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We design generative neural networks that generate Monte Carlo configurations with complete absence of autocorrelation and from which direct measurements of physical observables can be employed, irrespective of the system locating at the classical critical point, fermionic Mott insulator, Dirac semimetal and quantum critical point. We further propose a generic parallel-chain Monte Carlo scheme based on such neural networks, which provides independent samplings and accelerates the Monte Carlo simulations by reducing the thermalization process. We demonstrate the performance of our approach on the two-dimensional Ising and fermion Hubbard models.
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Efficient sampling of complex high-dimensional probability densities is a central task in computational science. Machine Learning techniques based on autoregressive neural networks have been recently shown to provide good approximations of probability distributions of interest in physics. In this work, we propose a systematic way to remove the intrinsic bias associated with these variational approximations, combining it with Markov-chain Monte Carlo in an automatic scheme to efficiently generate cluster updates, which is particularly useful for models for which no efficient cluster update scheme is known. Our approach is based on symmetry-enforced cluster updates building on the neural-network representation of conditional probabilities. We demonstrate that such finite-cluster updates are crucial to circumvent ergodicity problems associated with global neural updates. We test our method for first- and second-order phase transitions in classical spin systems, proving in particular its viability for critical systems, or in the presence of metastable states.
We propose a minimal generalization of the celebrated Markov-Chain Monte Carlo algorithm which allows for an arbitrary number of configurations to be visited at every Monte Carlo step. This is advantageous when a parallel computing machine is available, or when many biased configurations can be evaluated at little additional computational cost. As an example of the former case, we report a significant reduction of the thermalization time for the paradigmatic Sherrington-Kirkpatrick spin-glass model. For the latter case, we show that, by leveraging on the exponential number of biased configurations automatically computed by Diagrammatic Monte Carlo, we can speed up computations in the Fermi-Hubbard model by two orders of magnitude.
Population annealing is a recent addition to the arsenal of the practitioner in computer simulations in statistical physics and beyond that is found to deal well with systems with complex free-energy landscapes. Above all else, it promises to deliver unrivaled parallel scaling qualities, being suitable for parallel machines of the biggest calibre. Here we study population annealing using as the main example the two-dimensional Ising model which allows for particularly clean comparisons due to the available exact results and the wealth of published simulational studies employing other approaches. We analyze in depth the accuracy and precision of the method, highlighting its relation to older techniques such as simulated annealing and thermodynamic integration. We introduce intrinsic approaches for the analysis of statistical and systematic errors, and provide a detailed picture of the dependence of such errors on the simulation parameters. The results are benchmarked against canonical and parallel tempering simulations.
We consider a monolayer of graphene under uniaxial, tensile strain and simulate Bloch oscillations for different electric field orientations parallel to the plane of the monolayer using several values of the components of the uniform strain tensor, but keeping the Poisson ratio in the range of observable values. We analyze the trajectories of the charge carriers with different initial conditions using an artificial neural network, trained to classify the simulated signals according to the strain applied to the membrane. When the electric field is oriented either along the Zig-Zag or the Armchair edges, our approach successfully classifies the independent component of the uniform strain tensor with up to 90% of accuracy and an error of $pm1%$ in the predicted value. For an arbitrary orientation of the field, the classification is made over the strain tensor component and the Poisson ratio simultaneously, obtaining up to 97% of accuracy with an error that goes from $pm5%$ to $pm10%$ in the strain tensor component and an error from $pm12.5%$ to $pm25%$ in the Poisson ratio.
We introduce a semistochastic implementation of the power method to compute, for very large matrices, the dominant eigenvalue and expectation values involving the corresponding eigenvector. The method is semistochastic in that the matrix multiplication is partially implemented numerically exactly and partially with respect to expectation values only. Compared to a fully stochastic method, the semistochastic approach significantly reduces the computational time required to obtain the eigenvalue to a specified statistical uncertainty. This is demonstrated by the application of the semistochastic quantum Monte Carlo method to systems with a sign problem: the fermion Hubbard model and the carbon dimer.
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