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

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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“…After we have completed a draft of the present work, we became aware of Ref. [28] which discusses a related approach.…”

Section: Discussion and Summarymentioning

confidence: 99%

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

Shi

Zhang

2017

Phys. Rev. B

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“…They appear in nuclear, condensed matter, solid-state, and cold-atom physics [1]. Many superconductors are SC [2]. Neutron matter (NM) is a SC system as well [3,4].…”

Section: Introductionmentioning

confidence: 99%

Exploring finite-size effects in strongly correlated systems

et al. 2018

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Abstract. Complexities greatly limit any study of strongly correlated systems to a small number of particles. Thus, any attempt at understanding infinite systems such as those arising from neutron matter (NM) must consider finite-size (FS) effects at play when below the thermodynamic limit (TL). In these conference proceedings we provide some examples of FS effects at work and discuss our prescription for extrapolating the physics of extended systems. We present our methodology and calculations performed for an assortment of strongly correlated (SC) systems. Ab initio, non-perturbative Quantum Monte Carlo (QMC) methods can be employed to accurately compute ground-state energies and finite-temperature properties. We apply these to periodically modulated NM and use our results to constrain phenomenological theories of nuclei and study the static response of NM.

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“…The norm kernels at play are more general as they explicitly incorporate many-body correlations and reduce to the mere overlap between two non-orthogonal Bogoliubov states whenever such correlations are omitted. Last but not least, the efficient computation of overlaps constitutes a key element of quantum monte carlo (QMC) approaches, especially when they rely on more elaborate walkers and/or trial states than Slater determinants [10][11][12][13].…”

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confidence: 99%

Calculating the norm matrix to solve the A-body Schrödinger equation within a set of non-orthogonal many-body states

Bally,

Duguet

2017

Preprint

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There are efficient many-body methods, such as the (symmetry-restored) generator coordinate method in nuclear physics, that formulate the A-body Schrödinger equation within a set of nonorthogonal many-body states. Solving the corresponding secular equation requires the evaluation of the norm matrix and thus the capacity to compute its entries consistently and without any phase ambiguity. This is not always a trivial task, e.g. it remained a long-standing problem for methods based on general Bogoliubov product states. While a solution to this problem was found recently in Ref. [L. M. Robledo, Phys. Rev. C79, 021302 (2009)], the present work introduces an alternative method that can be generically applied to other classes of states of interest in many-body physics. The method is presently exemplified in the case of Bogoliubov states and numerically illustrated on the basis of a toy model.

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

Cited by 4 publications

References 83 publications

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

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

Exploring finite-size effects in strongly correlated systems

Calculating the norm matrix to solve the A-body Schrödinger equation within a set of non-orthogonal many-body states

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