We investigate the unitary evolution following a quantum quench in quantum spin models possessing a (nearly) flat band in the linear excitation spectrum. Inspired by the perspective offered by ensembles of individually trapped Rydberg atoms, we focus on the paradigmatic trasverse-field Ising model on two dimensional lattices featuring a flat band as a result of destructive interference effects (Lieb and Kagomé lattice); or a nearly flat band due to a strong energy mismatch among sublattices (triangular lattice). Making use of linear spin-wave theory, we show that quantum quenches, equipped with single-spin imaging, can directly reveal the spatially localized nature of the dispersionless excitations, and their slow propagation or lack of propagation altogether. Moreover we show that Fourier analysis applied to the post-quench time evolution of wavevector-dependent quantities allows for the spectroscopic reconstruction of the flat bands. Our results pave the way for future experiments with Rydberg quantum simulators, which can extend our linear spin-wave study to the fully nonlinear regime, characterized by the appearance of dense, strongly interacting gases of dispersionless excitations.

Disorder in quantum systems can lead to the disruption of long-range order in the ground state and to the localization of the elementary excitations -famous examples thereof being the Bose glass of interacting bosons in a disordered or quasi-periodic environment, or the localized phase of spin chains mapping onto fermions. Here we present a two-dimensional quantum Ising modelrelevant to the physics of Rydberg-atom arrays -in which positional disorder of the spins induces a randomization of the spin-spin couplings and of an on-site longitudinal field. This form of disorder preserves long-range order in the ground state, while it localizes the elementary excitations above it, faithfully described as spin waves: the spin-wave spectrum is partially localized for weak disorder (seemingly exhibiting mobility edges between localized and extended, yet non-ergodic states), while it is fully localized for strong disorder. The regime of partially localized excitations exhibits a very rich non-equilibrium dynamics following a low-energy quench: correlations and entanglement spread with a power-law behavior whose exponent is a continuous function of disorder, interpolating between ballistic and arrested transport. Our findings expose a stark dichotomy between static and dynamical properties of disordered quantum spin systems, which is readily accessible to experimental verification using quantum simulators of closed quantum many-body systems.

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The study of non-equilibrium dynamics is one of the most important challenges of modern quantum many-body physics, in relationship with fundamental questions in quantum statistical mechanics, as well as with the fields of quantum simulation and computing. In this work we propose a Gaussian Ansatz for the study of the nonequilibrium dynamics of quantum spin systems. Within our approach, the quantum spins are mapped onto Holstein-Primakoff bosons, such that a coherent spin state -chosen as the initial state of the dynamics -represents the bosonic vacuum. The state of the system is then postulated to remain a bosonic Gaussian state at all times, an assumption which is exact when the bosonic Hamiltonian is quadratic; and which is justified in the case of a nonlinear Hamiltonian if the boson density remains moderate. We test the accuracy of such an Ansatz in the paradigmatic case of the S = 1/2 transverse-field Ising model, in one and two dimensions, initialized in a state aligned with the applied field. We show that the Gaussian Ansatz, when applied to the bosonic Hamiltonian with nonlinearities truncated to quartic order, is able to reproduce faithfully the evolution of the state, including its relaxation to the equilibrium regime, for fields larger than the critical field for the paramagnetic-ferromagnetic transition in the ground state. In particular the spatio-temporal pattern of correlations reconstructed via the Gaussian Ansatz reveals the dispersion relation of quasiparticle excitations, exhibiting the softening of the excitation gap upon approaching the critical field. Our results suggest that the Gaussian Ansatz correctly captures the essential effects of nonlinearities in quantum spin dynamics; and that it can be applied to the study of fundamental phenomena such as quantum thermalization and its breakdown.

We analyse the dynamics of quantum correlations between two qubits coupled to a linear chain of oscillators. The qubits undergo an effective open-system dynamics in the presence of a non-Markovian reservoir, constituted by the chain's vibrations. The model is amenable to an analytical solution when the chain is initially in a thermal state. We study the dynamics of the qubits concurrence starting from a separable state and assuming that the chain spectrum is gapped. We identify three relevant regimes that depend on the strength of the qubit-chain coupling in relation to the spectral gap. These are (i) the weak coupling regime, where the qubits are entangled at the asymptotics; (ii) the strong coupling regime, where the concurrence can exhibit collapses followed by revivals with exponentially attenuated amplitude; and (iii) the thermal damping regime, where the concurrence rapidly vanishes due to the chain's thermal excitation. In all cases, if entanglement is generated, this occurs after a finite time has elapsed. This time scale depends exponentially on the qubits distance and is determined by the spectral properties of the chain. Entanglement irreversible decay, on the other hand, is due to the dissipative effect induced by the coupling with the chain and is controlled by the coupling strength between the chain and qubits. This study identifies the resources of an environment for realising quantum coherent dynamics of open systems.