renormalization and quantum Hall systems
• The integer quantum Hall transition: an $S$-matrix approach to random networks
• Quantum Hall criticality in an amorphous Chern insulator
• Random Magnetic Field and the Dirac Fermi Surface
• Extreme-Value Criticality and Gain Decomposition at the Integer Quantum Hall Transition