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...

We consider two semi-infinite quantum Ising chains initially at thermal equilibrium at two different temperatures and subsequently joined by an interaction between their end points. Transport properties such as the heat current are determined by the dynamics of the left- and right-moving fermionic quasiparticles which characterize the ensuing unitary dynamics. Within the so-called semiclassical space-time scaling limit we extend known results by determining the full space and time dependence of the density and current of energy and of fermionic quasiparticles. Upon approaching the edge of the propagating front, these quantities as well as the two-point correlation function display qualitatively different behaviors depending on the transverse field of the chain being critical or not. While in the latter case corrections to the leading behavior are described, as expected, by the Airy kernel, in the former a novel scaling form emerges with universal features.

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