Topological phase transitions in the 1D multichannel Dirac equation with random mass and a random matrix model

Abstract

We establish the connection between a multichannel disordered model --the 1D Dirac equation with $N\times N$ matricial random mass-- and a random matrix model corresponding to a deformation of the Laguerre ensemble. This allows us to derive exact determinantal representations for the density of states and identify its low energy ($\epsilon \to 0$) behaviour $\rho (\epsilon )\sim |\epsilon {|}^{\alpha -1}$. The vanishing of the exponent $\alpha$ for $N$ specific values of the averaged mass over disorder ratio corresponds to $N$ phase transitions of topological nature characterised by the change of a quantum number (Witten index) which is deduced straightforwardly in the matrix model.

7+4 pages, 9+1 pdf figures ; v2: paper reorganised, discussion of non-isotropic case added

References in corpus (7)

• Classification of topological insulators and superconductors in three spatial dimensions
• Anderson Transitions
• Multichannel Generalization of Kitaev's Majorana End States and a Practical Route to Realize Them in Thin Films
• Localization in disordered superconducting wires with broken spin-rotation symmetry
• Anderson localization and the topology of classifying spaces
• The Lyapunov exponent of products of random $2\times 2$ matrices close to the identity
• Density of states at disorder-induced phase transitions in a multichannel Majorana wire

Cited by in corpus (9)

• Wigner time delay and related concepts -- Application to transport in coherent conductors
• Full counting statistics for interacting trapped fermions
• Matrix Kesten Recursion, Inverse-Wishart Ensemble and Fermions in a Morse Potential
• Wigner-Smith time-delay matrix in chaotic cavities with non-ideal contacts
• Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain
• Fluctuations of the product of random matrices and generalized Lyapunov exponent
• Dyson's disordered linear chain from a random matrix theory viewpoint
• Wigner-Smith matrix, exponential functional of the matrix Brownian motion and matrix Dufresne identity
• Chiral chains with two valleys and disorder of finite correlation length