Out-of-equilibrium quantum many-body systems stand at the forefront of modern theoretical physics, addressing fundamental questions on thermalization, transport, and universal phenomena. These fields, already well established in condensed matter, statistical physics, quantum optics, and quantum information theory, are progressively gaining even greater relevance with the rapid development of quantum technologies and simulation, which inherently operate in dynamical regimes. In recent years, the traditional paradigm of unitary quantum evolution has been expanded to include measurements, opening new directions in out-of-equilibrium physics. At the core of these advances lie measurement-induced phase transitions (MIPTs), which have emerged as a new class of dynamical critical phenomena characterizing the general behavior of monitored quantum dynamics. When external monitoring intertwines with unitary evolution, many-body quantum correlations change their structure, giving rise to distinct entanglement phases of matter. This discovery has sparked enormous interest in MIPTs, leading to significant advances in open quantum systems, entanglement theory, and more broadly quantum complexity. Despite much progress, a full understanding of monitored many-body dynamics is far from complete, leaving several open questions on the nature of MIPTs, their experimental observability, and the possibilities offered by measurements to enhance control over synthetic quantum matter. These issues persist due to the intrinsic complexity of the problem and the lack of efficient tools to study it, mainly caused by the stochastic character of monitored evolution. This thesis addresses these challenges by expanding the investigation of measurement-induced phenomena in new settings and introducing innovative probes of entanglement and many-body quantum complexity for MIPTs. A core question we investigate is the role of symmetries, non-ergodicity, and especially integrability in measurement-induced criticality, which dramatically affect the non-equilibrium phases. We further explore how these phenomena extend beyond bipartite quantum correlations to multipartite entanglement and quantum non-stabilizerness, highlighting the non-trivial interplay between measurements and complexity notions rooted in quantum information theory. Finally, we focus on the compelling problem of decoherence, modeling how noise spoils entanglement structures. These findings, supported by advanced numerical simulations and theoretical analysis, deepen the current understanding of entanglement, complexity, and integrability in monitored quantum many-body systems, offering new perspectives on their rich behavior. In parallel, we address the experimental problem of dissipation in MIPTs, which is of key relevance for practical implementations. We anticipate the present investigation to foster future research on the nature of monitored dynamical critical phenomena and, more broadly, the applications of measurements in quantum state evolution.
Out-of-equilibrium quantum many-body systems stand at the forefront of modern theoretical physics, addressing fundamental questions on thermalization, transport, and universal phenomena. These fields, already well established in condensed matter, statistical physics, quantum optics, and quantum information theory, are progressively gaining even greater relevance with the rapid development of quantum technologies and simulation, which inherently operate in dynamical regimes. In recent years, the traditional paradigm of unitary quantum evolution has been expanded to include measurements, opening new directions in out-of-equilibrium physics. At the core of these advances lie measurement-induced phase transitions (MIPTs), which have emerged as a new class of dynamical critical phenomena characterizing the general behavior of monitored quantum dynamics. When external monitoring intertwines with unitary evolution, many-body quantum correlations change their structure, giving rise to distinct entanglement phases of matter. This discovery has sparked enormous interest in MIPTs, leading to significant advances in open quantum systems, entanglement theory, and more broadly quantum complexity. Despite much progress, a full understanding of monitored many-body dynamics is far from complete, leaving several open questions on the nature of MIPTs, their experimental observability, and the possibilities offered by measurements to enhance control over synthetic quantum matter. These issues persist due to the intrinsic complexity of the problem and the lack of efficient tools to study it, mainly caused by the stochastic character of monitored evolution. This thesis addresses these challenges by expanding the investigation of measurement-induced phenomena in new settings and introducing innovative probes of entanglement and many-body quantum complexity for MIPTs. A core question we investigate is the role of symmetries, non-ergodicity, and especially integrability in measurement-induced criticality, which dramatically affect the non-equilibrium phases. We further explore how these phenomena extend beyond bipartite quantum correlations to multipartite entanglement and quantum non-stabilizerness, highlighting the non-trivial interplay between measurements and complexity notions rooted in quantum information theory. Finally, we focus on the compelling problem of decoherence, modeling how noise spoils entanglement structures. These findings, supported by advanced numerical simulations and theoretical analysis, deepen the current understanding of entanglement, complexity, and integrability in monitored quantum many-body systems, offering new perspectives on their rich behavior. In parallel, we address the experimental problem of dissipation in MIPTs, which is of key relevance for practical implementations. We anticipate the present investigation to foster future research on the nature of monitored dynamical critical phenomena and, more broadly, the applications of measurements in quantum state evolution.
Open quantum many-body systems are an important setting that allows us to study the interplay between dissipation and interactions, contributing to a more accurate description of real-life phenomena and experiments, and providing new features to be exploited both on theoretical and technological grounds. This thesis deals with the study of such systems across a wide range of settings. Beyond providing the theoretical tools to analyze and understand this framework, the thesis also addresses some important and modern concepts. A key goal is to show how dissipation enables the realization of new phases of matter, such as quantum synchronization and time-crystal phases. To achieve this, various theoretical tools will be employed, ranging from path integral formalism to a Lindblad master equation approach. These same tools will also allow us to pursue another important goal: studying the dynamics of many-body systems subject to continuous measurements. This will lead to observing the emergence of a recently discovered phenomenon, known as measurement-induced phase transitions, and will provide a natural framework for addressing the complexity arising from the stochastic nature of quantum measurements. This thesis constitutes a modern and comprehensive view of the field of open quantum many-body systems, with a special focus on novel phases of matter emerging from interactions with an external environment or with a measuring device.
This thesis investigates universality and complexity in classical and quantum statistical physics, with a particular emphasis on nonequilibrium phenomena. While the emergence of universal behavior in equilibrium systems stands as one of the cornerstones of statistical physics, the extension of these ideas to nonequilibrium settings presents fundamental and still open challenges. The inherently diverse and system-specific nature of nonequilibrium dynamics calls for a broad spectrum of conceptual and analytical tools. Furthermore, nonequilibrium dynamics is nowadays accessible to experiments in both classical and quantum regimes. These modern experiments produce a large amount of experimental data, which calls for analysis of physics through data-driven methods, complexity theory and high-dimensional statistics. The possibility of probing and accessing correlated states of matter out of equilibrium in modern experiments raises several questions. Can we understand the output of experiments in terms of complexity theory and dimensional reduction? Is it possible to extend concepts of universality to data structures arising in simulations? Can we describe phase transitions (either classical or quantum) concepts of modern data science? How to control entanglement in quantum dynamics? Which nonequilibrium phenomena can we hope to observe in quantum simulators? The research work presented in this thesis is an attempt to answer to these questions. In this thesis, we argue that order parameters and diagnostics of criticality in nonequilibrium classical systems can be found by unsupervised learning and dimensional reduction, which allow to reduce the complexity of datasets by projections on lower-dimensional spaces, while still preserving essential universal features. We then move to the study of models of quantum dynamics relevant for quantum simulators. In particular, we show that the same concepts of dimensional reduction apply also to quantum systems, allowing for the extraction of information from outputs of quantum simulators. We then study a protocol to prepare complex, entangled states via unitary evolution and enhance entanglement via measurements in a fermionic model. Finally, we study the emergence of anomalous transport in one-dimensional chiral systems with non-Abelian symmetries.
The notion of complexity pervades physics, with manifestations rang- ing from classical networks to quantum many-body dynamics. This thesis investigates the complexity of open quantum systems, focus- ing on the interplay between unitary evolution and dissipation, with particular emphasis on measurement processes. Two complementary perspectives are developed: an approach based on quantum resource theories and a data-driven analysis of quantum trajectories. In the first part, quantum complexity is characterized in terms of resources such as entanglement, non-stabilizerness, and non-Gaussianity. These resources capture the non-classical features that enable quantum com- putational advantage. We analyze the generation of resources in mon- itored systems, where the competition between coherent dynamics and measurements gives rise to novel phase transitions. Through semiclassical analyses, tensor networks, and Gaussian and stabilizer techniques, we identify distinct dynamical regimes and clarify the interplay between different resources under repeated quantum mea- surements. The second part focuses on a classical complexity measure inspired by non-parametric machine learning methods, known as the intrinsic dimension. We employ this measure to quantify the com- plexity of ensembles of quantum trajectories, demonstrating that it is sensitive to structural properties such as integrability, fragmenta- tion, and the decoupling of correlation functions, thereby witnessing the complexity of the underlying dynamics. By combining resource- theoretic and unsupervised learning approaches, this thesis provides a wide perspective on the complexity of monitored quantum systems, bridging statistical physics, quantum information, and data science.
Isolated, many-body quantum systems, evolving under their intrinsic dynamics, exhibit a multitude of exotic phenomena and raise foundational questions about statistical mechanics. A flurry of theoretical work has been devoted to understanding how these systems reach thermal equilibrium in the absence of coupling to an external bath and, when thermalization does not occur, investigating the emergent non-equilibrium phases of matter. With the advent of synthetic quantum systems, such as ultra-cold atoms in optical lattices or trapped ions, these questions are no longer academic and can be directly studied in the laboratory. This dissertation explores the non-equilibrium phenomena that stem from the interplay between interactions, disorder, symmetry, topology, and external driving. First, we study how strong disorder, leading to many-body localization, can arrest the heating of a Floquet system and stabilize symmetry-protected topological order that does not have a static analogue. We analyze its dynamical and entanglement properties, highlight its duality to a discrete time crystal, and propose an experimental implementation in a cold-atom setting.Quenched disorder and the many-body localized state are crucial ingredients in protecting macroscopic quantum coherence. We explore the stability of many-body localization in two and higher dimensions and analyze its robustness to rare regions of weak disorder.We then study a second example of non-thermal behavior, namely integrability. We show that a class of random spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram, which includes regions of integrability, classical chaos, and of a novel integrable structure whose conservation laws are reminiscent of the integrals of motion found in a many-body localized phase.The third group of disordered, non-ergodic systems we consider, spin glasses, have fascinating connections to complexity theory and the hardness of constraint satisfaction. We define a statistical ensemble that interpolates between the classical and quantum limits of such a problem and show that there exists a sharp boundary separating satisfiable and unsatisfiable phases.
Quantum many-body systems exhibit highly complex interactions that give rise to emergent collective phenomena beyond the behavior of individual particles. One of the most intriguing challenges in modern quantum physics is understanding how isolated quantum systems evolve toward thermal equilibrium despite following fundamentally reversible quantum dynamics. Quantum entanglement has emerged as a central mechanism governing information propagation, thermalization, and the development of statistical equilibrium in isolated many-body systems. Simultaneously, recent advances in quantum information science have enabled researchers to investigate the relationship between entanglement dynamics, information scrambling, and emergent quantum behavior using computational and analytical approaches. This study proposes a Quantum Information Analytics Framework for investigating thermalization processes in isolated many-body quantum systems through the integration of entanglement dynamics, quantum information measures, statistical mechanics, and computational modeling. The proposed framework evaluates system evolution using multiple performance indicators, including entanglement entropy, information propagation, thermal equilibrium, quantum coherence, and computational stability. The findings indicate that quantum entanglement plays a fundamental role in driving thermalization while preserving the underlying unitary evolution of isolated quantum systems. The proposed analytical framework contributes to a deeper understanding of emergent quantum dynamics and provides valuable insights for quantum computing, quantum simulation, condensed matter physics, and next-generation quantum information technologies.
In the past decades, rapid advances in the experimental control of quantum systems have opened up unparalleled capabilities of engineering exotic quantum states. Nowadays, we may consider ourselves witnesses of a second quantum revolution as strongly correlated quantum matter is regularly created, on a daily basis, within the most diverse platforms, e.g. arrays of Rydberg atoms, ultra-cold atoms in optical lattices, superconducting qubits, trapped ions, and quantum dots. In this era, dubbed Noisy-Intermediate Scale Quantum (NISQ) era, the effort in pursuing research for realizing quantum technologies with practical purposes, such as quantum computing, simulations, communication and metrology, has greatly accelerated, and we are just starting to experience the immense progress that could be achieved. The remarkable breakthrough we are facing builds upon seminal theoretical and experimental advances in quantum physics. The key achievements in atomic, molecular, and optical (AMO) physics have opened up the possibility of controlling, trapping, and measuring single atoms, one by one, with high accuracy and reliability. In parallel, from a theoretical point of view, the study of quantum entanglement and correlations has bridged AMO physics and quantum information with crucial proposals for the realization of universal quantum computers. In this context, entanglement has emerged as one of the key tools to characterize and to exploit quantum many-body systems for quantum information purposes. We will study quantum entanglement in several scenarios to investigate and probe complex quantum many-body systems. We will consider examples ranging from generic mixed states in equilibrium to out-of-equilibrium dynamics, with and without dissipation, and topologically non-trivial systems. The leitmotif of this work will be how entanglement and correlations can be exploited to characterize the many-body quantum state describing a physical system and how entanglement can be detected in an experimentally efficient manner.