Simulating open quantum dynamics with time-dependent variational matrix product states: Towards microscopic correlation of environment dynamics and reduced system evolution

Alex W. Chin; Florian A. Y. N. Schr\"oder

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Simulating open quantum dynamics with time-dependent variational matrix product states: Towards microscopic correlation of environment dynamics and reduced system evolution

Mesoscale and Nanoscale Physics · Submitted 8 Jul 2015

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The authors' main claim We highlight how theoretical 'environmental spectra' could yield valuable insights into a wide range of complex dissipative processes, by showing that correlated motion of modes entangled with the spin can appear with persistent vibrational coherence, in spite of incoherent spin relaxation.

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arXiv ID1507.02202 (version 2)

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CitationAlex W. Chin, Florian A. Y. N. Schr\"oder. "Simulating open quantum dynamics with time-dependent variational matrix product states: Towards microscopic correlation of environment dynamics and reduced system evolution." arXiv:1507.02202 (2015). https://pith.science/paper/6KK73VJP

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Many-body approaches to open quantum systems have recently become powerful tools for investigating the detailed role of dissipative environments in diverse non-equilibrium molecular and condensed matter processes. Here, we report the development of an efficient algorithm that utilises a time-dependent variational principle for matrix product states to evolve large system-environment states. By thus capturing all system-environment correlations, we reproduce the highly non-perturbative, quantum-critical dynamics of the zero temperature spin-boson model, and then exploit the many-body information to output a complete time-frequency spectrum of the environmental excitations. We highlight how theoretical 'environmental spectra' could yield valuable insights into a wide range of complex dissipative processes, by showing that correlated motion of modes entangled with the spin can appear with persistent vibrational coherence, in spite of incoherent spin relaxation.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Many-body approaches to open quantum systems have recently become powerful tools for investigating the detailed role of dissipative environments in diverse non-equilibrium molecular and condensed matter processes.	background 1.00	0.04	0.03	asserted 1.00
s1	Here, we report the development of an efficient algorithm that utilises a time-dependent variational principle for matrix product states to evolve large system-environment states.	contribution 0.71	0.96	0.09	asserted 1.00
s2	By thus capturing all system-environment correlations, we reproduce the highly non-perturbative, quantum-critical dynamics of the zero temperature spin-boson model, and then exploit the many-body information to output a complete time-frequency spectrum of the environmental excitations.	result 0.94	0.95	0.42	asserted 1.00
s3	We highlight how theoretical 'environmental spectra' could yield valuable insights into a wide range of complex dissipative processes, by showing that correlated motion of modes entangled with the spin can appear with persistent vibrational coherence, in spite of incoherent spin relaxation.	interpretation 0.94	0.83	0.43	hedged possibility 0.71

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Original abstract

Many-body approaches to open quantum systems have recently become powerful tools for investigating the detailed role of dissipative environments in diverse non-equilibrium molecular and condensed matter processes. Here, we report the development of an efficient algorithm that utilises a time-dependent variational principle for matrix product states to evolve large system-environment states. By thus capturing all system-environment correlations, we reproduce the highly non-perturbative, quantum-critical dynamics of the zero temperature spin-boson model, and then exploit the many-body information to output a complete time-frequency spectrum of the environmental excitations. We highlight how theoretical 'environmental spectra' could yield valuable insights into a wide range of complex dissipative processes, by showing that correlated motion of modes entangled with the spin can appear with persistent vibrational coherence, in spite of incoherent spin relaxation.

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8 arXiv papers cite this in 15 sentences

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Papers citing it · 7 sentences without a confident label

Uses its method or tool 1 paper

The model is simulated with tree tensor network states (TTNS) [ref] , which extend matrix-product state (MPS) methods for open quantum systems [ref] to models with multiple bosonic environments.

Multi-dimensional Tensor Network Simulation of Open Quantum Dynamics in Singlet Fission · Introduction · 0.91

Compares with it 2 papers

Also, we point out that our setting is more general than previous spin-boson approaches using related density-matrix renormalization group (DMRG) methods, in which each spin was coupled locally to a single boson [ref] , a single spin was coupled to many bosons [ref] , or a single collective boson mode was coupled to many spins [ref] .

Simulating generic spin-boson models with matrix product states · Formalism · 0.89
(For comparison, dimensions $d=30$ and $D=5$ were reported in Ref. [ref] .)

Matrix-product-state method with a dynamical local basis optimization for bosonic systems out of equilibrium · Introduction · 0.94

Cites it as support 1 paper

[ref] The stability of the PSI with respect to nearly rank-deficient wavefunction parametrizations can be attributed to the fact that the EOMs solved are always well-conditioned.

Time Evolution of ML-MCTDH Wavefunctions II: Application of the Projector Splitting Integrator · Discussion of the PSI · 0.97

Cites it as background 1 paper

Details about the TDVP algorithm we have developed for the TTNS evolution are given in the Sec. II and further background can be found in Refs. [ref] .

Multi-dimensional Tensor Network Simulation of Open Quantum Dynamics in Singlet Fission · Tensor Network States · 0.87

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To prove that this can be done and to derive the appropriate integration scheme, we will present in Sec. [ref] the derivation of the tangent space projector $P̂_T_|Ψ_MPS⟩ℳ$ in the formalism established by Ref. [ref] .

Time integration of tensor trains · Time-dependent variational principle · 0.88

Uses the method or tool of 5 papers

In this article, we present a versatile new approach to this problem, based on the recently proposed time-dependent variational principle (TDVP) for variational matrix product states (VMPS) [ref] .

Time integration of tensor trains · Introduction · 1.00
In this article, we present a versatile new approach to this problem, based on the recently proposed time-dependent variational principle (TDVP) for variational matrix product states (VMPS) [ref] .

Unifying time evolution and optimization with matrix product states · Introduction · 1.00
In this article, we present a versatile new approach to this problem, based on the recently proposed time-dependent variational principle (TDVP) for variational matrix product states (VMPS) [ref] .

The density-matrix renormalization group in the age of matrix product states · Introduction · 1.00

Compares with 1 paper

The scaling behavior of OBB-TDVP is also more preferable in comparison with the common time-evolving block decimation (TEBD) ($𝒪(d^3D^3)$) and the very recently proposed TEBD with local basis optimization (TEBD-LBO) of Brockt et al. [ref] with a scaling of $𝒪(max(d_OBB^3D^3,d^3D^2))$.

Matrix-product-state method with a dynamical local basis optimization for bosonic systems out of equilibrium · 1-tensor update scheme · 0.99

Cites as background 1 paper

A range of novel phenomena related to non-detailed balance and phase-dependent relaxation have recently been predicted to exist prior to this time [ref] , though we will not explore this further here.

Phase-dependent exciton transport and energy harvesting from thermal environments · Environment dynamics and spectroscopy · 0.93

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