Quantum phase transition in a random-tiling model

The analogue of a Mott-Hubbard transition is discussed, which appears at an incommensurate filling in a model of a two-dimensional plane, randomly tiled with CuO_4 `molecules’, simulating the copper-oxide planes of high-T_c superconductors. It is shown to be a quantum phase transition, which can be crossed either in doping, at a fixed hopping overlap t, or in t, when the doping is fixed in a certain range below half-filling. It is first-order, closely analogous to a liquid-gas transition.