Recent interest in aspects common to quantum information and condensed matter has prompted a flurry of activity at the border of these disciplines that were far distant until a few years ago. Numerous interesting questions have been addressed so far. Here an important part of this field, the properties of the entanglement in many-body systems, are reviewed. The zero and finite temperature properties of entanglement in interacting spin, fermion, and boson model systems are discussed. Both bipartite and multipartite entanglement will be considered. In equilibrium entanglement is shown tightly connected to the characteristics of the phase diagram. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium entangled states are generated and manipulated by means of many-body Hamiltonians.
Recent interest in aspects common to quantum information and condensed matter has prompted a flurry of activity at the border of these disciplines that were far distant until a few years ago. Numerous interesting questions have been addressed so far. Here an important part of this field, the properties of the entanglement in many-body systems, are reviewed. The zero and finite temperature properties of entanglement in interacting spin, fermion, and boson model systems are discussed. Both bipartite and multipartite entanglement will be considered. In equilibrium entanglement is shown tightly connected to the characteristics of the phase diagram. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium entangled states are generated and manipulated by means of many-body Hamiltonians.
One of the most important predictions of quantum mechanics is the existence of quantum entanglement. Since the inception of quantum theory, the study of entanglement has become ubiquitous in several branches of physics, from high energy to condensed matter physics and quantum information. To this avail, different measures of entanglement in quantum systems have been introduced. The most successful ones are the von Neumann and the Rényi entanglement entropies, which have been heavily studied both in lattice models and in quantum field theories (QFTs). A different, more complete characterization of entanglement is provided by the entanglement (or modular) Hamiltonian, defined as the logarithm of the reduced density matrix. One of the key property of this operator is that, under generic conditions, in 1+1-dimensional conformal field theories (CFTs) presents a local and few-body structure. Beyond just being of theoretical interest, this property has been recently used to efficiently construct the ground state of spin chains in quantum simulators. A recently introduced generalisation of the entanglement Hamiltonian is the negativity Hamiltonian, a non-Hermitian operator which is more useful for mixed states and tripartite entanglement. In this thesis we study these quantifications in many-body quantum systems and in QFTs. In the first part of the thesis, we focus on fermionic systems at equilibrium, and we obtain analytical expressions for the entanglement and the negativity Hamiltonians in the massless Dirac fermion QFT, both in presence of boundaries and at finite temperature. We compare these predictions in the continuum QFT with numerical calculations on the lattice, showing that a proper comparison requires a non-trivial continuum limit of the lattice expression, which we detail. We also investigate a lattice realisation of a non-unitary CFT, the bc-ghost theory, showing that the entanglement Hamiltonian presents an additional term with respect to the unitary case. In the second part, we study the entanglement entropies in an integrable QFT, the massless renormalisation group flow from the tricritical to the critical Ising CFT, demonstrating that the entropy is monotonically decreasing under the renormalisation group flow, as expected from the entropic c-theorem. In the third part we consider out-of-equilibrium problems. We study the melting of a domain wall configuration, computing analytically the entanglement Hamiltonian and showing that the insertion of a defect dramatically modifies the entanglement properties, changing the growth of the entropies from logarithmic to linear in time. Finally, we study generic quantum quenches in free fermionic theories, using the celebrated quasiparticle picture to obtain a prediction for the evolution of the entanglement Hamiltonian during the quench.
Abstract We briefly review recent work on entanglement with particular emphasis on its behaviour in interacting spin systems. As already pointed out by several authors a general understanding of the properties of entanglement in condensed matter systems may lead to a deeper comprehension of both dynamics and thermodynamics of many‐body systems. After a brief resume of known means to identify and quantify entanglement, we take interacting spins on a network as an example. We briefly discuss critical properties of entanglement, if the system undergoes a quantum phase transition, and some aspects of its dynamical behaviour.
Technological and scientific advances have given rise to an era in which coherent quantum-mechanical phenomena can be probed and experimentally-realised over unprecedented timescales in condensed matter physics. In turn, scientific interest in non-equilibrium dynamics and irreversibility signatures of thermodynamics has taken place in recent decades, particularly in relation to cold-atom platforms and thermoelectric devices. In this PhD thesis I summarise some of the most important results obtained over the duration of my PhD, on the topic of thermodynamics involving interacting many-body quantum systems. The topics of discussion encompass three main themes: spin/particle transport in non-integrable systems, explorations in eigenstate thermalisation and finite-temperature transport in autonomous thermal machines. By questioning the effect of local integrability-breaking perturbations, I describe the subtle effects that may rise from conservation laws and their connection to linear response transport using microscopic models. Then, I describe thermalisation in the context of the eigenstate thermalisation hypothesis and its consequence to multipartite entanglement and high-order correlation functions. Finally, motivated by the necessity of describing quantum thermal machines in the finite-temperature regime, I introduce a novel tensor-network based method to investigate thermodynamic properties of autonomous machines that employ interacting many-body systems as working media.
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum many-body phenomena. In the first part we introduce a new approach to the study of entanglement by considering its manipulation under operations not capable of generating entanglement and show there is a total order for multipartite quantum states in this framework. We also present new results on hypothesis testing of correlated sources and give further evidence on the existence of NPPT bound entanglement. In the second part, we study the potential as well as the limitations of a quantum computer for calculating properties of many-body systems. First we analyse the usefulness of quantum computation to calculate additive approximations to partition functions and spectral densities of local Hamiltonians. We then show that the determination of ground state energies of local Hamiltonians with an inverse polynomial spectral gap is QCMA-hard. In the third and last part, we approach the problem of quantum simulating many-body systems from a more pragmatic point of view. We analyze the realization of paradigmatic condensed matter Hamiltonians in arrays of coupled microcavities, such as the Bose-Hubbard and the anisotropic Heisenberg models, and discuss the feasibility of an experimental realization with state-of-the-art current technology.
Over the past twenty years, experimental and technological progresses have motivated a renewed attention to the study of non-equilibrium isolated many-body systems, leading to a relatively well-established paradigm in the case of local Hamiltonians. In the present thesis, I have used quantum information theoretical tools to study out-of-equilibrium dynamics, with particular attention on long-range interacting many-body systems. I have explored the dynamics of bipartite and multipartite entanglement in connection to chaos and scrambling in various long-range (clean and disordered) models. The results contained in this thesis contribute to establishing semi-classical tools as powerful techniques for the description of the quantum information spreading in long-range systems. I have further considered a different, yet connected question, concerning the multipartite entanglement structure of chaotic eigenstates and its generic 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.