Constrained-Path Quantum Monte Carlo Approach for the Nuclear Shell Model

Bonnard, J.; Juillet, O.

doi:10.1103/physrevlett.111.012502

Cited by 9 publications

(29 citation statements)

References 19 publications

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“…In addition, no approximated QMC scheme can be recovered through the use of the biased weights (55) because Ψ T |Φ strictly remains on the real axis throughout the evolution. Hence, as soon as the dynamics only explores real Bogoliubov transformations, no reliability can be granted to the approach (23,44,45). With Slater determinants to guide and start the Brownian motion, we actually showed [50] that the QMC scheme considered here is equivalent to the samplings proposed in 2004 [51] and 2007 [52] for the Hubbard model and free from sign problems.…”

Section: Control Of the Phase And Infinite-variance Problemsmentioning

confidence: 99%

“…Up to date, no numerical applications involving Slater determinants have taken into account an imaginary-time dependence of the gauges {g s }, and the choices g s = 0 or g s = Ô s Ψ T ,Ψ T have been proposed [42]. It should be finally noted that the Brownian motion (44,45) of HFB walkers allows to find the usual reconstruction scheme (23) …”

Section: Stochastic Reformulation Of the Imaginary-time Dependent Schmentioning

confidence: 99%

“…In view of the expression (46) of the factor Π, a phase problem arises with the sampling (23,44,45) as soon as some coefficients ω s < 0 are required. This situation is in fact systematic for all realistic Hamiltonian rewritten as a quadratic form of one-body operators [46,47].…”

Section: Control Of the Phase And Infinite-variance Problemsmentioning

confidence: 99%

“…Here,Π and the quasiparticles {γ n } of the walkers |Φ must be determined up to time τ K + τ B via the evolution equations (44,55) with the trial state |Ψ T = |Φ …”

Section: General Considerationsmentioning

confidence: 99%

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Phaseless quantum Monte-Carlo approach to strongly correlated superconductors with stochastic Hartree–Fock–Bogoliubov wavefunctions

Juillet¹,

Leprévost²,

Bonnard³

et al. 2017

J. Phys. A: Math. Theor.

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Abstract. The so-called phaseless quantum Monte-Carlo method currently offers one of the best performing theoretical framework to investigate interacting Fermi systems. It allows to extract an approximate ground-state wavefunction by averaging independent-particle states undergoing a Brownian motion in imaginary-time. Here, we extend the approach to a random walk in the space of Hartree-Fock-Bogoliubov (HFB) vacua that are better suited for superconducting or superfluid systems. Wellcontrolled statistical errors are ensured by constraining stochastic paths with the help of a trial wavefunction. It also guides the dynamics and takes the form of a linear combination of HFB ansätze. Estimates for the observables are reconstructed through an extension of Wick's theorem to matrix elements between HFB product states. The usual combinatory complexity associated to the application of this theorem for fourand more-body operators is bypassed with a compact expression in terms of Pfaffians. The limiting case of a stochastic motion within Slater determinants but guided with HFB trial wavefunctions is also considered. Finally, exploratory results for the spinpolarized Hubbard model in the attractive regime are presented.Phaseless quantum Monte-Carlo approach 2

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Section: Control Of the Phase And Infinite-variance Problemsmentioning

confidence: 99%

Section: Stochastic Reformulation Of the Imaginary-time Dependent Schmentioning

confidence: 99%

Section: Control Of the Phase And Infinite-variance Problemsmentioning

confidence: 99%

“…Here,Π and the quasiparticles {γ n } of the walkers |Φ must be determined up to time τ K + τ B via the evolution equations (44,55) with the trial state |Ψ T = |Φ …”

Section: General Considerationsmentioning

confidence: 99%

See 2 more Smart Citations

Phaseless quantum Monte-Carlo approach to strongly correlated superconductors with stochastic Hartree–Fock–Bogoliubov wavefunctions

Juillet¹,

Leprévost²,

Bonnard³

et al. 2017

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…Symmetry properties can be imposed [19][20][21] . A constrained-path 12 or phaseless 13 approximation can be introduced to control the sign problem.…”

Section: Qmc Formalismmentioning

confidence: 99%

Many-body computations by stochastic sampling in Hartree-Fock-Bogoliubov space

Shi

Zhang

2017

Phys. Rev. B

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We describe the computational ingredients for an approach to treat interacting fermion systems in the presence of pairing fields, based on path-integrals in the space of Hartree-Fock-Bogoliubov (HFB) wave functions. The path-integrals can be evaluated by Monte Carlo, via random walks of HFB wave functions whose orbitals evolve stochastically. The approach combines the advantage of HFB theory in paired fermion systems and many-body quantum Monte Carlo (QMC) techniques. The properties of HFB states, written in the form of either product states or Thouless states, are discussed. The states preserve forms when propagated by generalized one-body operators. They can be stabilized for numerical iteration. Overlaps and one-body Green's functions between two such states can be computed. A constrained-path or phaseless approximation can be applied to the random walks of the HFB states if a sign problem or phase problem is present. The method is illustrated with an exact numerical projection in the Kitaev model, and in the Hubbard model with attractive interaction under an external pairing field.

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A constrained-path quantum Monte-Carlo approach for the nuclear shell model

Bonnard

Juillet

2016

J. Phys.: Conf. Ser.

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A new Quantum Monte-Carlo (QMC) approach is proposed to investigate low-lying states of nuclei within the shell model. The formalism relies on a variational symmetry-restored wave-function to guide the underlying Brownian motion. Sign/phase problems that usually plague QMC fermionic simulations are controlled by constraining stochastic paths through a fixed-node like approximation. Exploratory results in the sd and pf valence spaces with realistic effective interactions are presented. They prove the ability of the scheme to yield nearly exact yrast spectroscopies for both even-and odd-mass nuclei.

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Constrained-Path Quantum Monte Carlo Approach for the Nuclear Shell Model

Cited by 9 publications

References 19 publications

Phaseless quantum Monte-Carlo approach to strongly correlated superconductors with stochastic Hartree–Fock–Bogoliubov wavefunctions

Phaseless quantum Monte-Carlo approach to strongly correlated superconductors with stochastic Hartree–Fock–Bogoliubov wavefunctions

Many-body computations by stochastic sampling in Hartree-Fock-Bogoliubov space

A constrained-path quantum Monte-Carlo approach for the nuclear shell model

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