Institute for Theoretical Condensed Matter physics

Karlsruhe Institute of Technology

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D-76131 Karlsruhe

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# Non-perturbative stochastic method for driven quantum impurity systems

Author: Peter P. Orth, Adilet Imambekov, Karyn Le Hur Phys. Rev. B 87, 014305 (2013) preprint: arXiv:1211.120 25.01.2013

We introduce and apply a numerically exact method for investigating the real-time dissipative dynamics of quantum impurities embedded in a macroscopic environment beyond the weak-coupling limit. We focus on the spin-boson Hamiltonian that describes a two-level system interacting with a bosonic bath of harmonic oscillators. This model is archetypal for investigating dissipation in quantum systems and tunable experimental realizations exist in mesoscopic and cold-atom systems. It finds abundant applications in physics ranging from the study of decoherence in quantum computing and quantum optics to extended dynamical mean-field theory. Starting from the real-time Feynman-Vernon path integral, we derive an exact stochastic Schr\"odinger equation that allows to compute the full spin density matrix and spin-spin correlation functions beyond weak coupling. We greatly extend our earlier work (P. P. Orth, A. Imambekov, K. Le Hur, Phys. Rev. A {\bf 82}, 032118 (2010)) by fleshing out the core concepts of the method and by presenting a number of interesting applications. Methodologically, we present an analogy between the dissipative dynamics of a quantum spin and that of a classical spin in a random magnetic field. This analogy is used to recover the well-known Non-Interacting-Blip-Approximation (NIBA) in the weak-coupling limit. We explain in detail how to compute spin-spin autocorrelation functions. As interesting applications of our method, we explore the non-Markovian effects of the initial spin-bath preparation on the dynamics of the coherence $\sigma^x(t)$ and of $\sigma^z(t)$ under a Landau-Zener sweep of the bias field. We also compute to a high precision the asymptotic long-time dynamics of $\sigma^z(t)$ without bias and demonstrate the wide applicability of our approach by calculating the spin dynamics at non-zero bias and different temperatures.