Imaginary time correlations and the phaseless auxiliary field quantum Monte Carlo

Motta, Mário; Galli, D. E.; Moroni, Saverio; Vitali, Ettore

doi:10.1063/1.4861227

Cited by 25 publications

(50 citation statements)

References 43 publications

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confidence: 99%

“…While in the absence of a sign problem, unbiased imaginary-time spectra can be obtained [6][7][8], the analytic continuation to physical, real-frequency functions is notoriously ill-conditioned and can lead to artefacts and smoothing of features. [9] For more general Fermionic systems, higher temperatures must be simulated to alleviate the sign problem [10], while nodal constraints bias towards a particular solution and are difficult to extend to spectra [1,7,11].…”

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confidence: 99%

“…[9] For more general Fermionic systems, higher temperatures must be simulated to alleviate the sign problem[10], while nodal constraints bias towards a particular solution and are difficult to extend to spectra [1,7,11]. Alternatively, projections into effective Hamiltonians have been able to obtain a few low-energy states, but again these are isolated states rather than practical approaches for thermal or spectral quantities [12,13], while a modification of the propagator can lead to debilitating timestep issues [14].…”

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Krylov-Projected Quantum Monte Carlo Method

2015

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We present an approach to the calculation of arbitrary spectral, thermal and excited state properties within the full configuration interaction quantum Monte Carlo framework. This is achieved via an unbiased projection of the Hamiltonian eigenvalue problem into a space of stochastically sampled Krylov vectors, thus enabling the calculation of real-frequency spectral and thermal properties and avoiding explicit analytic continuation. We use this approach to calculate temperature-dependent properties and one-and two-body spectral functions for various Hubbard models, as well as isolated excited states in ab initio systems.Quantum Monte Carlo (QMC) in its various guises, is undoubtedly one of the most important approaches for accurate elucidation of properties for correlated systems [1][2][3][4][5]. However, these successes have focused primarily on the ground state energy and observables which commute with the Hamiltonian. Critical importance for a deeper understanding of correlated systems comes from dynamic correlation functions and spectral quantities. These mirror how we perceive our environment, namely by perturbing a system and measuring its response -the basis of nearly all spectroscopic and experimental approaches. This gives us direct insight into optical, magnetic and other beyond-ground-state properties, and allow for direct comparison to experimental results.Direct access to dynamic properties is a persistent difficulty for QMC approaches in general. While in the absence of a sign problem, unbiased imaginary-time spectra can be obtained [6][7][8], the analytic continuation to physical, real-frequency functions is notoriously ill-conditioned and can lead to artefacts and smoothing of features.[9] For more general Fermionic systems, higher temperatures must be simulated to alleviate the sign problem[10], while nodal constraints bias towards a particular solution and are difficult to extend to spectra [1,7,11]. Alternatively, projections into effective Hamiltonians have been able to obtain a few low-energy states, but again these are isolated states rather than practical approaches for thermal or spectral quantities [12,13], while a modification of the propagator can lead to debilitating timestep issues [14].Here, we present a new QMC approach for computing dynamic correlation functions, temperature-dependent quantities and isolated excited states for correlated quantum systems, even in the presence of a sign-problem. These correlation functions are unbiased in the limit of large averaging, and exact in the limit of large walker number. This is achieved by extending the recently developed Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method [2,15,16], by combining it with ideas from the dynamical and finite-temperature Lanczos (FTLM) methods. [17][18][19] The key advantage of the approach is that it avoids any explicit storage over the full Hilbert space, instead only storing occupied states in the * nsb37@cam.ac.uk † george.booth@kcl.ac.uk discretized wavefunction at each snapshot. This all...

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Krylov-Projected Quantum Monte Carlo Method

2015

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“…Standard approaches [32,33,34,35] to evaluate the expression in Eq. (42) require computational cost of O(N 3 s ).…”

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confidence: 99%

Response Functions for the Two-Dimensional Ultracold Fermi Gas: Dynamical BCS Theory and Beyond

et al. 2017

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Response functions are central objects in physics. They provide crucial information about the behavior of physical systems, and they can be directly compared with scattering experiments involving particles like neutrons, or photons. Calculations of such functions starting from the many-body Hamiltonian of a physical system are challenging, and extremely valuable. In this paper we focus on the two-dimensional (2D) ultracold Fermi atomic gas which has been realized experimentally. We present an application of the dynamical BCS theory to obtain response functions for different regimes of interaction strengths in the 2D gas with zero-range attractive interaction. We also discuss auxiliary-field quantum Monte Carlo (AFQMC) methods for the calculation of imaginary-time correlations in these dilute Fermi gas systems. Illustrative results are given and comparisons are made between AFQMC and dynamical BCS theory results to assess the accuracy of the latter.

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“…The first application of quantum Monte Carlo (QMC) methods to the calculation of the dynamical structure factor dates back to [25][26][27] for lattice systems and [28] for homogeneous systems. Further developments have made possible the calculation of S(q, ω) in systems of 4 He atoms [20,23], as well as in two-dimensional (2D) homogeneous electron gases and systems of 3 He atoms [29][30][31], and systems of Bose hard spheres [8,10].…”

Section: Introductionmentioning

confidence: 99%

Roton Excitations and the Fluid–Solid Phase Transition in Superfluid 2D Yukawa Bosons

et al. 2016

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We compute several groundstate properties and the dynamical structure factor of a 0-temperature system of Bosons interacting with the 2D screened Coulomb (2D-SC) potential. We resort to the exact shadow path-integral ground-state (SPIGS) quantum Monte Carlo method to compute the imaginary-time correlation function of the model, and to the genetic algorithm via falsification of theories (GIFT) to retrieve the dynamical structure factor. We provide a detailed comparison of groundstate properties and collective excitations of 2D-SC and 4 He atoms. The roton energy of the 2D-SC system is an increasing function of density, and not a decreasing one as in 4 He. This result is in contrast with the view that the roton is the soft mode of the fluid-solid transition. We uncover a remarkable quasi-universality of backflow and of other properties when expressed in terms of the amount of short range order as quantified by the height of the first peak of the static structure factor.

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Imaginary time correlations and the phaseless auxiliary field quantum Monte Carlo

Cited by 25 publications

References 43 publications

Krylov-Projected Quantum Monte Carlo Method

Krylov-Projected Quantum Monte Carlo Method

Response Functions for the Two-Dimensional Ultracold Fermi Gas: Dynamical BCS Theory and Beyond

Roton Excitations and the Fluid–Solid Phase Transition in Superfluid 2D Yukawa Bosons

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