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Journal of Physics Condensed Matter

Dynamics of an impurity spin coupled to a spin-boson dissipative system

Tabish Qureshi, Sushanta Dattagupta

Published Mar 4, 1991• 3 citations
Publisher

Abstract

The authors study the dynamics of an impurity spin coupled to a spin-boson dissipative system. They calculate the transverse correlation function of the impurity spin and compare the result with that obtained from an equivalent stochastic model. A phenomenological rate parameter in the stochastic model is represented in terms of microscopically obtained quantities. The authors also calculate the NMR lineshapes for various temperatures which are relevant in the context of a particular physical realization of the model. Motional narrowing of lines is observed at high temperatures.

DOI
10.1088/0953-8984/3/9/005

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The authors study the dynamics of an impurity spin coupled to a spin-boson dissipative system. They calculate the transverse correlation function of the impurity spin and compare the result with that obtained from an equivalent stochastic model. A phenomenological rate parameter in the stochastic model is represented in terms of microscopically obtained quantities. The authors also calculate the NMR lineshapes for various temperatures which are relevant in the context of a particular physical realization of the model. Motional narrowing of lines is observed at high temperatures.
Abstract The dynamics of an impurity spin coupled to a spin‐boson dissipative system is studied using the resolvent expansion technique. In one particular physical realization the model simulates a highly anisotropic Kondo system. The transverse correlation function of the impurity spin is calculated and the result obtained is analyzed in various limiting cases. NMR lineshapes are also calculated for various temperatures which are relevant in another physical realization of the model. Motional narrowing is observed at high temperature.
We present results for the dynamics of an impurity spin coupled to a magnetic field and to two ohmic baths that are out of equilibrium due to the application of a bias voltage. Both the nonequilibrium steady state and the rate constants describing the approach to the steady state are found to depend sensitively on the relative strengths of a magnetic field and a voltage dependent decoherence rate. Computation of physical quantities, including the frequency dependent ratio of the response to the correlation functions and the probabilities of the two spin states, allows the extraction of voltage dependent effective temperatures. The temperatures extracted from different quantities differ from one another in magnitude and in their dependence on parameters, and, in general, are nonmonotonic.
Recent developments in density matrix renormalization group/matrix product state techniques allow today for a quantitative computation of dynamical correlations at finite temperature in low-dimensional quantum spin systems. By combining numerical results and field theoretical asymptotic methods, e.g., bosonization, it is now possible to give a full description of the dynamical quantity one is interested in for the range of temperatures experimentally accessible. This enhances of course the possibility of one-to-one comparisons with experiments without having to resort to uncontrolled approximations. Here, the authors focus on the temperature dependence of the NMR spin-lattice relaxation rate 1/T11/{T}_{1}1/T1​ in spin-12\frac{1}{2}21​ chain systems. This quantity is directly related to local, dynamical spin-spin correlation functions. The results agree in the low-temperature regime with bosonization predictions, and show interesting deviations from this behavior at intermediate temperatures.
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 σx(t)\sigma^x(t)σx(t) and of σz(t)\sigma^z(t)σz(t) under a Landau-Zener sweep of the bias field. We also compute to a high precision the asymptotic long-time dynamics of σz(t)\sigma^z(t)σz(t) without bias and demonstrate the wide applicability of our approach by calculating the spin dynamics at non-zero bias and different temperatures.
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 us 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, and K. Le Hur, Phys. Rev. A 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 noninteracting-blip approximation 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 ${\ensuremath{\sigma}}^{x}(t)$ and of ${\ensuremath{\sigma}}^{z}(t)$ under a Landau-Zener sweep of the bias field. We also compute to a high precision the asymptotic long-time dynamics of ${\ensuremath{\sigma}}^{z}(t)$ without bias and demonstrate the wide applicability of our approach by calculating the spin dynamics at nonzero bias and different temperatures.
The characteristics of the nuclear magnetic resonance (NMR), the contributions to the spin-lattice relaxation rate, and Knight shift of the resonance position are calculated exactly for a model spin-1/21/21/2 XYXYXY chain with the magnetic impurity. It is shown that the deviations of the impurity's coupling to the chain and the effective impurity's ggg factor from the values in the host spin chain yield special features in the temperature and magnetic field behavior for these NMR characteristics. The role of impurity-induced local levels in the NMR low-energy spin dynamics of spin chains is determined.