Quantum transport and hydrodynamics in strongly interacting systems: Symmetries, Quantum criticality and Entanglement

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Over the last decade or so, there has been enormous growing interest from both theorists and various experimental physics communities in quantum dynamics in strongly interacting regimes. Impressive theoretical progress has been made on various research fronts. On the experimental side, the cutting edge pulsed-laser based pump-probe technique that many solid state labs are developing and perfecting is opening a door to more studies of quantum dynamics. Very recent observation of Planckian transport and scale invariant transport in strongly interacting materials further indicates universal transport phenomena in a broad class of very different interacting condensed matter states. The transport dynamics observed further suggest a possible intimate connection between the universal Planckian transport and fastest information spreading near a black hole. Hydrodynamics of Dirac fermions had also been observed in graphene and a few months ago, viscous flow due to mutual-interactions between Dirac fermions was imaged. These studies, theoretical and experimental ones, have revealed fascinating and unexpected aspects of dynamics.These intensive experimental efforts and impressive successes further demand new theoretical efforts on non-equilibrium quantum phenomena in strongly interacting regimes. In this proposal, we will research on quantum dynamics including transport dynamics and hydrodynamics in strongly interacting quantum critical regimes that are (nearly) scale invariant. We will explore universal transport dynamics and quantum hydrodynamics that can potentially and naturally emerge in these interacting systems. We will specially examine and identify new dimensions in parameter spaces where deviations from universal dynamics can be studied in a controllable and pronounced way. The main objective of is to test the robustness of potential universal dynamic phenomena against experimental variables and understand the resultant dynamics, transport and hydrodynamics in quantum critical regimes. To achieve these objectives, we divide the proposal into two parts, each of which emphasizes a few particular universal aspects of dynamic phenomena as outlined below. And these aspects will be examined in different condensed matter systems including cold gases, depending on which are experimentally more relevant and more practical to realize in labs. Part I addresses Planckian transport phenomena and hydrodynamics in strongly interacting Dirac fermions in 2D and 3D semi-metals near charge neutrality points. Dirac points can be considered to be critical ones and further strong interactions can result in Planckian transport and relativistic viscous hydrodynamic flow in ultra clean semi-metals where impurity and phonon scatterings are negligible. Part II concerns emergent universal conformal dynamics in strongly interacting cold gases and Fermi-Bose quantum mixtures near Feshbach resonance, as well as in interacting solid states near Lifshitz transitions.