Condensed Matter Theory Forum - Dr Alessio Lerose

In this talk, I will introduce an approach to study out-of-equilibrium dynamics of extended quantum many-body systems, inspired by the Feynman-Vernon influence functional theory of quantum baths. We take an open-quantum-system viewpoint and describe evolution of a local subsystem in terms of an influence matrix (IM) - an operator acting on the space of temporal trajectories of the subsystem. The IM fully encodes the effects of the many-body system on its local subregions, and thus characterizes its properties as a quantum bath. This approach trades the high complexity of non-local spatial correlations in the time-evolved many-body state for that of local temporal correlations, which are expected to decay quickly in generic thermalizing systems. Furthermore, it naturally allows to work in the thermodynamic limit and to implement exact ensemble averaging. I will show that this complementary angle of attack offers many advantages, both conceptually and practically. In one spatial dimension, one can exploit space-time duality to write an  exact linear self-consistency equation for the IM. This equation possesses remarkable solutions in a class of maximally chaotic quantum circuits - corresponding to perfect Markovian dephasing dynamics of subsystems - which provide a convenient starting point to analyze the structural properties of the thermalizing phase. Away from such special points, quantum many-body systems exert a non-Markovian influence on subsystems, associated with  temporal entanglement (TE) in the IM. Analyzing a wide range of models with analytical methods and numerical matrix-product-state computations, we study the scaling of TE in several dynamical regimes, ranging from strongly chaotic to (quasi-)integrable and many-body localized (MBL). We find that TE scales favorably away from dynamical phase transition regions, and represents a sensitive probe to characterize dynamical phases, including the emergence of non-trivial edge physics such as strong zero modes. In particular, MBL can be given a neat formulation in terms of  temporal long-range order in the IM. 

Mainly based on a series of recent papers in collaboration with Dmitry Abanin and Michael Sonner.