This leads to a more formal definition of a topological insulator: an insulator which cannot be adiabatically transformed into an ordinary insulator without passing through an intermediate conducting state. In other words, topological insulators and trivial insulators are separate regions in the phase diagram, connected only by conducting phases. In this way, topological insulators provide an example of a state of matter not described by the Landau symmetry-breaking theory that defines ordinary states of matter.