During recent years the interest to dynamics of quantum systems has grown considerably. Quantum many body systems out of equilibrium often manifest behavior, different from the one predicted by standard statistical mechanics and thermodynamics in equilibrium. Since the dynamics of a many body quantum system typically involve many excited eigenstates, with a non-thermal distribution, the time evolution of such a system provides an unique way for investigation of non-equilibrium quantum statistical mechanics. Last decade such new subjects like quantum quenches, thermalization, pre-thermalization, equilibration, generalized Gibbs ensemble, etc. are among the most attractive topics of investigation in modern quantum physics. One of the most interesting themes in the study of dynamics of quantum many-body systems out of equilibrium is connected with the recently proposed important concept of dynamical quantum phase transitions. During the last few years a great progress has been achieved in studying of those singularities in the time dependence of characteristics of quantum mechanical systems, in particular, in understanding how the quantum critical points of equilibrium thermodynamics affect their dynamical properties. Dynamical quantum phase transitions reveal universality, scaling, connection to the topology, and many other interesting features. Here we review the recent achievements of this quickly developing part of low temperature quantum physics. The study of dynamical quantum phase transitions is especially important in context of their connection to the problem of the modern theory of quantum information, where namely non-equilibrium dynamics of many-body quantum system plays the major role.
During recent years the interest to dynamics of quantum systems has grown considerably. Quantum many body systems out of equilibrium often manifest behavior, different from the one predicted by standard statistical mechanics and thermodynamics in equilibrium. Since the dynamics of a many body quantum system typically involve many excited eigenstates, with a non-thermal distribution, the time evolution of such a system provides an unique way for investigation of non-equilibrium quantum statistical mechanics. Last decade such new subjects like quantum quenches, thermalization, pre-thermalization, equilibration, generalized Gibbs ensemble, etc. are among the most attractive topics of investigation in modern quantum physics. One of the most interesting themes in the study of dynamics of quantum many-body systems out of equilibrium is connected with the recently proposed important concept of dynamical quantum phase transitions. During the last few years a great progress has been achieved in studying of those singularities in the time dependence of characteristics of quantum mechanical systems, in particular, in understanding how the quantum critical points of equilibrium thermodynamics affect their dynamical properties. Dynamical quantum phase transitions reveal universality, scaling, connection to the topology, and many other interesting features. Here we review the recent achievements of this quickly developing part of low temperature quantum physics. The study of dynamical quantum phase transitions is especially important in context of their connection to the problem of the modern theory of quantum information, where namely non-equilibrium dynamics of many-body quantum system plays the major role.
During recent years the interest to dynamics of quantum systems has grown considerably. Quantum many body systems out of equilibrium often manifest behavior, different from the one predicted by standard statistical mechanics and thermodynamics in equilibrium. Since the dynamics of a many-body quantum system typically involve many excited eigenstates, with a non-thermal distribution, the time evolution of such a system provides an unique way for investigation of non-equilibrium quantum statistical mechanics. Last decade such new subjects like quantum quenches, thermalization, pre-thermalization, equilibration, generalized Gibbs ensemble, etc. are among the most attractive topics of investigation in modern quantum physics. One of the most interesting themes in the study of dynamics of quantum many-body systems out of equilibrium is connected with the recently proposed important concept of dynamical quantum phase transitions. During the last few years a great progress has been achieved in studying of those singularities in the time dependence of characteristics of quantum mechanical systems, in particular, in understanding how the quantum critical points of equilibrium thermodynamics affect their dynamical properties. Dynamical quantum phase transitions reveal universality, scaling, connection to the topology, and many other interesting features. Here we review the recent achievements of this quickly developing part of low-temperature quantum physics. The study of dynamical quantum phase transitions is especially important in context of their connection to the problem of the modern theory of quantum information, where namely non-equilibrium dynamics of many-body quantum system plays the major role.
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→∞ 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 τ is applied to the system instead of a sudden quench. In particular, we will show that when τ→∞ the critical point tends to the equilibrium critical point (at zero temperature) in a power-law fashion and that for every finite τ 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.
In recent years, various notions of dynamical phase transitions have emerged to describe far-from-equilibrium criticality. A unifying framework connecting these different concepts is still missing, and would provide significant progress toward understanding far-from-equilibrium quantum many-body universality. Initializing our system in a thermal ensemble and subsequently performing quantum quenches in the Lipkin-Meshkov-Glick model, we establish a direct connection between excited-state quantum phase transitions (ESQPTs) and two major types of dynamical phase transitions (DPTs), by relating the phases of the latter to the critical energies and conservation laws in the former. Our work provides further insight into how various concepts of non-ground-state criticality are intimately connected, paving the way for a unified framework of far-from-equilibrium universality. Published by the American Physical Society 2024
This thesis investigates quantum-many body systems out of equilibrium in a variety of physically relevant and intriguing settings. It provides an overview of the recent developments in this field and based on the author’s recent review illuminates many interesting connections and summarises open questions. In this general framework, the various results of the author are embedded. While they often rely on advanced mathematics, great care is taken to present them in an intuitive way and most technical material is discussed separately in appendices. In the context of equilibration, work created as part of this thesis is able to capture the Gaussification of correlated initial states for a large class of free models. This allows to significantly extend equilibration results of free models, which are of crucial importance, as they provide reasonable relaxation time scales and immediately connect to our physical intuition in terms of ballistic spreading. Building on two surprising connections between static and dynamic features of Hamiltonians, which in general are hard to obtain, the results of this thesis further greatly contribute to the recent debate on the true nature of quantum many- body localisation. For those interacting models, we derive the localised structure of eigenstates from a dynamical suppression of information propagation on the low-energy sector. Further, we show how a non-degenerate spectrum, indicating the presence of interactions, and the existence of an approximately local constant of motion are sufficient to show information propagation, if arbitrary energies are allowed. In the context of quantum phase transitions, we continue such connections between static and dynamic features. We specifically investigate the Mott-superfluid transition of the Bose-Hubbard model and ask to what extent it has a universal dynamical signature. In a joint experimental, numerical and analytical effort, complex behaviour of these dynamics is uncovered, thus challenging the common believe that the Kibble-Zurek mechanism is sufficient to fully capture such transitions. We embed such experimental investigation in the recent debate on quantum simulators, which give the exciting perspective of solving notoriously and even provably hard problems efficiently in the laboratory. For such devices, we argue that the final read-out of the results is an important out- standing problem to be solved. We approach this issue in the case of a continuous quantum field, in which the notion of reconstructing the quantum state is even conceptually unclear. Based on tensor network methods, we demonstrate that in an experiment of ultra-cold atoms in a continuous setup, states can nevertheless efficiently be obtained. Thus, this thesis constitutes not only an important review of the field of quantum many-body systems out of equilibrium, but, using advanced mathematical and numerical tools, has significantly contributed to our understanding of various important out- standing questions in interacting many-body systems.
The study of non-equilibrium behaviors of quantum matter is one of the research directions at the frontiers of condensed matter physics and, in general, of theoretical and experimental physics. Understanding the mechanisms which prevent many quantum particles from reaching thermal equilibrium can ultimately shed light on the foundations of statistical physics and provide insight into the anomalous long-time collective behaviors observed in experiments. In this thesis, we present new theoretical developments in this direction. In the first part of the thesis we discuss the non-equilibrium dynamics of the two-dimensional quantum Ising model, the prototypical model of magnetism. In particular, we investigate the dynamics of interfaces separating different spin domains. In some regimes, we can provide an exact description of their unitary time evolution, but we also discuss the robustness of our predictions away from the exactly-solvable limit. Moreover, we address the same problem in the presence of disorder and provide a hydrodynamic interpretation of our findings. In the second part of the thesis, we investigate the localization properties of disordered quantum systems. In particular, we develop a renormalization-group picture of the Anderson localization transition in generic geometries. This provides a new framework to understand the phase diagram of such systems and their critical behavior beyond the usual finite-size scaling analysis. We also provide further insights on this topic both by studying resonances and their connection with observables and by employing unsupervised non-parametric learning techniques to probe disordered systems in an experimentally accessible form. The results presented in this thesis constitute a step forward in understanding the non-equilibrium phases and regimes of quantum matter and they pave the way to interesting future developments.
Experimental progress in atomic, molecular, and optical platforms in the last decade has stimulated strong and broad interest in the quantum coherent dynamics of many long-range interacting particles. The prominent collective character of these systems enables novel non-equilibrium phenomena with no counterpart in conventional quantum systems with local interactions. Much of the theory work in this area either focussed on the impact of variable-range interaction tails on the physics of local interactions or relied on mean-field-like descriptions based on the opposite limit of all-to-all infinite-range interactions. In this Report, we present a systematic and organic review of recent advances in the field. Working with prototypical interacting quantum spin lattices without disorder, our presentation hinges upon a versatile theoretical formalism that interpolates between the few-body mean-field physics and the many-body physics of quasi-local interactions. Such a formalism allows us to connect these two regimes, providing both a formal quantitative tool and basic physical intuition. We leverage this unifying framework to review several findings of the last decade, including the peculiar non-ballistic spreading of quantum correlations, counter-intuitive slowdown of entanglement dynamics, suppression of thermalization and equilibration, anomalous scaling of defects upon traversing criticality, dynamical phase transitions, and genuinely non-equilibrium phases stabilized by periodic driving. The style of this Report is on the pedagogical side, which makes it accessible to readers without previous experience in the subject matter.