Dynamical Phase Transitions in a 2D Quantum Dimer Model*

The study of dynamical properties in systems with local constraints has attracted a lot of interest, spurred by experiments with Rydberg blockaded atoms, that naturally implement constrained many-body models.
We study the quench dynamics in a 2D quantum dimer model to identify dynamical phase transitions in constrained models by means of exact diagonalization on systems of sizes up to 8x8 sites. We find that the quenched quantum system thermalizes efficiently by determining the relaxation dynamics of both the order parameter (OP) and local correlation functions. The observed fast relaxation to thermal expectation values allows us to study the underlying thermal BKT-transition between a columnar ordered valence bond solid (VBS) and a symmetric liquid (VBL) phase in the form of a dynamical phase transition. The existence of this finite-temperature transition in the dynamics is confirmed by the long-time averaged values of the OP. Moreover, upon quenching across the VBS-VBL phase boundary, the dynamical transition can be shown to be manifest in the Loschmidt-echo, whose rate-function displays kinks at the zero-crossings of the columnar OP.