Low-temperature dynamical simulation of spin-boson systems

Abstract

The dynamics of spin-boson systems at very low temperatures has been studied using a real-time path-integral simulation technique which combines a stochastic Monte Carlo sampling over the quantum fluctuations with an exact treatment of the quasiclassical degrees of freedoms. To a large degree, this special technique circumvents the dynamical sign problem and allows the dynamics to be studied directly up to long real times in a numerically exact manner. This method has been applied to two important problems: (1) crossover from nonadiabatic to adiabatic behavior in electron transfer reactions, (2) the zero-temperature dynamics in the antiferromagnetic Kondo region 1/2<K<1 where K is Kondo's parameter.Comment: Phys. Rev. B (in press), 28 pages, 6 figure

Path-integral Monte Carlo simulations for electronic dynamics on molecular chains. I. Sequential hopping and super exchange

“…The sum paths are also considered as "quasi-classical", while the difference paths capture quantum fluctuations [18,26]. Equation (14) finally can be written as…”

“…Various procedures to mitigate the sign problem have been proposed in the past, like maximum entropy methods [27], filter techniques [28,29] or the multilevel blocking approach [25,31]. Here we employ a filter technique optimized for dissipative spin systems as suggested by Egger and Mak [26] which exploits the special symmetries of the influence functional.…”

“…[25,26]. For the forward and backward paths the time axis is sliced via q uniformly spaced points with discretization steps τ = t/q.…”

“…Known as the dynamical sign problem [22], it turns out that the number of sample paths needed to achieve a sufficient signal-to-noise ratio increases exponentially with the simulated system time. To partially circumvent this drawback various techniques have been introduced and shown to stabilize the simulations considerably [26,27,28,29,31].…”

Reduced density matrix hybrid approach: An efficient and accurate method for adiabatic and non-adiabatic quantum dynamics

“…20 To make such approaches manageable, perturbation theory in the system-bath coupling (Bloch-Redfield) and in the nonadiabatic coupling (NIBA, Förster) are typically carried out only to second-order and hence performance degrades when these terms become large. In addition, path integral approaches, such as quantum Monte Carlo [21][22][23] and the quasi-adiabatic propagator path integral (QUAPI) 24 have also been developed to propagate the RDM. While these approaches can be made numerically exact, they are frequently difficult to converge in practice when the system-bath coupling is strong or the bath is slow.…”