QJC: Spontaneous symmetry breaking and symmetry protected topological phases in the Z2 Bose Hubbard model

The concept of symmetry breaking plays a fundamental role in condensed matter physics. A phase transition is characterized by the change of a local order parameter. A famous example of such transition is the Peierls mechanism, where the interactions between the electrons and the phonons induce a phase transition from a metal to an insulator.
Topological insulators are exotic phases that go beyond the Ginzburg-Landau theory of phase transitions: instead of being characterized by a local order parameter, they are classified by a global order parameter called the topological invariant. The latter makes them very robust against local perturbations.
In this talk, we will explore a bosonic analogue of the Peierls mechanism, where interacting bosons are coupled to a dynamical Z2 field. Such a model can be realized in cold atom experiment. We will in particular discuss the interplay between spontaneous symmetry breaking and symmetry protection and characterize the topology nature of the symmetry protected phases.