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Iranian Journal of Physics Research

Excitation transfer in a three-site spin chain; global vs local approach

Laleh Memarzadeh

Published Sep 1, 2021• 0 citations
Publisher

Abstract

We study excitation transfer in a spin chain in presence of noise. To model noise, we assume that each ‎qubit of the spin chain is interacting with a Bosonic environment and has Markovian evolution. ‎We derive the explicit form of master equation both in global and local approaches. Comparing the ‎results of each approach, we discuss the noise effect on excitation transfer and in addition to that we ‎show that the results of local approach are not a limiting case of global approach‎.‎‎

DOI
10.47176/ijpr.21.2.21177

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We study excitation transfer in a spin chain in presence of noise. To model noise, we assume that each ‎qubit of the spin chain is interacting with a Bosonic environment and has Markovian evolution. ‎We derive the explicit form of master equation both in global and local approaches. Comparing the ‎results of each approach, we discuss the noise effect on excitation transfer and in addition to that we ‎show that the results of local approach are not a limiting case of global approach‎.‎‎
We study energy and spin transport in a one-dimensional Ising chain which is connected to two separate heat baths on both sides. By applying the Born-Markov approximation, within the global approach, we derive the Markovian master equation of the system, and also the explicit form of the Lindblad operators and the steady state. Thereafter, we investigate the behavior of energy and spin dynamics of the system in the global regime. Finally, we solve the problem with the local approach, and we show that the results are not the same for both approaches.
Within the standard weak-coupling limit, the reduced dynamics of open quantum spin chains with their two end spins coupled to two distinct heat baths at different temperatures are mainly derived using the so-called global and local approaches, in which, respectively, the spin self-interaction is and is not taken into account. In order to compare the differences between the two regimes, we concentrate on an open three-site XXXXXX spin chain, provide systematic techniques to address the global and local asymptotic states, and then compare the asymptotic spin-transport features by studying the spin flux through the middle site. Based on the analytical expressions of the stationary states in the two regimes, we find that the local approach misses important global effects emerging as spin sink and source terms that can only be due to nonnegligible interspin interactions. Moreover, we show that the local asympotic transport features cannot be recovered from the global ones by letting the interspin coupling vanish, thus pointing to the existence of different coupling ranges where only one approach is physically tenable and possibly a region where the two descriptions may coexist.
We investigate the influence of environmental noise on spin networks and spin chains. In addition to the common model of an independent bath for each spin in the system we also consider noise with a finite spatial correlation length. We present the emergence of decoherence-free subspaces and different dynamics with increasing correlation length for both dephasing and dissipating environments. This leads to relaxation blocking of one spin by uncoupled surrounding spins. We then consider perfect state transfer through a spin chain in the presence of decoherence and discuss the dependence of the transfer quality on spatial noise correlation length. We identify qualitatively different features for dephasing and dissipative environments in spin-transfer problems.
In various fields from quantum physics to biology, the open quantum dynamics of a system consisting of interacting subsystems emphasizes its fundamental functionality. The local approach, deriving a dissipator in a master equation by ignoring the inter-subsystem interaction, has been widely used to describe the reduced dynamics due to its robustness to keep the positivity of a density operator. However, one critique is that a stationary state obtained by the approach in the limit of weak system-environment coupling is written in the form of the Gibbs state for the partial Hamiltonian by excluding the inter-subsystem interaction from the total one of the relevant system. As an alternative, the global approach, deriving a dissipator with including the inter-subsystem interaction, under the Born--Markov and secular approximations has attracted much attention, and there is debate concerning its violation of positivity in the short-term region and/or limited parameter region for the Bohr frequencies of the subsystems. In this study, we present a formalism that leads to the time-convolutionless (time-local) master equation obtained by extending the global approach beyond the Born-Markov and secular approximations. We apply it to the excitation energy transfer between interacting sites in which only the terminal site weakly interacts with a bosonic environment of finite temperature in a manner beyond the rotating-wave approximation. We find that the formulation (1) gives the short-time behavior while preserving positivity, (2) shows the oscillatory features that the secular approximation would obscure, and (3) leads to a stationary state very near to the Gibbs state for the total Hamiltonian of the relevant system.
In various fields from quantum physics to biology, the open quantum dynamics of a system consisting of interacting subsystems emphasizes its fundamental functionality. The local approach, deriving a dissipator in a master equation by ignoring the intersubsystem interaction, has been widely used to describe the reduced dynamics due to its robustness to keep the positivity of a density operator. However, one critique is that a stationary state obtained by the approach in the limit of weak system-environment coupling is written in the form of the Gibbs state for the partial Hamiltonian by excluding the intersubsystem interaction from the total one of the relevant system. As an alternative, the global approach, deriving a dissipator with including the intersubsystem interaction, under the Born-Markov and secular approximations has attracted much attention, and there is debate concerning its violation of positivity in the short-time region and/or limited parameter region for the Bohr frequencies of the subsystems. In this paper, we present a formalism that leads to the time-convolutionless (time-local) master equation obtained by extending the global approach beyond the Born-Markov and secular approximations. We apply it to the excitation energy transfer between interacting sites in which only the terminal site weakly interacts with a bosonic environment of finite temperature in a manner beyond the rotating-wave approximation. We find that the formulation (1) gives the short-time behavior while preserving positivity, (2) shows the oscillatory features that the secular approximation would obscure, and (3) leads to a stationary state very near to the Gibbs state for the total Hamiltonian of the relevant system.
We analyze the role of bath temperature, coherence and entanglement on excitation transfer in a spin chain induced by the environment. In Markovian regime, we show that coherence and entanglement are very sensitive to bath temperature and vanish in time in contrary to the case of having zero-temperature bath. That is while, finding the last qubit of the chain in excited state increases by increasing the bath temperature. The obtained results show the destructive role of temperature on coherence and entanglement and confirm that these quantum mechanical features cannot affect probability of finding the last qubit in excited state.