Efficient real-time path integrals for non-Markovian spin-boson models

Strathearn, Aidan; Lovett, Brendon W.; Kirton, Peter

doi:10.1088/1367-2630/aa8744

Cited by 34 publications

(34 citation statements)

References 70 publications

(117 reference statements)

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“…The TRN is closely related to the recent reformulations of the Feynman-Vernon path integrals [63,[70][71][72][73] and the process tensor [68,[74][75][76]…”

Section: The Total Hamiltonian Readsmentioning

confidence: 99%

“…(a) Process tensor T (t1; t3; tn)[68,[74][75][76]. (b) Influence functional[63,[70][71][72][73]. (c) Timeline reservoir network.MP approximation of states MP approximation of TRN position of m'th particle in space time moment tm = mτ on timeline dimension of a particle's Hilbert twice the number of subsystem's space degrees of freedom plus one, 2n + 1 rank, bond dimension r square of dimension (dimension of ancillary space) of effective reservoir, d 2 ER correlation length, L reservoir correlation time, T…”

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confidence: 99%

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Simulation Complexity of Open Quantum Dynamics: Connection with Tensor Networks

et al. 2019

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The difficulty to simulate the dynamics of open quantum systems resides in their coupling to many-body reservoirs with exponentially large Hilbert space. Applying a tensor network approach in the time domain, we demonstrate that effective small reservoirs can be defined and used for modeling open quantum dynamics. The key element of our technique is the timeline reservoir network (TRN), which contains all the information on the reservoir's characteristics, in particular, the memory effects timescale. The TRN has a one-dimensional tensor network structure, which can be effectively approximated in full analogy with the matrix product approximation of spinchain states. We derive the sufficient bond dimension in the approximated TRN with a reduced set of physical parameters: coupling strength, reservoir correlation time, minimal timescale, and the system's number of degrees of freedom interacting with the environment. The bond dimension can be viewed as a measure of the open dynamics complexity. Simulation is based on the semigroup dynamics of the system and effective reservoir of finite dimension. We provide an illustrative example showing scope for new numerical and machine learning-based methods for open quantum systems.

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“…The TRN is closely related to the recent reformulations of the Feynman-Vernon path integrals [63,[70][71][72][73] and the process tensor [68,[74][75][76]…”

Section: The Total Hamiltonian Readsmentioning

confidence: 99%

mentioning

confidence: 99%

Simulation Complexity of Open Quantum Dynamics: Connection with Tensor Networks

et al. 2019

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“…In the absence of external bias, σ z (t) takes the exponential form which is also recovered in the NIBA approximation. Different numerical approaches have been devised in order to compute the real time dynamics of this problem in the range of coupling strengths 0 < α < 1/2, where no exact analytical solution is known to exist [45,[49][50][51][52][53]. Here we apply the numerical SIL technique (see App.…”

Section: Spin Boson Modelmentioning

confidence: 99%

Dissipative dynamics of a driven qubit: Interplay between nonadiabatic dynamics and noise effects from the weak to strong coupling regime

et al. 2019

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We study the exact solution of the Schrödinger equation for the dissipative dynamics of a qubit, achieved by means of Short Iterative Lanczos method (SIL), which allows us to describe the qubit and the bath dynamics from weak to strong coupling regimes. We focus on two different models of a qubit in contact with the external environment: the first is the Spin Boson Model (SBM), which gives a description of the qubit in terms of static tunnelling energy and a bias field. The second model describes an externally driven qubit, where both the bias field and the tunnelling rate are controlled by a time-dependent magnetic field obeying to a finite time protocol. We show that in the SBM case, our solution correctly describes the crossover from coherent to incoherent behavior of the magnetization, occurring at the Toulouse point. Furthermore, we show that the bath response dramatically changes during the system dynamics, going from non-resonant at small times to resonant behavior at long times. When the external driving field is present, for fixed values of the drive duration our results show that the bath can provide beneficial effects to the success of the protocol. We find evidence for a complex interplay between non-adiabaticity of the protocol due to the external drive and dissipation effects, which strongly depends on the detailed form of the qubit-bath interaction.

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“…However, it is argued that al least for the case of the Ohmic bath the numerical complexity scales polynomially with t cut . In [51] the case of the superohmic bath is considered. In that work, the technique of augmented density tensor (ADT) [52,53] is employed.…”

Section: Introductionmentioning

confidence: 99%

Dressed quantum trajectories: novel approach to the non-Markovian dynamics of open quantum systems on a wide time scale

Polyakov

Rubtsov

2019

New J. Phys.

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A new approach to theory and simulation of the non-Markovian dynamics of open quantum systems is presented. It is based on identification of a parameter which is uniformly bounded on wide time intervals: the occupation of the virtual cloud of quanta. By 'virtual' we denote those bath excitations which were emitted by the open system, but eventually will be reabsorbed before any measurement of the bath state. A useful property of the virtual cloud is that the number of its quanta is expected to saturate on long times, since physically this cloud is a (retarded) polarization of the bath around the system. Therefore, the joint state of open system and virtual cloud (we call it dressed state) can be accurately represented in a truncated basis of Fock states, on a wide time scale. At the same time, there can be an arbitrarily large number of the observable quanta (which survive up to measurement), especially if the open system is under driving. However, it turns out that the statistics of the bathmeasurement outcomes is classical (in a suitable measurement basis): one can employ a Monte Carlo sampling of these outcomes. Therefore, it is possible to efficiently simulate the dynamics of the observable quantum field. In this work we consider the bath measurement with respect to the coherent states, which yields the Husimi function as the positive (quasi)probability distribution of the outcomes. The joint evolution of the dressed state and the corresponding outcome is called the dressed quantum trajectory. The Monte Carlo sampling of these trajectories yields a stochastic simulation method with promising convergence properties on wide time scales.

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Efficient real-time path integrals for non-Markovian spin-boson models

Cited by 34 publications

References 70 publications

Simulation Complexity of Open Quantum Dynamics: Connection with Tensor Networks

Simulation Complexity of Open Quantum Dynamics: Connection with Tensor Networks

Dissipative dynamics of a driven qubit: Interplay between nonadiabatic dynamics and noise effects from the weak to strong coupling regime

Dressed quantum trajectories: novel approach to the non-Markovian dynamics of open quantum systems on a wide time scale

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