A theoretical analysis of non-Markovian open system dynamics in correlated quantum materials

Abstract

Gaining fine control over the behaviours of open quantum systems requires a finer understanding of the ways in which their environments impact their dynamics. While frequent approaches invoke Markovian approximations, the modern push towards picosecond quantum technologies highlights the practical need for treatments that go beyond this paradigm. In non-Markovian dynamical regimes, excitations within the environment of a system have lifetimes long enough to mediate a time-delayed self-coupling. These memory effects can lead to quantitatively distinct features in the resulting dynamics of the system, and so a precise understanding of their origin is crucial. Building upon a robust theoretical framework, we perform a systematic analysis of the dynamics of an impurity spin coupled to strongly correlated materials. As a theoretically and experimentally accessible model, we start with the Luttinger liquid, which allows us to study how strong correlations and interactions alter the response of the bath to the impurity and the resulting dynamics. Under this framework, non-Markovian behaviour emerges in the form of an initial slip prior to the spin decoherence, and we find that the signatures of spin-charge separation within the Luttinger liquid play a direct role in mediating this response. We further uncover the precise link between the strengths of interactions in modulating the rate and amplitude of this feature, which can be either greatly enhanced or suppressed. Equipped with this knowledge, we demonstrate that additional advantage can be gained out of cooling protocols that operate based on the non-Markovian dynamical response. We also consider scenarios where the massive Klein-Gordon model is an emergent theory of the bath, uncovering rich theoretical insights into the relationship between massive and massless limits via transient generalised Gibbs ensembles. Remarkably, we find that this transient regime is characterised by a massless theory with a mass-dependent effective temperature.