Short-Range Interactions and Scaling Near Integer Quantum Hall Transitions

Abstract

We study the influence of short-range electron-electron interactions on scaling behavior near the integer quantum Hall plateau transitions. Short-range interactions are known to be irrelevant at the renormalization group fixed point which represents the transition in the non-interacting system. We find, nevertheless, that transport properties change discontinuously when interactions are introduced. Most importantly, in the thermodynamic limit the conductivity at finite temperature is zero without interactions, but non-zero in the presence of arbitrarily weak interactions. In addition, scaling as a function of frequency, $\omega$, and temperature, $T$, is determined by the scaling variable $\omega /T^p$ (where $p$ is the exponent for the temperature dependence of the inelastic scattering rate) and not by $\omega /T$, as it would be at a conventional quantum phase transition described by an interacting fixed point. We express the inelastic exponent, $p$, and the thermal exponent, $z_T$, in terms of the scaling dimension, $-\alpha <0$, of the interaction strength and the dynamical exponent $z$ (which has the value $z=2$), obtaining $p=1+2\alpha /z$ and $z_T=2/p$.

9 pages, 4 figures, submitted to Physical Review B

Cited by in corpus (45)

• Anderson Transitions
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Theory of Anomalous Quantum Hall Effects in Graphene
• Enhancement of superconductivity by Anderson localization
• Effects of dissipation on quantum phase transitions
• Dynamics and transport in random quantum systems governed by strong-randomness fixed points
• Marginal Anderson localization and many body delocalization
• Wave function multifractality and dephasing at metal-insulator and quantum Hall transitions
• Classification and symmetry properties of scaling dimensions at Anderson transitions
• Geometrically disordered network models, quenched quantum gravity, and critical behavior at quantum Hall plateau transitions
• Dynamical scaling of the quantum Hall plateau transition
• Integer quantum Hall transition on a tight-binding lattice
• Scaling Behavior of the Quantum Phase Transition from a Quantum Anomalous Hall Insulator to an Axion Insulator
• Temperature enhancement of thermal Hall conductance quantization
• Integer quantum Hall transition in the presence of a long-range-correlated quenched disorder
• Random network models with variable disorder of geometry
• Multifractality and electron-electron interaction at Anderson transitions
• Surface transport coefficients for three-dimensional topological superconductors
• Disorder and interaction in chiral chains: Majoranas vs complex fermions
• Liouvillian Approach to the Integer Quantum Hall Effect Transition
• Criticality Across the Energy Spectrum from Random, Artificial Gravitational Lensing in Two-Dimensional Dirac Superconductors
• Fragility of surface states in non-Wigner Dyson topological insulators
• Tunneling into the localized phase near Anderson transitions with Coulomb interaction
• Generalized multifractality at spin quantum Hall transition
• Electron-electron interactions, quantum Coulomb gap, and dynamical scaling near integer quantum Hall transitions
• Interaction effects on quantum Hall transitions: dynamical scaling laws and superuniversality
• Numerical Study of a Dual Representation of the Integer Quantum Hall Transition
• Taming two interacting particles with disorder
• Weakly chiral networks and 2D delocalized states in a weak magnetic field
• Self-duality of the integer quantum Hall to insulator transition: composite fermion description
• Generalized surface multifractality in 2D disordered systems
• Thermodynamic and Tunneling Density of States of the Integer Quantum Hall Critical State
• Low-frequency conductivity of a non-degenerate 2D electron liquid in strong magnetic fields
• Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators
• Transport Properties near the z=2 Insulator-Superconductor Transition
• Composite Fermion Nonlinear Sigma Models
• Interplay of Short-Range Interactions and Quantum Interference Near the Integer Quantum Hall Transition
• Two parameter flow of σ_{xx}(ω) - σ_{xy}(ω) for the graphene quantum Hall system in ac regime
• Critical behavior at the integer quantum Hall transition in a network model on the Kagome lattice
• The integer quantum Hall transition: an $S$-matrix approach to random networks
• Mesoscopic fluctuations of the local density of states in interacting electron systems
• Quantum Hall criticality in an amorphous Chern insulator
• Single electron magneto-conductivity of a nondegenerate 2D electron system in a quantizing magnetic field
• Supersymmetry approach to delocalization transitions in a network model of the weak field quantum Hall effect and related models
• Scaling in the Integer Quantum Hall Effect: interactions and low magnetic fields