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The laws of thermodynamics require any initial macroscopic inhomogeneity in extended manybody systems to be smoothed out by the time evolution through the activation of transport processes. In generic, non-integrable quantum systems, transport is expected to be governed by a diffusion law, whereas a sufficiently strong quenched disorder can suppress it completely due to many-body localization of quantum excitations. Here we show that the confinement of quasi-particles can also lead to transport suppression even if the dynamics are generated by homogeneous Hamiltonians. We demonstrate this in the quantum Ising chain with transverse and longitudinal magnetic fields in the paradigmatic case of the evolution of domain-wall states. We perform extensive numerical simulations of the dynamics which turn out to be in excellent agreement with an effective analytical description valid within both weak and strong confinement regimes. Our results show that the energy flow from "hot" to "cold" regions of the chain is suppressed for all accessible times. We argue that this phenomenon is connected with the presence of atypical states in the many-body energy spectrum which violate the eigenstate thermalization hypothesis, as recently reported in the literature.Introduction-Recent times have witnessed an increasing attention in the non-equilibrium dynamics of isolated quantum many-body systems [1][2][3]. This interest has been prompted by an impressive advance in experimental techniques with cold atoms that made it possible to maintain coherent quantum dynamics for sufficiently long times [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The simplest protocol to drive a system out of equilibrium is the so-called quantum quench [19][20][21], in which the dynamics of the system are monitored after a sudden change of a parameter of its Hamiltonian.In this context, a fundamental question concerns whether and how the transport of globally conserved physical quantities such as particle and energy densities arises in these non-equilibrium quantum many-body systems [22,23]. The spatial spreading of local inhomogeneities in isolated systems is generically expected to obey a diffusion law, whose microscopic origin is usually traced back to the occurrence of inelastic collisions [24,25].These transport processes can be conveniently studied via inhomogeneous quenches [26,27] in which two subsystems initially prepared in two different equilibrium states, are joined by means of a local interaction. In this framework, transport may be enhanced by the existence of stable quasi-particles traveling ballistically with certain characteristic velocities, as in the case of integrable systems. Indeed, around the junction, a non-equilibrium stationary state may arise, supporting ballistic transport and thus finite currents at long times. These currentcarrying states have been investigated in conformal field theories [28][29][30] and in non-interacting models, where, in addition, exact expressions can be obtained for the nonequilibrium profiles of l...

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The dynamics after a quantum quench is determined by the weights of the initial state in the eigenspectrum of the final Hamiltonian, i.e., by the distribution of overlaps in the energy spectrum. We present an analysis of such overlap distributions for quenches of the anisotropy parameter in the one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide an overview of the form of the overlap distribution for quenches from various initial anisotropies to various final ones, using numerical exact diagonalization. We show that if the system is prepared in the antiferromagnetic Néel state (infinite anisotropy) and released into a non-interacting setup (zero anisotropy, XX point) only a small fraction of the final eigenstates gives contributions to the post-quench dynamics, and that these eigenstates have identical overlap magnitudes. We derive expressions for the overlaps, and present the selection rules that determine the final eigenstates having nonzero overlap. We use these results to derive concise expressions for time-dependent quantities (Loschmidt echo, longitudinal and transverse correlators) after the quench. We use perturbative analyses to understand the overlap distribution for quenches from infinite to small nonzero anisotropies, and for quenches from large to zero anisotropy.

We study the non-equilibrium quench dynamics from free to hard-core one-dimensional bosons in the presence of a hard-wall confining potential. We characterise the density profile and the two-point fermionic correlation function in the stationary state as well as their full time evolution. We find that for long times the system relaxes to a uniform density profile, but the correlation function keeps memory of the initial state with a stationary algebraic long-distance decay as opposite to the exponential behaviour found for the same quench in the periodic setup. We also compute the stationary bosonic two-point correlator which turns out to decay exponentially for large distances. We show that a two-step mechanism governs the time evolution: a quick approach to an almost stationary value is followed by a slow algebraic relaxation to the true stationary state.

Quantum spin systems with kinetic constraints have become paradigmatic for exploring collective dynamical behaviour in many-body systems. Here we discuss a facilitated spin system which is inspired by recent progress in the realization of Rydberg quantum simulators. This platform allows to control and investigate the interplay between facilitation dynamics and the coupling of spin degrees of freedom to lattice vibrations. Developing a minimal model, we show that this leads to the formation of polaronic quasiparticle excitations which are formed by many-body spin states dressed by phonons. We investigate in detail the properties of these quasiparticles, such as their dispersion relation, effective mass and the quasiparticle weight. Rydberg lattice quantum simulators are particularly suited for studying this phonon-dressed kinetically constrained dynamics as their exaggerated length scales permit the site-resolved monitoring of spin and phonon degrees of freedom.

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We explore the relaxation dynamics of elementary spin clusters in a kinetically constrained spin system. Inspired by experiments with Rydberg lattice gases, we focus on the situation in which an excited spin leads to a "facilitated" excitation of a neighboring spin. We show that even weak interactions that extend beyond nearest neighbors can have a dramatic impact on the relaxation behavior: they generate a linear potential, which under certain conditions leads to the onset of Bloch oscillations of spin clusters. These hinder the expansion of a cluster and more generally the relaxation of many-body states towards equilibrium. This shows that non-ergodic behavior in kinetically constrained systems may occur as a consequence of the interplay between reduced connectivity of many-body states and weak interparticle interactions. We furthermore show that the emergent Bloch oscillations identified here can be detected in experiment through measurements of the Rydberg atom density, and discuss how spin-orbit coupling between internal and external degrees of freedom of spin clusters can be used to control their relaxation behavior.