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

### Aur Grabsch 1, 2 Christophe Texier 2

#### Europhys.Lett., 2016, 〈10.1209/0295-5075/116/17004〉

We establish the connection between a multichannel disordered model —the 1D Dirac equation with $N\times N$ matrix 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 $(\varepsilon\to0)$ behaviour $\rho(\varepsilon)\sim|\varepsilon|^{\alpha-1}$ . The vanishing of the exponent α 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.

• 1. ENS Cachan - École normale supérieure - Cachan
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques