The characterization of the dynamical structure of quantum many-body systems is an important and very active endeavor both experimentally and theoretically. Several tools, such as quantum-information theoretic observables and spectral measures, provide a powerful lens for characterizing correlations and their dynamics in quantum many-body systems. These quantities can reveal important features of experimentally realizable systems and provide insight into their control and dynamical behaviour. This thesis investigates nonequilibrium settings in which the spreading and redistribution of quantum correlations exhibit unconventional behaviour, with particular emphasis on the role of extended-range correlations. We consider two main classes of systems: lattice models undergoing quantum quenches and central-spin models motivated by experimental applications. For lattice systems, we study the dynamics of entanglement and local symmetry breaking in free fermionic and bosonic models, interacting integrable systems, and quantum circuits. We first investigate symmetry restoration following quenches from ground states of long-range fermionic Hamiltonians. We show that two states undergoing symmetry restoration can exhibit multiple inversions, manifested through multiple crossings of the distance measure, implying either the evasion of the quantum Mpemba effect or a more intricate route to its occurrence. This demonstrates that anomalous relaxation is not restricted to short times and can be understood through the momentum-dependent distribution and velocities of quasiparticle excitations. We then study quenches from initial states possessing extensive, spatially organized entanglement, moving beyond the conventional setting of weakly entangled initial states. For crosscap states, characterized by antipodal correlations and volume-law entanglement entropy, we uncover unconventional entanglement dynamics and formulate an antipodal quasiparticle picture in which initially entangled degrees of freedom originate from macroscopically separated points. We subsequently generalize this construction to entangled multipodal states, whose polygon-like correlation structure produces richer equilibrium and dynamical entanglement patterns. We further investigate charge-deformed crosscap states and show that their local symmetry-breaking dynamics can display the unusual phenomenon of dynamical symmetry breaking under symmetry-preserving evolution. Finally, we extend the crosscap construction to bosonic systems and describe the dynamics of the entanglement entropy, mutual information, and logarithmic negativity within a corresponding quasiparticle framework. The second class of systems considered concerns central-spin models and their application to quantum memories in semiconductor quantum dots. We investigate how disorder in couplings and frequencies modifies collective many-body dynamics and affects the storage and retrieval of quantum information. Using spectral, dynamical, and information-theoretic diagnostics, we characterize the resulting dynamical regimes and relate the loss of collectivity and the spreading of information through the spin bath to the performance of quantum-memory protocols. Overall, the results demonstrate how extended-range correlations, whether encoded in an initial state or generated by the interaction structure, can qualitatively reshape entanglement spreading, symmetry dynamics, and information retention in nonequilibrium quantum many-body systems.
The characterization of the dynamical structure of quantum many-body systems is an important and very active endeavor both experimentally and theoretically. Several tools, such as quantum-information theoretic observables and spectral measures, provide a powerful lens for characterizing correlations and their dynamics in quantum many-body systems. These quantities can reveal important features of experimentally realizable systems and provide insight into their control and dynamical behaviour. This thesis investigates nonequilibrium settings in which the spreading and redistribution of quantum correlations exhibit unconventional behaviour, with particular emphasis on the role of extended-range correlations. We consider two main classes of systems: lattice models undergoing quantum quenches and central-spin models motivated by experimental applications. For lattice systems, we study the dynamics of entanglement and local symmetry breaking in free fermionic and bosonic models, interacting integrable systems, and quantum circuits. We first investigate symmetry restoration following quenches from ground states of long-range fermionic Hamiltonians. We show that two states undergoing symmetry restoration can exhibit multiple inversions, manifested through multiple crossings of the distance measure, implying either the evasion of the quantum Mpemba effect or a more intricate route to its occurrence. This demonstrates that anomalous relaxation is not restricted to short times and can be understood through the momentum-dependent distribution and velocities of quasiparticle excitations. We then study quenches from initial states possessing extensive, spatially organized entanglement, moving beyond the conventional setting of weakly entangled initial states. For crosscap states, characterized by antipodal correlations and volume-law entanglement entropy, we uncover unconventional entanglement dynamics and formulate an antipodal quasiparticle picture in which initially entangled degrees of freedom originate from macroscopically separated points. We subsequently generalize this construction to entangled multipodal states, whose polygon-like correlation structure produces richer equilibrium and dynamical entanglement patterns. We further investigate charge-deformed crosscap states and show that their local symmetry-breaking dynamics can display the unusual phenomenon of dynamical symmetry breaking under symmetry-preserving evolution. Finally, we extend the crosscap construction to bosonic systems and describe the dynamics of the entanglement entropy, mutual information, and logarithmic negativity within a corresponding quasiparticle framework. The second class of systems considered concerns central-spin models and their application to quantum memories in semiconductor quantum dots. We investigate how disorder in couplings and frequencies modifies collective many-body dynamics and affects the storage and retrieval of quantum information. Using spectral, dynamical, and information-theoretic diagnostics, we characterize the resulting dynamical regimes and relate the loss of collectivity and the spreading of information through the spin bath to the performance of quantum-memory protocols. Overall, the results demonstrate how extended-range correlations, whether encoded in an initial state or generated by the interaction structure, can qualitatively reshape entanglement spreading, symmetry dynamics, and information retention in nonequilibrium quantum many-body systems.
In this thesis, we first present a review on the background and research related to our published works. We then present our first work, which investigates entanglement entropy free-fermionic systems of D-spatial dimensions using an effective quasiparticle description. In particular, we consider a quantum quench to the D-dimensional tight-binding model from an initial state invariant under translation by nu sites. We develop an efficient Monte Carlo scheme to implement the quasiparticle solution to arbitrary connected subsystems, and show that, in two dimensions, the shape and orientation of the subsystem with respect to the underlying lattice is able to effect qualitative behaviour of the entanglement growth. In our second work, we investigate the breaking and restoration of translation symmetry in the same quench setup restricted to the one-dimensional setting. We establish the presence of the so-called quantum Mpemba effect in this setting, which had hitherto been almost exclusively considered with respect to continuous U(1) symmetry breaking. We also apply a quasiparticle picture to our chosen measure of symmetry breaking and find that this picture does not agree with the solution obtained by exact diagonalisation. From this we conclude that the restoration of discrete symmetries in integrable systems goes beyond the leading hydrodynamic order. Finally, in this thesis we also present a brief review related to our most recent work, which considers the recently proposed hierarchical dual-unitary circuit in two dimensions. We then present the current iteration of this work, which defines the set of DU2 conditions on the two-dimensional gates that may be used to fully simplify two-point spatio-temporal correlation functions in terms of the repeat action of quantum channels. Furthermore, we identify directions of these correlations along the edge of the causal lightcone with no 1D counterpart that are generically non-vanishing with respect to these DU2 conditions. This is demonstrated for a particular family of gate with site dimension d=6.
The linear growth of entanglement after a quench from a state with short-range correlations is a universal feature of many body dynamics. It has been shown to occur in integrable and chaotic systems undergoing either Hamiltonian, Floquet or circuit dynamics and has also been observed in experiments. The entanglement dynamics emerging from long-range correlated states is far less studied, although no less viable using modern quantum simulation experiments. In this work, we investigate the dynamics of the bipartite entanglement entropy and mutual information from initial states which have long-range entanglement with correlation between antipodal points of a finite and periodic system. Starting from these crosscap states, we study both brickwork quantum circuits and Hamiltonian dynamics and find distinct patterns of behaviour depending on the type of dynamics and whether the system is integrable or chaotic. Specifically, we study both dual unitary and random unitary quantum circuits as well as free and interacting fermion Hamiltonians. For integrable systems, we find that after a time delay the entanglement experiences a linear in time decrease followed by a series of revivals, while, in contrast, chaotic systems exhibit constant entanglement entropy. On the other hand, both types of systems experience an immediate linear decrease of the mutual information in time. In chaotic systems this then vanishes, whereas integrable systems instead experience a series of revivals. We show how the quasiparticle and membrane pictures of entanglement dynamics can be modified to describe this behaviour, and derive explicitly the quasiparticle picture in the case of free fermion models which we then extend to all integrable systems.
Quantum systems display counterintuitive features, escaping our everyday-life intuition, whose origin is related to entanglement. This phenomenon arises when different parts of the same systems display correlations, which cannot be understood via classical mechanics, and they are dubbed as quantum. To characterize the correlations above, it is necessary to find good entanglement measures which are able to capture quantitatively the quantum features of a given system. This motivates the investigation and the computation of quantities such as the von Neumann entropy of regions, which provides information about how a system is entangled. Our focus is quantum one-dimensional systems close to their critical point, where quantum correlations are enhanced, and a characterization via Quantum Field Theory (QFT) can be provided. In particular, we aim to understand the role of symmetries and localized defects on the entanglement properties. Those aspects display an intimate connection. First, via replica trick, the entropy is expressed via a replica permutation symmetry. Then, single defects break symmetries that are present in the corresponding homogeneous systems. Due to these reasons, the characterization of symmetry actions on subsystems can be viewed as a unifying framework for quantifying entanglement. We split this thesis into two parts. The first part is devoted to the symmetry-resolved entanglement. We first compute it in massive integrable field theories, giving analytical predictions for free fermions/bosons and the 3-state Potts model. For instance, we characterize the universal corrections to area law via form factor bootstrap. We also study excited states of field theories, and we characterize both low-energy states of Conformal Field Theory (CFT) and quasi-particle states. The second part deals with quantum correlations across defects. We provide a CFT framework to compute Rényi entropy and negativity in the ground state of conformal junctions, giving analytical predictions for free fermions and bosons. We find logarithmic growth of the entanglement measures above, and we relate the universal prefactor to the boundary conditions, encoded in a boundary scattering matrix. Then, we focus on the entanglement dynamics, and we study the time evolution of correlations for two paradigmatic classes of quench protocols. For a global quench, we find a linear growth of entropy across the defect whose slope is computed both in CFT, for thermal states, and for free fermions, via a modification of the quasi-particle picture. For a domain wall melting protocol, also known as inhomogeneous quench, we find that, while local observables are easily understood via hydrodynamics and local generalized Gibbs ensembles, the same is not true for the entropy. In contrast, by employing the quasi-particle picture, we provide precise predictions for the dynamics of entanglement, revealing the influence of long-range correlations between points that are specular with respect to the defect.
In a periodic lattice system an entangled antipodal pair state, otherwise known as a crosscap state, is a simple two site product state in which spins at antipodal sites are prepared in Bell pairs. Such states have maximal bipartite entanglement and serve as a useful platform for studying the quench dynamics of systems which have large initial entanglement. In this paper, we study a generalization of these states which we dub entangled mutipodal states. These states, which are defined for fermionic systems, generalize the crosscap states by having correlations among more than two sites, specifically, those which sit at the vertices of regular polygons. By construction, the states are Gaussian and translationally invariant allowing many of their properties to be understood. We study the bipartite entanglement entropy of these states both in and out of equilibrium. In equilibrium, the entanglement profile as a function of subsystem size exhibits two distinct regimes, a volume-law growth followed by a saturation to a constant value, thus generalizing the Page-curve profile of the crosscap state. In the non-equilibrium setting, we study quenches from these initial states to the free-fermion chain, whose ensuing dynamics displays a far richer structure compared to the crosscap case. We interpret our results in terms of the quasiparticle picture, which requires multiplets of quasiparticles to be excited non-locally around the system. This scenario is confirmed by the appearance of a post-quench, negative tripartite information.
Quantum simulation platforms such as cold atoms, superconducting circuits, and trapped ions enable the experimental investigation of quantum many-body systems, with important implications for quantum technologies. In this thesis, we investigate how entanglement and correlations develop in such systems and how they can be harnessed both for the theoretical study of models relevant to condensed matter physics and for practical applications in quantum metrology. We begin by focusing on the adiabatic preparation of quantum many-body ground states. In particular, we show that quantum simulators can probe the link between spectral degeneracy and Spontaneous Symmetry Breaking, as pioneered by P.W. Anderson. We prove that odd-sized spin-½ systems exhibiting time-reversal symmetry sustain a net magnetization even away from the thermodynamic limit, thanks to an exact spectral degeneracy. Moreover, the symmetry-broken state exhibits scalable spin squeezing, a key resource for quantum metrology. We then turn to a different paradigm of evolution: quench dynamics. In particular, we show that monitoring the real-time evolution of correlations allows for the experimental measurement of the dispersion relation of fundamental excitations. In the case of two-dimensional long-range ordered systems, such as the dipolar XY model, these excitations are spin waves, leading to sharp features in the evolution of two-point correlation functions. Conversely, in one-dimensional systems, fundamental excitations have a fermionic nature, and their detection requires the measurement of non-local correlation functions. The latter, while inaccessible in condensed matter, are instead well suited to quantum simulators with individually addressable degrees of freedom.
In a non-equilibrium many-body system, the quantum information dynamics between non-complementary regions is a crucial feature to understand the local relaxation towards statistical ensembles. Unfortunately, its characterization is a formidable task, as non-complementary parts are generally in a mixed state. We show that for integrable systems, this quantum information dynamics can be quantitatively understood within the quasiparticle picture for the entanglement spreading. Precisely, we provide an exact prediction for the time evolution of the logarithmic negativity after a quench. In the space-time scaling limit of long times and large subsystems, the negativity becomes proportional to the Rényi mutual information with Rényi index α = 1 / 2 . We provide robust numerical evidence for the validity of our results for free-fermion and free-boson models, but our framework applies to any interacting integrable system.