Lyapunov spectra for all symmetry classes of quasi-one-dimensional disordered systems of non-interacting Fermions

Abstract

A random phase property is proposed for products of random matrices drawn from any one of the classical groups associated with the ten Cartan symmetry classes of non-interacting disordered Fermion systems. It allows to calculate the Lyapunov spectrum explicitly in a perturbative regime. These results apply to quasi-one-dimensional random Dirac operators which can be constructed as representatives for each of the ten symmetry classes. For those symmetry classes that correspond to two-dimensional topological insulators or superconductors, the random Dirac operators describing the one-dimensional boundaries have vanishing Lyapunov exponents and almost surely an absolutely continuous spectrum, reflecting the gapless and conducting nature of the boundary degrees of freedom.

abstract and title corrected, article file identical, to appear in J. Stat. Phys

References in corpus (3)

• Symmetries, Dimensions, and Topological Insulators: the mechanism behind the face of the Bott clock
• Weak disorder expansion for localization lengths of quasi-1D systems
• The random phase property and the Lyapunov spectrum for disordered multi-channel systems

Cited by in corpus (5)

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• Topological phase transitions in the 1D multichannel Dirac equation with random mass and a random matrix model
• Fluctuations of the product of random matrices and generalized Lyapunov exponent
• Topological Modes in Monitored Quantum Dynamics
• Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States