The time-dependent Gutzwiller approximation

The time-dependent Gutzwiller Approximation (t-GA) [1,2] is shown to be capable of tracking the off-equilibrium evolution both of coherent quasiparticles and of incoherent Hubbard bands. The method is used to demonstrate that the sharp dynamical crossover observed by time-dependent DMFT in the quench-dynamics of a half-filled Hubbard model can be identified within the t-GA as a genuine dynamical transition separating two distinct physical phases [3]. This result, strictly variational for lattices of infinite coordination number, is intriguing as it actually questions the occurrence of thermalization. Next, we shall present how t-GA works in a multi-band model for V$_{2}$O$_{3}$ that displays a first-order Mott transition. We shall show that a physically accessible excitation pathway is able to collapse the Mott gap down and drive off-equilibrium the insulator into a metastable metal phase [4].\\[4pt] [1] M. Schir\'{o} and M. Fabrizio, Phys. Rev. Lett. \textbf{105}, 076401 (2010).\\[0pt] [2] M. Schir\'{o} and M. Fabrizio, Phys. Rev. B \textbf{83},165105 (2011).\\[0pt] [3] M. Sandri, M. Schir\'{o} and M. Fabrizio, Phys. Rev. B \textbf{86}, 075122 (2012). \\[0pt] [4] M. Sandri and M. Fabrizio, arXiv:1410.4442.