Decimation Studies of Bloch Electrons in a Magnetic Field: Higher Order Limit Cycles Underlying the Phase Diagram

TL;DR

This paper investigates the complex phase diagram of Bloch electrons in a magnetic field using a decimation approach, revealing higher order limit cycles and strange attractors in the critical phase of a 2D electron gas model.

Contribution

It introduces a decimation method to analyze fractal spectra and wave functions, uncovering higher order limit cycles and strange attractors in the phase diagram.

Findings

Critical phase exhibits fractal spectrum and wave functions.

Higher order limit cycles are found in renormalization flow.

Most of the critical phase is characterized by strange attractors.

Abstract

A decimation method is applied to the tight binding model describing the two dimensional electron gas with next nearest neighbor interaction in the presence of an inverse golden mean magnetic flux. The critical phase with fractal spectrum and wave function exists in a finite window in two-dimensional parameter space. There are special points on the boundaries as well as inside the critical phase where the renormalization flow exhibits higher order limit cycles. Our numerical results suggest that most of the critical phase is characterized by a strange attractor of the renormalization equations.