Fast and scalable quantum Monte Carlo simulations of electron-phonon models

Cohen-Stead, Benjamin; Bradley, Owen; Miles, Cole; Batrouni, G. G.; Scalettar, Richard; Barros, Kipton

doi:10.1103/physreve.105.065302

Cited by 21 publications

(16 citation statements)

References 69 publications

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“…Below we highlight some of the relevant parameter values used in the simulation and refer the reader to Ref. [34] for more information on their definitions.…”

Section: Discussionmentioning

confidence: 99%

“…We solve the model using a recently proposed set of algorithms [34]. Specifically, HMC [40,41] and Fourier acceleration are used to efficiently sample decorrelated phonon fields [42].…”

Section: Model and Methodsmentioning

confidence: 99%

“…Here we study of the CDW transition in BaBiO 3 , the parent compound of the bismuthate superconductors, using a scalable hybrid Monte Carlo (HMC) algorithm [34]. We consider a multi-orbital model that includes the Bi 6s and O 2p σ orbitals and coupling to the Bi-O bond-stretching branch of optical phonons via the Su-Schrieffer-Heeger (SSH)-like (or Peierls-like) modulation of the Bi-O hopping integral.…”

Section: Introductionmentioning

confidence: 99%

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A hybrid Monte Carlo study of bond-stretching electron-phonon interactions and charge order in the bismuthate family of superconductors

Cohen-Stead¹,

Barros²,

Scalettar³

et al. 2022

Preprint

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The role of electron-phonon (e-ph) interactions and their relationship to charge-density-wave (CDW) order in the bismuthate family of high-temperature superconductors remains unresolved. We address this question using state-of-the-art nonperturbative hybrid quantum Monte Carlo calculations for the parent compound BaBiO3. Our model includes the Bi 6s and O 2pσ orbitals and coupling to the Bi-O bond-stretching branch of optical phonons via the modulation of the Bi-O hopping integral. Using recently proposed algorithms that are fast and scalable, we perform simulations on large three-dimensional clusters of up to 4000 orbitals, with input model parameters taken directly from ab initio electronic structure calculations and a physically motivated phonon energy Ω0 = 60 meV. Our results demonstrate that the coupling to the bond-stretching modes is sufficient to account for the CDW transition in this system, despite the relatively small dimensionless coupling to this branch predicted by density functional theory. We also find that the transition deviates from the weak-coupling Peierls picture, despite the noninteracting Fermi surface being well-nested at the CDW ordering vector. Our results highlight the richness of e-ph interactions that are off-diagonal in orbital space and suggest that such interactions play a crucial role in establishing the bismuthate phase diagram.

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“…Below we highlight some of the relevant parameter values used in the simulation and refer the reader to Ref. [34] for more information on their definitions.…”

Section: Discussionmentioning

confidence: 99%

“…We solve the model using a recently proposed set of algorithms [34]. Specifically, HMC [40,41] and Fourier acceleration are used to efficiently sample decorrelated phonon fields [42].…”

Section: Model and Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A hybrid Monte Carlo study of bond-stretching electron-phonon interactions and charge order in the bismuthate family of superconductors

Cohen-Stead¹,

Barros²,

Scalettar³

et al. 2022

Preprint

Self Cite

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“…Another context where a continuous HS transformation for the Hubbard interaction may be beneficial is in simulations of correlated systems with strong electronphonon interactions. Langevin and HMC are known to be highly effective in sampling decorrelated phonon fields [16][17][18]. Future work could perform simultaneous dynamical sampling of the phonon and HS auxiliary fields.…”

Section: Discussionmentioning

confidence: 99%

A flexible class of exact Hubbard-Stratonovich transformations

Karakuzu¹,

Cohen-Stead²,

Batista³

et al. 2022

Preprint

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We consider a class of Hubbard-Stratonovich transformations suitable for treating Hubbard interactions in the context of quantum Monte Carlo simulations. A tunable parameter p allows us to continuously vary from a discrete Ising auxiliary field (p = ∞) to a compact auxiliary field that couples to electrons sinusoidally (p = 0). In tests on the single-band Hubbard model, we find that the severity of the sign problem decreases systematically with increasing p. Selecting p finite, however, enables continuous sampling methods like the Langevin or Hamiltonian Monte Carlo methods. We explore the tradeoffs between various simulation methods through numerical benchmarks.

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“…Here we study the CDW transition in BaBiO 3 , the parent compound of the bismuthate superconductors, using a scalable hybrid Monte Carlo (HMC) algorithm 34 . We consider a multiorbital model that includes the Bi 6s and O 2p σ orbitals and coupling to the Bi-O bond-stretching branch of optical phonons via the Su-Schrieffer-Heeger (SSH)-like (or Peierls-like) modulation of the Bi-O hopping integral.…”

Section: Introductionmentioning

confidence: 99%

A hybrid Monte Carlo study of bond-stretching electron–phonon interactions and charge order in BaBiO3

et al. 2023

Self Cite

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The relationship between electron–phonon (e-ph) interactions and charge-density-wave (CDW) order in the bismuthate family of high-temperature superconductors remains unresolved. We address this question using nonperturbative hybrid Monte Carlo calculations for the parent compound BaBiO3. Our model includes the Bi 6s and O 2pσ orbitals and coupling to the Bi-O bond-stretching branch of optical phonons via modulations of the Bi-O hopping integral. We simulate three-dimensional clusters of up to 4000 orbitals, with input model parameters taken from ab initio electronic structure calculations and a phonon energy ℏΩ0 = 60 meV. Our results demonstrate that the coupling to the bond-stretching modes is sufficient to reproduce the CDW transition in this system, despite a relatively small dimensionless coupling. We also find that the transition deviates from the weak-coupling Peierls’ picture. This work demonstrates that off-diagonal e-ph interactions in orbital space are vital in establishing the bismuthate phase diagram.

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Fast and scalable quantum Monte Carlo simulations of electron-phonon models

Cited by 21 publications

References 69 publications

A hybrid Monte Carlo study of bond-stretching electron-phonon interactions and charge order in the bismuthate family of superconductors

A hybrid Monte Carlo study of bond-stretching electron-phonon interactions and charge order in the bismuthate family of superconductors

A flexible class of exact Hubbard-Stratonovich transformations

A hybrid Monte Carlo study of bond-stretching electron–phonon interactions and charge order in BaBiO3

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