Non-Hermitian quantum many-body systems are attracting widespread interest for their exotic properties, including unconventional quantum criticality and topology. Here, we study how quantum information and correlations spread under a quantum quench generated by a prototypical non-Hermitian spin chain. Using the mapping to fermions, we solve exactly the problem and compute the entanglement entropy and the correlation dynamics in the thermodynamic limit. Depending on the quench parameters, we identify two dynamical phases. One is characterized by rapidly saturating entanglement and correlations. The other presents a logarithmic entanglement growth in time and correlations spreading faster than the associated unitary system, with collapses and revivals giving rise to a modulated light-cone structure. Here, in the long-time limit, we analytically compute the entanglement entropy that follows a logarithmic law, with an effective central charge that we obtain in closed form. Our results provide an example of an exactly solvable non-Hermitian many-body problem that shows rich physics, including entanglement and spectral transitions.
Non-Hermitian quantum many-body systems are attracting widespread interest for their exotic properties, including unconventional quantum criticality and topology. Here, we study how quantum information and correlations spread under a quantum quench generated by a prototypical non-Hermitian spin chain. Using the mapping to fermions, we solve exactly the problem and compute the entanglement entropy and the correlation dynamics in the thermodynamic limit. Depending on the quench parameters, we identify two dynamical phases. One is characterized by rapidly saturating entanglement and correlations. The other presents a logarithmic entanglement growth in time and correlations spreading faster than the associated unitary system, with collapses and revivals giving rise to a modulated light-cone structure. Here, in the long-time limit, we analytically compute the entanglement entropy that follows a logarithmic law, with an effective central charge that we obtain in closed form. Our results provide an example of an exactly solvable non-Hermitian many-body problem that shows rich physics, including entanglement and spectral transitions.
The nonequilibrium dynamics of disordered many-body quantum systems after a quantum quench unveils important insights about the competition between interactions and disorder, yielding, in particular, an interesting perspective toward the understanding of many-body localization. Still, the experimentally relevant effect of bond randomness in long-range interacting spin chains on their dynamical properties have so far not been investigated. In this Letter, we examine the entanglement entropy growth after a global quench in a quantum spin chain with randomly placed spins and long-range tunable interactions decaying with distance with power $\ensuremath{\alpha}$. Using a dynamical version of the strong disorder renormalization group we find for $\ensuremath{\alpha}>{\ensuremath{\alpha}}_{c}$ that the entanglement entropy grows logarithmically with time and becomes smaller with larger $\ensuremath{\alpha}$ as $S(t)={S}_{p}ln(t)/(2\ensuremath{\alpha})$. Here, ${S}_{p}=2ln2\ensuremath{-}1$. We present results of numerical exact diagonalization calculations for system sizes up to $N\ensuremath{\sim}16$ spins, in good agreement with the analytical results for sufficiently large $\ensuremath{\alpha}>{\ensuremath{\alpha}}_{c}\ensuremath{\approx}1.8$. For $\ensuremath{\alpha}<{\ensuremath{\alpha}}_{c}$, we find that the entanglement entropy grows as a power law with time, $S(t)\ensuremath{\sim}{t}^{\ensuremath{\gamma}(\ensuremath{\alpha})}$ with $0<\ensuremath{\gamma}(\ensuremath{\alpha})<1$ a decaying function of the interaction exponent $\ensuremath{\alpha}$.
Quantum quench is a non-equilibrium process where the Hamiltonian is suddenly changed during the quantum evolution. The change can be made by spatially local perturbations (local quench) or globally switching to a completely different Hamiltonian (global quench). This thesis investigates the post-quench non-equilibrium dynamics with an emphasis on the time dependence of the quantum entanglement. We inspect the scaling of entanglement entropy (EE) to learn how correlation and entanglement built up in a quench. We begin with two local quench examples. In Chap. 2, we apply a local operator to the groundstate of the quantum Lifshitz model and monitor the change of the EE. We find that the entanglement grows according to the dynamical exponent z = 2 and then saturates to the scaling dimension of the perturbing operator -- a value representing its strength. In Chap. 3, we study the evolution after connecting two different one-dimensional critical chains at their ends. The Loschmidt echo which measures the similarity between the evolved state and the initial one decays with a power law, whose exponent is the scaling dimension of the defect (junction). Among other conclusions, we see that the local quench dynamics contain universal information of the (critical) theory. In the global quench scenario, the change of the Hamiltonian affects all parts of the system. In this thesis, we focus on the global chaotic quench driven by generic non-integrable Hamiltonians. In Chap. 4, we propose to use the operator entanglement entropy of the unitary operator as a probe. Its fast linear entanglement production is sharply contrasted to the slow logarithmic spreading of the many-body localized system. The entanglement saturation suggests that the evolution operator in the long time can be modeled by a random unitary matrix. In Chap. 5, we construct a random tensor network which consists of random unitary matrices connected locally to model chaotic evolution with local interactions. We find that the entanglement dynamics is mapped to the statistical mechanics of interacting random walks. This appealing emergent picture allows us to understand the universal linear growth as well as the fluctuations of entanglement in a chaotic quench.
We investigate a quantum quench from a critical to an exceptional point. The initial state, prepared in the ground state of a critical Hermitian system, is time evolved with a non-Hermitian SSH model, tuned to its exceptional point. The single particle density matrix exhibits supersonic modes and multiple light cones, characteristic of non-Hermitian time evolution. These propagate with integer multiples of the original Fermi velocity. In the long time limit, the fermionic Green's function decays spatially as 1/x2, in sharp contrast to the usual 1/x decay of noninteracting fermions. The entanglement entropy is understood as if all these supersonic modes arise from independent quasiparticles (though they do not), traveling with the corresponding supersonic light cone velocity. The entropy production rate decreases with time and develops plateaus during the time evolution, signaling the distinct velocities in the propagation of nonlocal quantum correlations. At late times, the entanglement entropy saturates to a finite value, satisfying a volume law.
The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, by combining a quasiparticle picture for the entanglement spreading with the exact knowledge of the stationary state provided by Bethe ansatz, it is possible to obtain an exact and analytic description of the evolution of the entanglement entropy. Here we discuss the application of these ideas to several integrable models. First we show that for non-interacting systems, both bosonic and fermionic, the exact time-dependence of the entanglement entropy can be derived by elementary techniques and without solving the dynamics. We then provide exact results for interacting spin chains that are carefully tested against numerical simulations. Finally, we apply this method to integrable one-dimensional Bose gases (Lieb-Liniger model) both in the attractive and repulsive regimes. We highlight a peculiar behaviour of the entanglement entropy due to the absence of a maximum velocity of excitations.
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.
Non-Hermiticity and dephasing, collaborating in an unusual wave-packet dynamics, realize unconventional entanglement evolution in a disordered, interacting, and asymmetric (nonreciprocal) quantum medium. Taking the Hatano-Nelson model as a concrete example, we first consider how wave packet spreads in a non-Hermitian disordered system for demonstrating that it is very different from the Hermitian case. Interestingly, a cascadelike wave-packet spreading as in the Hermitian case is suppressed in the clean limit and at weak disorder, while it revives in the vicinity of the localization-delocalization transition. Based on this observation, we then analyze how the entanglement entropy of the system evolves in the interacting non-Hermitian model, revealing its nonmonotonic evolution in time. We clarify the different roles of dephasing in the time evolution of entanglement entropy in Hermitian and non-Hermitian systems, and show that the many-body dynamics is governed by a principle different from the Hermitian case. The size dependence of the results suggests with the increase of disorder, an unusual area-volume--area-law crossover of the maximal entanglement entropy. To analyze the effects of disorder on a firm basis, using the Hermitian limit as a benchmark, we employ a quasiperiodic disorder (Aubry-Andr\'e model) in the analyses.