Path integral Monte Carlo ground state approach: formalism, implementation, and applications

Yan, Yangqian; Blume, D.

doi:10.1088/1361-6455/aa8d7f

Cited by 22 publications

(10 citation statements)

References 99 publications

(245 reference statements)

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“…These surfaces focus on describing low-energy vibrational states, although modification of the training protocols could extend the region covered by the neural network. There are other methods such as path integral ground state (PIGS) methods , and path integral Monte Carlo , that require dozens to hundreds of potential energy evaluations per step. These methods can also take advantage of parallel evaluation of these potential energy values on a GPU.…”

Section: Discussionmentioning

confidence: 99%

GPU-Accelerated Neural Network Potential Energy Surfaces for Diffusion Monte Carlo

2021

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Diffusion Monte Carlo (DMC) provides a powerful method for understanding the vibrational landscape of molecules that are not well-described by conventional methods. The most computationally demanding step of these calculations is the evaluation of the potential energy. In this work, a general approach is developed in which a neural network potential energy surface is trained by using data generated from a small-scale DMC calculation. Once trained, the neural network can be evaluated by using highly parallelizable calls to a graphics processing unit (GPU). The power of this approach is demonstrated for DMC simulations on H2O, CH5 +, and (H2O)2. The need to include permutation symmetry in the neural network potentials is explored and incorporated into the molecular descriptors of CH5 + and (H2O)2. It is shown that the zero-point energies and wave functions obtained by using the neural network potentials are nearly identical to the results obtained when using the potential energy surfaces that were used to train the neural networks at a substantial savings in the computational requirements of the simulations.

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Section: Discussionmentioning

confidence: 99%

GPU-Accelerated Neural Network Potential Energy Surfaces for Diffusion Monte Carlo

2021

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“…the disordered phase disappears), analogously to what was observed in [36] for the the Quantum Adiabatic Correction (QAC) of the Curie-Weiss model in a transverse-field. Whether this is the correct zero-temperature behaviour or it is an artefact of the first-order perturbation theory is an open question, which one could in principle explore either through LC-QMC by appropriately taking the limit β → ∞, or by adapting a LC-QMC PIGS [37] approach. Additionally, while our empirical rescaling of the transverse-field strength Γ works reasonably well in capturing the distortion that the embedding produces in the distribution of the order parameter, it is not exact.…”

Section: Discussionmentioning

confidence: 99%

Perils of embedding for sampling problems

Marshall

Gioacchino

Rieffel

2020

Phys. Rev. Research

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Sampling from certain distributions is a prohibitively challenging task. Special-purpose hardware such as quantum annealers may be able to more efficiently sample from such distributions, which could find application in optimization, sampling tasks, and machine learning. Current quantum annealers impose certain constraints on the structure of the cost Hamiltonian due to the connectivity of the individual processing units. This means that in order to solve many problems of interest, one is required to embed the native graph into the hardware graph. The effect of embedding for sampling is more pronounced than for optimization; for optimization one is just concerned with mapping ground states to ground states, whereas for sampling one needs to consider states at all energies. We argue that as the problem size grows, or the embedding size grows, the chance of a sample being in the logical subspace is exponentially suppressed. It is therefore necessary to construct post-processing techniques to evade this exponential sampling overhead, techniques that project from the embedded distribution one is physically sampling from, back to the logical space of the native problem. We show that the most naive (and most common) projection technique, known as majority vote, can fail quite spectacularly at preserving distribution properties. We show that, even with care, one cannot avoid bias in the general case. Specifically we prove through a simple and generic (counter) example that no post-processing technique, under reasonable assumptions, can avoid biasing the statistics in the general case. On the positive side, we demonstrate a new resampling technique for performing this projection which substantially out-performs majority vote and may allow one to much more effectively sample from graphs of interest.

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“…At T = 0 K, the path integral ground state quantum Monte Carlo (QMC) algorithm [81][82][83] provides access to ground state properties of a many-body system by statistically sampling the imaginary time propagator e −βH . Starting from a trial wave function |Ψ T , in the long imaginary time limit β → ∞, e −βH |Ψ T converges to the exact ground state, |Ψ 0 , provided Ψ 0 |Ψ T = 0.…”

Section: E Quantum Monte Carlomentioning

confidence: 99%

Two-Dimensional Bose-Hubbard Model for Helium on Graphene

Yu,

Lauricella,

Elsayed

et al. 2021

Preprint

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An exciting development in the field of correlated systems is the possibility of realizing twodimensional (2D) phases of quantum matter. For a systems of bosons, an example of strong correlations manifesting themselves in a 2D environment is provided by helium adsorbed on graphene. We construct the effective Bose-Hubbard model for this system which involves hard-core bosons (U ≈ ∞), repulsive nearest-neighbor (V > 0) and small attractive (V < 0) next-nearest neighbor interactions. The mapping onto the Bose-Hubbard model is accomplished by a variety of many-body techniques which take into account the strong He-He correlations on the scale of the graphene lattice spacing. Unlike the case of dilute ultracold atoms where interactions are effectively point-like, the detailed microscopic form of the short range electrostatic and long range dispersion interactions in the helium-graphene system are crucial for the emergent Bose-Hubbard description. The result places the ground state of the first layer of 4 He adsorbed on graphene deep in the commensurate solid phase with 1/3 of the sites on the dual triangular lattice occupied. Because the parameters of the effective Bose-Hubbard model are very sensitive to the exact lattice structure, this opens up an avenue to tune quantum phase transitions in this solid-state system.

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Path integral Monte Carlo ground state approach: formalism, implementation, and applications

Cited by 22 publications

References 99 publications

GPU-Accelerated Neural Network Potential Energy Surfaces for Diffusion Monte Carlo

GPU-Accelerated Neural Network Potential Energy Surfaces for Diffusion Monte Carlo

Perils of embedding for sampling problems

Two-Dimensional Bose-Hubbard Model for Helium on Graphene

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