Density-matrix quantum Monte Carlo method

Blunt, Nick S.; Rogers, Thomas W.; Spencer, James; Foulkes, W. M. C.

doi:10.1103/physrevb.89.245124

Cited by 113 publications

(165 citation statements)

References 54 publications

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“…Our approach combines two independent methods, configuration path-integral Monte Carlo (CPIMC) [35][36][37] and permutation blocking PIMC [38,39], which allow for accurate simulations at high (r s 1) and moderate densities (r s 1 and θ 0.5), respectively. An independently developed third approach, density matrix QMC [40,41], confirmed the excellent quality of these results. The only significant errors remaining are finite-size effects [37,[42][43][44][45][46], which arise from the difference between the small systems simulated and the infinite [thermodynamic limit (TDL)] system of interest.…”

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confidence: 48%

Ab InitioQuantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit

et al. 2016

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We perform ab initio quantum Monte Carlo (QMC) simulations of the warm dense uniform electron gas in the thermodynamic limit. By combining QMC data with linear response theory we are able to remove finite-size errors from the potential energy over the entire warm dense regime, overcoming the deficiencies of the existing finite-size corrections by Brown et al. [PRL 110, 146405 (2013)]. Extensive new QMC results for up to N = 1000 electrons enable us to compute the potential energy V and the exchange-correlation free energy Fxc of the macroscopic electron gas with an unprecedented accuracy of |∆V |/|V |, |∆Fxc|/|F |xc ∼ 10 −3 . A comparison of our new data to the recent parametrization of Fxc by Karasiev et al. [PRL 112, 076403 (2014)] reveals significant deviations to the latter.The uniform electron gas (UEG), consisting of electrons on a uniform neutralizing background, is one of the most important model systems in physics [1]. Besides being a simple model for metals, the UEG has been central to the development of linear response theory and more sophisticated perturbative treatments of solids, the formulation of the concepts of quasiparticles and elementary excitations, and the remarkable successes of density functional theory.The practical application of ground-state density functional theory in condensed matter physics, chemistry and materials science rests on a reliable parametrization of the exchange-correlation energy of the UEG [2], which in turn is based on accurate quantum Monte Carlo (QMC) simulation data [3]. However, the charged quantum matter in astrophysical systems such as planet cores and white dwarf atmospheres [4,5] is at temperatures way above the ground state, as are inertial confinement fusion targets [6][7][8], laser-excited solids [9], and pressure induced modifications of solids, such as insulator-metal transitions [10,11]. This unusual regime, in which strong ionic correlations coexist with electronic quantum effects and partial ionization, has been termed "warm dense matter" and is one of the most active frontiers in plasma physics and materials science.The warm dense regime is characterized by the existence of two comparable length scales and two comparable energy scales. The length scales are the mean interparticle distance,r, and the Bohr radius, a 0 ; the energy scales are the thermal energy, k B T , and the electronic Fermi energy, E F . The dimensionless parameters [12] r s =r/a 0 and Θ = k B T /E F are of order unity. Because Θ ∼ 1, the use of ground-state density functional theory is inappropriate and extensions to finite T are indispensible; these require accurate exchange-correlation functionals for finite temperatures [13][14][15][16][17]. Because neither r s nor Θ is small, there are no small parameters, and weakcoupling expansions beyond Hartree-Fock such as the Montroll-Ward (MW) and e 4 (e4) approximations [18,19], as well as linear response theory within the random- phase approximation (RPA) break down [20,21]. Finite-T Singwi-Tosi-Land-Sjölander (STLS) [22,23] local-fiel...

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confidence: 48%

Ab InitioQuantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit

et al. 2016

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“…Unbiased density matrices can be calculated with the introduction of a second, uncorrelated walker ensemble, to which the stochastic spawning, death, and annihilation steps are applied independently, and whose statistics are acquired separately, from the first. 29 This adaptation, known as replica sampling, achieves the unbiasing by ensuring that all the products of determinant amplitudes are calculated using populations from both simulations and has previously found application in the stochastic sampling of the N-electron density matrix known as density matrix quantum Monte Carlo 42 and the recently introduced Krylov-projected quantum Monte Carlo. 34 That is, for example, a successful spawning event from |D i ⟩ to |D j ⟩ in replica 1, occurring with a probability p (1) c D j |D i , gives rise to a contribution of…”

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confidence: 99%

Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo

Thomas

Opalka

Overy

et al. 2015

The Journal of Chemical Physics

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Articles you may be interested in A deterministic alternative to the full configuration interaction quantum Monte Carlo method J. Chem. Phys. 145, 044112 (2016) Unbiased stochastic sampling of the one-and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, "replica" ensemble of walkers, whose population evolves in imaginary time independently from the first and which entails only modest additional computational overheads. The matrices obtained from this approach are shown to be representative of full configuration-interaction quality and hence provide a realistic opportunity to achieve high-quality results for a range of properties whose operators do not necessarily commute with the Hamiltonian. A density-matrix formulated quasi-variational energy estimator having been already proposed and investigated, the present work extends the scope of the theory to take in studies of analytic nuclear forces, molecular dipole moments, and polarisabilities, with extensive comparison to exact results where possible. These new results confirm the suitability of the sampling technique and, where sufficiently large basis sets are available, achieve close agreement with experimental values, expanding the scope of the method to new areas of investigation. C 2015 AIP Publishing LLC. [http://dx

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“…In this work, quadratic quantities are required, but now E[q † i q j ] = ψ † i ψ j , due to correlations between walker amplitudes, where E[q i ] denotes the expectation value. To compute these, two independent replica sets of walkers are propagated simultaneously (indexed via superscripts), such that the amplitudes are uncorrelated between them [25,26], allowing for unbiased es-…”

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confidence: 99%

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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Density-matrix quantum Monte Carlo method

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Cited by 113 publications

References 54 publications

Ab InitioQuantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit

Ab InitioQuantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit

Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo

Krylov-Projected Quantum Monte Carlo Method

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