Zero-temperature localization in a sub-Ohmic spin-boson model investigated by an extended hierarchy equation of motion

Duan, Chenru; Tang, Zhoufei; Cao, Jianshu; Wu, Juan

doi:10.1103/physrevb.95.214308

Cited by 93 publications

(71 citation statements)

References 35 publications

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“…[17], reproducing the transition from damped coherent motion at weak coupling to localization upon increasing the coupling strength. Note, the spin dynamics for that particular case has also been calculated using the eHEOM method [25]. The influence of a low temperature initial condition (T =0.2∆) is almost negligible for the initial oscillations but becomes evident in the long time behavior suppressing the localization (see insets of Fig.…”

Section: A Special Treatment Of Thermal Initial Conditionsmentioning

confidence: 96%

“…For example a HEOM based approach has been successfully used to study quantum impurity systems at low temperature [23,24]. Further, an extended version of HEOM (eHEOM [22]) allows to treat sub-Ohmic environments at high temperatures [22] as well as zero temperature in the very demanding strong coupling regime [25]. A stochastic state vector based alternative -applicable to zero and non-zero temperature environments, also in the strong coupling regime -is the hierarchy of pure states (HOPS) method, first introduced by Süß et al [5] and successfully used to calculate 2D electronic spectra [26].…”

Section: Introductionmentioning

confidence: 99%

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Exact Open Quantum System Dynamics Using the Hierarchy of Pure States (HOPS)

Hartmann

Strunz

2017

J. Chem. Theory Comput.

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We show that the general and numerically exact Hierarchy of Pure States method (HOPS) is very well applicable to calculate the reduced dynamics of an open quantum system. In particular we focus on environments with a sub-Ohmic spectral density (SD) resulting in an algebraic decay of the bath correlation function (BCF). The universal applicability of HOPS, reaching from weak to strong coupling for zero and non-zero temperature, is demonstrated by solving the spin-boson model for which we find perfect agreement with other methods, each one suitable for a special regime of parameters. The challenges arising in the strong coupling regime are not only reflected in the computational effort needed for the HOPS method to converge but also in the necessity for an importance sampling mechanism, accounted for by the non-linear variant of HOPS. In order to include non-zero temperature effects in the strong coupling regime we found that it is highly favorable for the HOPS method to use the zero temperature BCF and include temperature via a stochastic Hermitian contribution to the system Hamiltonian.

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Section: A Special Treatment Of Thermal Initial Conditionsmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Exact Open Quantum System Dynamics Using the Hierarchy of Pure States (HOPS)

Hartmann

Strunz

2017

J. Chem. Theory Comput.

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“…The inchworm Monte Carlo method and the new integro-differential equation formulation will be proved to be applicable for the Ohmic spin-boson model, which is a simple open quantum system widely used as benchmark problems [15,30,59]. Based on the integro-differential equation, part of the Monte Carlo integration can be replaced by classical time-integration methods to achieve higher accuracy.…”

Section: Abstract: Quantummentioning

confidence: 99%

“…While the answers to these questions are not detailed in the original derivation of the inchworm method [4,10], in this paper, we will show the validity of the inchworm method with mathematical rigor. The rigorous proof not only justifies the original algorithm, but also leads us to a new formulation of the open quantum system as an integro-differential equation, based on which more accurate and efficient numerical approaches can be developed.The inchworm Monte Carlo method and the new integro-differential equation formulation will be proved to be applicable for the Ohmic spin-boson model, which is a simple open quantum system widely used as benchmark problems [15,30,59]. Based on the integro-differential equation, part of the Monte Carlo integration can be replaced by classical time-integration methods to achieve higher accuracy.…”

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confidence: 99%

Inchworm Monte Carlo Method for Open Quantum Systems

Cai

Yang

2020

Comm Pure Appl Math

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We investigate in this work a recently proposed diagrammatic quantum Monte Carlo method -the inchworm Monte Carlo method -for open quantum systems. We establish its validity rigorously based on resummation of Dyson series. Moreover, we introduce an integro-differential equation formulation for open quantum systems, which illuminates the mathematical structure of the inchworm algorithm. This new formulation leads to an improvement of the inchworm algorithm by introducing classical deterministic time-integration schemes. The numerical method is validated by applications to the spin-boson model. Keywords: quantumMonte Carlo, open quantum system, diagrammatic methods, spin-boson model to obtain a Markovian approximation, known as the Lindblad equation [12,13], which is the quantum analog of the Langevin dynamics. The Markovian approximation however breaks down for open systems with stronger coupling, so that one has to keep track of the non-Markovian dynamics of the projected density matrix describing the system of interests [3]. For classical systems, such dynamics is often modeled and studied as generalized Langevin equations [24,63], while for quantum systems, the non-Markovian dynamics is much more complicated, and many works have been devoted to this topic. Analogously to the generalized Langevin equations, generalized quantum master equation with memory kernel has been used to model non-Markovian open quantum dynamics [29,42,43,52], though it is often complicated to come up with a good estimate of the memory kernel, especially when the memory is long range.Besides the quantum master equation framework, the non-Markovian evolution of the system can be also directly modeled and simulated using the path-integral approaches such as the QuAPI (quasi-adiabatic propagator path integral) methods [36,41] and the HEOM (hierarchical equations of motion) technique [56]. These methods yield accurate numerical results (often referred as "numerically exact" in the literature), while the computational cost is extremely huge, often unaffordable. To reduce the computational cost, one common strategy is to replace the exact summation or numerical integration in these methods by Monte Carlo methods. In this paper, we are going to study a specific type of path-integral methods called the diagrammatic quantum Monte Carlo method [60] to solve the time-dependent open quantum systems. In particular, our study is largely motivated by the inchworm Monte Carlo method recently proposed in [4,10] to reduce the variance in quantum Monte Carlo by diagrammatic resummation.The basis of the diagrammatic quantum Monte Carlo method has been established as early as 1960s [28]. However, as other quantum Monte Carlo methods, this type of methods also suffer from the notorious dynamical sign problem, meaning that the number of Monte Carlo samples is required to grow at least exponentially in time in order to keep the accuracy of the simulation. To relieve the dynamical sign problem, Stockburger and Grabert introduced stochastic unraveling of influence...

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“…This is an overdamped Ohmic limit of the (multi-state) quantum hierarchical Fokker-Planck equations ((MS-)QHFPE) approach [27,[37][38][39][40][41], which is a variant of the hierarchical equations of motion (HEOM) theories [36,42,43]. While general spectral densities can be treated by HEOM theories [44][45][46][47], here we employ the MS-LT-QSE theory for an Ohmic spectral density to simplify the analysis and to reduce the numerical costs for simulations.…”

Section: Introductionmentioning

confidence: 99%

Modeling and analyzing a photo-driven molecular motor system: Ratchet dynamics and non-linear optical spectra

Ikeda

Dijkstra

Tanimura

2019

The Journal of Chemical Physics

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A light-driven molecular motor system is investigated using a multi-state Brownian ratchet model described by a single effective coordinate with multiple electronic states in a dissipative environment. The rotational motion of the motor system is investigated on the basis of wavepacket dynamics. A current determined from the interplay between a fast photochemical isomerization (photoisomerization) process triggered by pulses and a slow thermal isomerization (thermalization) process arising from an overdamped environment is numerically evaluated. For this purpose, we employ the multi-state low-temperature quantum Smoluchowski equations that allow us to simulate the fast quantum electronic dynamics in the overdamped environment, where conventional approaches, such as the Zusman equation approach, fail to apply due to the positivity problem. We analyze the motor efficiency by numerically integrating the equations of motion for a rotator system driven by repeatedly impulsive excitations. When the timescales of the pulse repetition, photoisomerization, and thermalization processes are separated, the average rotational speed of the motor is determined by the timescale of thermalization. In this regime, the average rotational current can be described by a simple equation derived from a rate equation for the thermalization process. When laser pulses are applied repeatedly and the timescales of the photoisomerization and pulse repetition are close, the details of the photoisomerization process become important to analyze the entire rotational process. We examine the possibility of observing the photoisomerization and the thermalization processes associated with stationary rotating dynamics of the motor system by spectroscopic means, e.g. pump-probe, transient absorption, and two-dimensional electronic spectroscopy techniques.

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Zero-temperature localization in a sub-Ohmic spin-boson model investigated by an extended hierarchy equation of motion

Cited by 93 publications

References 35 publications

Exact Open Quantum System Dynamics Using the Hierarchy of Pure States (HOPS)

Exact Open Quantum System Dynamics Using the Hierarchy of Pure States (HOPS)

Inchworm Monte Carlo Method for Open Quantum Systems

Modeling and analyzing a photo-driven molecular motor system: Ratchet dynamics and non-linear optical spectra

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