Mapping the Current-Current Correlation Function Near a Quantum Critical Point
arXiv:1512.02476 · doi:10.1016/j.aop.2016.01.022
Abstract
The current-current correlation function is a useful concept in the theory of electron transport in homogeneous solids. The finite-temperature conductivity tensor as well as Anderson's localization length can be computed entirely from this correlation function. Based on the critical behavior of these two physical quantities near the plateau-insulator or plateau-plateau transitions in the integer quantum Hall effect, we derive an asymptotic formula for the current-current correlation function, which enables us to make several theoretical predictions about its generic behavior. For the disordered Hofstadter model, we employ numerical simulations to map the current-current correlation function, obtain its asymptotic form near a critical point and confirm the theoretical predictions.
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Cited by in corpus (5)
- Non-Commutative Chern Numbers for Generic Aperiodic Discrete Systems
- Generalized Kubo Formulas for the Transport Properties of Incommensurate 2D Atomic Heterostructures
- Disordered Crystals from First Principles I: Quantifying the Configuration Space
- Disordered Crystals from First Principles II: Transport Coefficients
- Quantization of Conductance in Quasi-Periodic Quantum Wires