Scale invariant distribution functions in quantum systems with few degrees of freedom

Scale invariance usually occurs in extended systems where correlation functions decay algebraically in space and/or time. Here we introduce a new type of scale invariance, occurring in the distribution functions of physical observables. At equilibrium these functions decay over a typical scale set by the temperature, but they can become scale invariant in a sudden quantum quench. We exemplify this effect through the analysis of linear and non-linear quantum oscillators. We find that their distribution functions generically diverge logarithmically close to the stable points of the classical dynamics. Our study opens the possibility to address integrability and its breaking in distribution functions, with immediate applications to matter-wave interferometers.Comment: 8+10 pages. Scipost Submissio

Non equilibrium phase transitions and Floquet Kibble-Zurek scaling

We study the slow crossing of non-equilibrium quantum phase transitions in periodically-driven systems. We explicitly consider a spin chain with a uniform time-dependent magnetic field and focus on the Floquet state that is adiabatically connected to the ground state of the static model. We find that this {\it Floquet ground state} undergoes a series of quantum phase transitions characterized by a non-trivial topology. To dinamically probe these transitions, we propose to start with a large driving frequency and slowly decrease it as a function of time. Combining analytical and numerical methods, we uncover a Kibble-Zurek scaling that persists in the presence of moderate interactions. This scaling can be used to experimentally demonstrate non-equilibrium transitions that cannot be otherwise observed.Comment: 7 pages, 3 figures, Supplemental Material. (In this last version, the one published in EPL, we provide a better discussion of the Floquet adiabatic theorem, the construction of the Floquet ground state as an adiabatic continuation and the nature of the phase transitions.

Complete characterization of spin chains with two Ising symmetries

Spin chains with two Ising symmetries are the Jordan-Wigner duals of one-dimensional interacting fermions with particle-hole and time-reversal symmetry. From earlier works on Majorana chains, it is known that this class of models has 10 distinct topological phases. In this paper, we analyze the physical properties of the correspondent 10 phases of the spin model. In particular, thanks to a set of two non-commuting dualities, we determine the local and non-local order parameters of the phases. We find that 4 phases are topologically protected by the Ising symmetries, while the other 6 break at least one symmetry. Our study highlights the non-trivial relation between the topological classifications of interacting bosons and fermions.Comment: 7 page

Dynamics and universality in noise driven dissipative systems

We investigate the dynamical properties of low dimensional systems, driven by external noise sources. Specifically we consider a resistively shunted Josephson junction and a one dimensional quantum liquid in a commensurate lattice potential, subject to $1/f$ noise. In absence of nonlinear coupling, we have shown previously that these systems establish a non-equilibrium critical steady state [Nature Phys. 6, 806 (2010)]. Here we use this state as the basis for a controlled renormalization group analysis using the Keldysh path integral formulation to treat the non linearities: the Josephson coupling and the commensurate lattice. The analysis to first order in the coupling constant indicates transitions between superconducting and localized regimes that are smoothly connected to the respective equilibrium transitions. However at second order, the back action of the mode coupling on the critical state leads to renormalization of dissipation and emergence of an effective temperature. In the Josephson junction the temperature is parametrically small allowing to observe a universal crossover between the superconducting and insulating regimes. The IV characteristics of the junction displays algebraic behavior controlled by the underlying critical state over a wide range. In the noisy one dimensional liquid the generated dissipation and effective temperature are not small as in the junction. We find a crossover between a quasi-localized regime dominated by dissipation and another dominated by temperature. However since in the thermal regime the thermalization rate is parametrically small, signatures of the non-equilibrium critical state can be seen in transient dynamics.Comment: 30 pages, 8 figures. Revised versio