The quantum Biroli-M\'ezard model: glass transition and superfluidity in a quantum lattice glass model

We study the quantum version of a lattice model whose classical counterpart captures the physics of structural glasses. We discuss the role of quantum fluctuations in such systems and in particular their interplay with the amorphous order developed in the glass phase. We show that quantum fluctuations might facilitate the formation of the glass at low enough temperature. We also show that the glass transition becomes a first-order transition between a superfluid and an insulating glass at very low temperature, and is therefore accompanied by phase coexistence between superfluid and glassy regions.