Universal energy distribution of quasi-particles emitted in a local time dependent quench

We study the emission of quasi-particles in the scaling limit of the 1d Quantum Ising chain at the critical point perturbed by a time dependent local transverse field. We compute \it exactly \rm and for a \it generic \rm time dependence the average value of the transverse magnetization, its correlation functions, as well as the statistic of both the inclusive and exclusive work. We show that, except for a cyclic perturbation, the probability distribution of the work at low energies is a power law whose exponent is universal, i.e. does not depend on the specific time dependent protocol, but only on the final value attained by the perturbation.Comment: 5 pages, 1 figure, Published Versio

Out of equilibrium many-body systems: adiabaticity, statistics of observables and dynamical phase transitions

This thesis reports the results obtained during my PhD research in the field of out of equilibrium quantum many-body systems. Chapter 1 consists in a brief introduction of the field and the introduction of concept that are useful for the following chapters. In Chapter 2 the statistics of the work as a tool for characterizing the dynamics of many-body quantum systems is introduced its general features discussed. Then, such a statistics is computed for generic time-dependent protocols (both global and local) in the quantum Ising chain and in the Gaussian field theory, showing, in particular, that in its low-energy part there are features that are independent of the details of the specific chosen protocol. Chapter 3 is devoted to the study of the dynamical phase transition in the $O(N)$ quantum vector model in the $N \rightarrow \infty$ limit, whose critical properties in generic dimensions are characterized. Moreover, a strong connection between such a transition and the statistics of excitations produced in a double quench as a function of the waiting time is showed. The chapter ends by studying the fate of the dynamical transition and the its critical properties when a ramp of finite duration $\tau$ is applied to the system instead of a sudden quench. In particular, we will show that when $\tau \rightarrow \infty$ the critical point tends to the equilibrium critical point (at zero temperature) in a power-law fashion and that for every finite $\tau$ the critical properties are always the same (and different from the equilibrium critical properties). Finally in Chapter 4 we will discuss the emergence of a non adiabatic behavior in the dynamics of the order parameter for a low dimensional quantum system driven within a gapped phase by considering in detail the case of a quantum Ising chain subject to a linear variation in time of the transverse field, showing that, no matter how slowly the ramp is performed, such a change leads eventually to the disruption of the order

Statistical mechanics of the Cluster-Ising model

We study a Hamiltonian system describing a three-spin-1/2 cluster-like interaction competing with an Ising-like anti-ferromagnetic interaction. We compute free energy, spin correlation functions and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Neverthless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.Comment: To be published in Physical Review

Nonadiabatic stationary behaviour in a driven low-dimensional gapped system

We discuss the emergence of nonadiabatic behavior in the dynamics of the order parameter in a low-dimensional quantum many-body system subject to a linear ramp of one of its parameters. While performing a ramp within a gapped phase seems to be the most favorable situation for adiabaticity, we show that such a change leads eventually to the disruption of the order, no matter how slowly the ramp is performed. We show this in detail by studying the dynamics of the one-dimensional quantum Ising model subject to linear variation of the transverse magnetic field within the ferromagnetic phase, and then propose a general argument applicable to other systems. © 2014 American Physical Society

Work distribution and edge singularities for generic time-dependent protocols in extended systems

We study the statistics of the work done by globally changing in time with a generic protocol the mass in a free bosonic field theory with relativistic dispersion and the transverse field in the one-dimensional Ising chain both globally and locally. In the latter case we make the system start from the critical point and we describe it in the scaling limit. We provide exact formulas in all these cases for the full statistics of the work and we show that the low-energy part of the distribution of the work displays an edge singularity whose exponent does not depend on the specifics of the protocol that is chosen and may only depend on the position of the initial and final values with respect to the critical point of the system. We also show that the condensation transition found in the bosonic system for sudden quenches is robust with respect to the choice of the protocol. \ua9 2013 American Physical Society

Linear ramps of the mass in the O(N) model: Dynamical transition and quantum noise of excitations

Nonthermal dynamical critical behavior can arise in isolated quantum systems brought out of equilibrium by a change in time of their parameters. While this phenomenon has been studied in a variety of systems in the case of a sudden quench, we consider here its sensitivity to a change of protocol by considering the experimentally relevant case of a linear ramp in time. Focusing on the O(N) model in the large-N limit, we will show that a dynamical phase transition is always present for all durations of the ramp, and we discuss the crossover between the sudden quench transition and one dominated by the equilibrium quantum critical point. We show that the critical behavior of the statistics of the excitations, signaling the nonthermal nature of the transition, is also robust. An intriguing crossover in the equal-time correlation function, related to an anomalous coarsening, is also discussed. \ua9 2016 American Physical Society