By means of the discrete truncated Wigner approximation, we study dynamical phase transitions arising in the steady state of transverse-field Ising models after a quantum quench. Starting from a fully polarized ferromagnetic initial condition, these transitions separate a phase with nonvanishing magnetization along the ordering direction from a disordered symmetric phase upon increasing the transverse field. We consider two paradigmatic cases, a one-dimensional long-range model with power-law interactions ∝ 1/r α decaying algebraically as a function of distance r and a two-dimensional system with short-range nearest-neighbor interactions. In the former case, we identify dynamical phase transitions for α 2 and we extract the critical exponents from a data collapse of the steady-state magnetization for up to 1200 lattice sites. We find identical exponents for α 0.5, suggesting that the dynamical transitions in this regime fall into the same universality class as the nonergodic mean-field limit. The two-dimensional Ising model is believed to be thermalizing, which we also confirm using exact diagonalization for small system sizes. Thus, the dynamical transition is expected to correspond to the thermal phase transition, which is consistent with our data upon comparing to equilibrium quantum Monte Carlo simulations. We further test the accuracy of the discrete truncated Wigner approximation by comparing against numerically exact methods such as exact diagonalization, tensor network, as well as artificial neural network states and we find good quantitative agreement on the accessible time scales. Finally, our work provides an additional contribution to the understanding of the range and the limitations of qualitative and quantitative applicability of the discrete truncated Wigner approximation.

We investigate the ground-state properties and the collective modes of a two-dimensional twocomponent Rydberg-dressed Fermi liquid in the dipole-blockade regime. We find instability of the homogeneous system toward phase separated and density ordered phases, using the Hartree-Fock and random-phase approximations, respectively. The spectral weight of collective density oscillations in the homogenous phase also signals the emergence of density-wave instability. We examine the effect of exchange-hole on the density-wave instability and on the collective mode dispersion using the Hubbard local-field factor. arXiv:1706.03222v1 [cond-mat.quant-gas]

We study synchronisation between periodically driven, interacting classical spins undergoing a Hamiltonian dynamics. In the thermodynamic limit there is a transition between a regime where all the spins oscillate synchronously for an infinite time with a period twice as the driving period (synchronized regime) and a regime where the oscillations die after a finite transient (chaotic regime). We emphasize the peculiarity of our result, having been synchronisation observed so far only in driven-dissipative systems. We discuss how our findings can be interpreted as a period-doubling time crystal and we show that synchronisation can appear both for an overall regular and an overall chaotic dynamics.synchronisation is a widespread phenomenon in Nature [1][2][3][4], from Huygens pendula to chemical reactions to modulated lasers and electrical generators, from neuronal networks to circadian rhythms in living organisms [1]. Classical non-linear and damped systems can converge to constant steady states, they can be chaotic, or they can asymptotically approach self-sustained oscillations. A tiny coupling between the systems can force the oscillations to happen with the same frequency and a constant phase difference. This is the essence of synchronisation.All the known systems undergoing synchronisation are driven and dissipative, undergoing asymptotically a limit cycle. In this work we will discuss a route to synchronisation in a conservative, time-dependent, many-body classical Hamiltonian system which, as far as we know, has never been noticed. As we will show in the rest of the paper, here synchronisation is an emerging phenomenon in the thermodynamic limit as any spontaneous symmetry breaking, as for example the Kuramoto model [25,26]. Indeed synchronisation among a finite number of interacting classical Hamiltonian systems is impossible. In general, the coupled system is not integrable and there is chaos. Even if the KAM theorem guarantees that only a part of the phase space is chaotic, if there are three or more degrees of freedom, Diffusion in phase space makes the dynamics chaotic and thermalising (at infinite temperature in the driven case) after a transient [30,31,37]: That means no synchronisation. The dynamical landscape may change in the thermodynamic limit. Here, depending on the relative scaling of the number of resonances and their density, the phase space can be fully chaotic or fully regular [31].A key, enabling property, in our analysis is that we will consider long-range interacting Hamiltonian systems. In this case indeed, the dynamics can be essentially regular [6,7] in the thermodynamic limit [8]. To the best of our knowledge, here we are proposing the first case of a driven classical Hamiltonian model which can show a reg-ular dynamics in the thermodynamic limit, thus allowing synchronisation to appear. The effect of periodic kicking on the regularity/chaoticity dynamics of classical Hamiltonian systems has been already widely investigated, see e.g. [5,17,[31][32][33][34]. Here we make a step furthe...