Energy transport in quantum many-body systems

Gianluca Morettini, Luca Capizzi, Maurizio Fagotti +1 more

We report the observation of unconventional transport phenomena in a spin-1 model that supports a tower of quantum many-body scars, and we discuss their properties uncovering their peculiar nature. In quantum many-body systems, the late-time dynamics of local observables are typically governed by conserved operators with local densities, such as energy and magnetization. In the model under investigation, however, there is an additional dynamical symmetry restricted to the subspace of the Hilbert space spanned by the quantum many-body scars. The latter significantly slows the decay of autocorrelation functions of certain coherent states of quantum many-body scars and is responsible for the unconventional form of transport that we detect numerically. We show that excited states with energy close to that of the quantum many-body scars play a crucial role in sustaining the transport. Finally, we propose a generalized eigenstate thermalization hypothesis to describe specific properties of states with energy close to the scars.

Marko Ljubotina, Jean-Yves Desaules, Maksym Serbyn +1 more

Kinetic constraints in many-body quantum systems can give rise to an intriguingly fast ``superdffusive'' transport of energy, suggesting a new class of transport behaviors whose origin remains to be understood.

D. J. Thouless, H. S. W. Massey, R. W. Hellwarth

Vipin Kerala Varma, Alessio Lerose, Francesca Pietracaprina +2 more

Abstract The phenomenon of many-body localization in disordered quantum many-body systems occurs when all transport is suppressed despite the fact that the excitations of the system interact. In this work we report on the numerical simulation of autonomous quantum dynamics for disordered Heisenberg chains when the system is prepared with an initial inhomogeneity in the energy density profile. Using exact diagonalisation and a dynamical code based on Krylov subspaces we are able to simulate dynamics for up to L = 26 spins. We find, surprisingly, the breakdown of energy diffusion even before the many-body localization transition whilst the system is still in the ergodic phase. Moreover, in the ergodic phase we also find a large region in parameter space where the energy dynamics remains diffusive but where spin transport has been previously evidenced to occur only subdiffusively: this is found to be true for initial states composed of infinitely many hydrodynamic modes (square-wave energy profile) or just the single longest mode (sinusoidal profile). This suggestive finding points towards a peculiar ergodic phase where particles are transported slower than energy, reminiscent of the situation in amorphous solids and of the gapped phase of the anisotropic Heisenberg model.