Propagating two-particle reduced density matrices without wave functions

Lackner, Fabian; Březinová, Iva; Sato, Takeshi; Ishikawa, Kenichi L.; Burgdörfer, Joachim

doi:10.1103/physreva.91.023412

Cited by 48 publications

(72 citation statements)

References 68 publications

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“…Implementing a dynamical purification scheme along the lines of that in Ref. that iteratively decreases the magnitude of the negative occupation numbers should be investigated.…”

Section: Resultssupporting

confidence: 72%

“…One has then the choice of propagating the equation for ρ 2 alone or propagating it simultaneously alongside the equation for ρ 1 . However, recently it was found that, in the former case, propagating while neglecting the three‐particle correlation term leads to the eventual violation of energy conservation . Now the p ‐RDM can be obtained from higher‐order RDMs via contraction (i.e., partial trace),

ρ_{p} (x_{1}^{'} .. x_{p}^{'}, x_{1} .. x_{p}, t) = \frac{1}{N - p} \int d x_{p + 1} ρ_{p + 1} (x_{1}^{'} .. x_{p}^{'}, x_{p + 1}, x_{1} .. x_{p}, x_{p + 1}, t),

as follows from the definition Eq.…”

Section: Introductionmentioning

confidence: 99%

“…In fact, in Ref. , it was shown that the reconstruction approximation of Refs. violated this condition; the underlying reason was that the spin‐decomposed three‐particle cumulant, neglected in this approximation, has non‐zero contraction.…”

Section: Introductionmentioning

confidence: 99%

“…This realization enabled the authors of Ref. to derive a “contraction‐consistent” reconstruction for ρ 3 by including the part of the three‐particle cumulant that has non‐zero contraction, which fortunately is exactly known as a functional of the 2RDM. This was able to conserve energy in the dynamical simulations.…”

Section: Introductionmentioning

confidence: 99%

“…The condition is in fact violated even by the contraction‐consistent reconstruction introduced in Ref. and by the joint 1RDM and 2RDM propagation in Ref. .…”

Section: Introductionmentioning

confidence: 99%

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Density‐matrix propagation driven by semiclassical correlation

Elliott

Maitra

2016

Int J of Quantum Chemistry

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Methods based on propagation of the one-body reduced density-matrix hold much promise for the simulation of correlated many-electron dynamics far from equilibrium, but difficulties with finding good approximations for the interaction term in its equation of motion have so far impeded their application. These difficulties include the violation of fundamental physical principles such as energy conservation, positivity conditions on the density, or unchanging natural orbital occupation numbers. We review some of the recent efforts to confront these problems, and explore a semiclassical approximation for electron correlation coupled to time-dependent Hartree-Fock propagation. We find that this approach captures changing occupation numbers, and excitations to doubly-excited states, improving over TDHF and adiabatic approximations in density-matrix propagation. However, it does not guarantee N -representability of the density-matrix, consequently resulting sometimes in violation of positivity conditions, even though a purely semiclassical treatment preserves these conditions.

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“…Implementing a dynamical purification scheme along the lines of that in Ref. that iteratively decreases the magnitude of the negative occupation numbers should be investigated.…”

Section: Resultssupporting

confidence: 72%

ρ_{p} (x_{1}^{'} .. x_{p}^{'}, x_{1} .. x_{p}, t) = \frac{1}{N - p} \int d x_{p + 1} ρ_{p + 1} (x_{1}^{'} .. x_{p}^{'}, x_{p + 1}, x_{1} .. x_{p}, x_{p + 1}, t),

as follows from the definition Eq.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The condition is in fact violated even by the contraction‐consistent reconstruction introduced in Ref. and by the joint 1RDM and 2RDM propagation in Ref. .…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Density‐matrix propagation driven by semiclassical correlation

Elliott

Maitra

2016

Int J of Quantum Chemistry

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Accelerating Nonequilibrium Green Functions Simulations: The G1–G2 Scheme and Beyond

Bonitz,

Joost,

Makait

et al. 2024

Physica Status Solidi (b)

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The theory of nonequilibrium Green functions (NEGF) has seen a rapid development over the recent three decades. Applications include diverse correlated many‐body systems in and out of equilibrium. Very good agreement with experiments and available exact theoretical results could be demonstrated if the proper selfenergy approximations were used. However, full two‐time NEGF simulations are computationally costly, as they suffer from a cubic scaling of the computation time with the simulation duration. Recently the G1–G2 scheme that exactly reformulates the generalized Kadanoff–Baym ansatz with Hartree–Fock propagators (HF‐GKBA) into time‐local equations is introduced, which achieves time‐linear scaling and allows for a dramatic speedup and extension of the simulations (Schluenzen et al. Phys. Rev. Lett. 2020, 124, 076601). Remarkably, this scaling is achieved quickly, and also for high‐level selfenergies, including the nonequilibrium GW and T‐matrix approximations (Joost et al. Phys. Rev. B 2020, 101, 245101). Even the dynamically screened ladder approximation is now feasible (Joost et al. Phys. Rev. B 2022, 105, 165155), and also applications to electron‐boson systems are demonstrated. Herein, an overview on recent results that are achieved with the G1–G2 scheme is presented. Problems and open questions are discussed and further ideas of how to overcome the current limitations of the scheme and present are presented. The G1–G2 scheme is illustrated by presenting applying it to the excitation dynamics of Hubbard clusters, to optical excitation of graphene, and to charge transfer during stopping of ions by correlated materials.

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Time-Dependent Complete-Active-Space Self-Consistent-Field Method for Ultrafast Intense Laser Science

Sato

Orimo

Teramura

et al. 2018

Springer Series in Chemical Physics

Self Cite

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We present the time-dependent complete-active-space self-consistent-field (TD-CASSCF) method to simulate multielectron dynamics in ultrafast intense laser fields from the first principles. While based on multiconfiguration expansion, it divides the orbital space into frozen-core (tightly bound electrons with no response to the field), dynamical-core (electrons tightly bound but responding to the field), and active (fully correlated to describe highly excited and ejected electrons) orbital subspaces. The subspace decomposition can be done flexibly, conforming to phenomena under investigation and desired accuracy. The method is gauge invariant and size extensive. Infinite-range exterior complex scaling in addition to maskfunction boundary is adopted as an efficient absorbing boundary. We show numerical examples and illustrate how to extract relevant physical quantities such as ion-

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Propagating two-particle reduced density matrices without wave functions

Cited by 48 publications

References 68 publications

Density‐matrix propagation driven by semiclassical correlation

Density‐matrix propagation driven by semiclassical correlation

Accelerating Nonequilibrium Green Functions Simulations: The G1–G2 Scheme and Beyond

Time-Dependent Complete-Active-Space Self-Consistent-Field Method for Ultrafast Intense Laser Science

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