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We present an algorithm to determine topological invariants of inhomogeneoussystems, such as alloys, disordered crystals, or amorphous systems. Based onthe kernel polynomial method, our algorithm allows us to study samples withmore than $10^7$ degrees of freedom. Our method enables the study of largecomplex compounds, where disorder is inherent to the system. We use it toanalyse Pb$_{1-x}$Sn$_{x}$Te and tighten the critical concentration for thephase transition.

Computation of topological phase diagram of disordered Pb$_{1-x}$Sn$_{x}$Te using the kernel polynomial method