Monte Carlo (MC) simulations are essential computational approaches with widespread use throughout all areas of science. We present a method for accelerating lattice MC simulations using fully connected and convolutional artificial neural networks that are trained to perform local and global moves in configuration space, respectively. Both networks take local spacetime MC configurations as input features and can, therefore, be trained using samples generated by conventional MC runs on smaller lattices before being utilized for simulations on larger systems. This approach is benchmarked for the case of determinant quantum Monte Carlo (DQMC) studies of the two-dimensional Holstein model. We find that both artificial neural networks are capable of learning an unspecified effective model that accurately reproduces the MC configuration weights of the original Hamiltonian and achieve an order of magnitude speedup over the conventional DQMC algorithm. Our approach is broadly applicable to many classical and quantum lattice MC algorithms.Monte Carlo (MC) simulations are essential computational approaches with widespread use throughout all areas of science. We present a method for accelerating lattice MC simulations using fully connected and convolutional artificial neural networks that are trained to perform local and global moves in configuration space, respectively. Both networks take local spacetime MC configurations as input features and can, therefore, be trained using samples generated by conventional MC runs on smaller lattices before being utilized for simulations on larger systems. This approach is benchmarked for the case of determinant quantum Monte Carlo (DQMC) studies of the two-dimensional Holstein model. We find that both artificial neural networks are capable of learning an unspecified effective model that accurately reproduces the MC configuration weights of the original Hamiltonian and achieve an order of magnitude speedup over the conventional DQMC algorithm. Our approach is broadly applicable to many classical and quantum lattice MC algorithms.

arXiv:1905.07440Physical review. B./Physical review. BJul 22, 201938 citations

Ground state properties of the one-dimensional Coulomb gas using the lattice regularized diffusion Monte Carlo method

Michele Casula, Sandro Sorella, Gaetano Senatore

We study the ground state properties of a quasi-one-dimensional electron gas interacting via an effective potential with a harmonic transversal confinement and long-range Coulomb tail. The exact correlation energy has been calculated for a wide range of electron densities by using the lattice regularized diffusion Monte Carlo method, which is a recent development of the standard projection Monte Carlo technique. In this case it is particularly useful as it allows one to sample the exact ground state of the system, even in the low-density regime when the exchange between electrons is extremely small. For different values of the width parameter $b$ $(0.1\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*}\ensuremath{\leqslant}b\ensuremath{\leqslant}4\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*})$, we give a simple parametrization of the correlation energy, which provides an accurate local density energy functional for quasi-one-dimensional systems. Moreover, we show that static correlations are in qualitative agreement with those obtained for the Luttinger liquid model with long-range interactions.We study the ground state properties of a quasi-one-dimensional electron gas interacting via an effective potential with a harmonic transversal confinement and long-range Coulomb tail. The exact correlation energy has been calculated for a wide range of electron densities by using the lattice regularized diffusion Monte Carlo method, which is a recent development of the standard projection Monte Carlo technique. In this case it is particularly useful as it allows one to sample the exact ground state of the system, even in the low-density regime when the exchange between electrons is extremely small. For different values of the width parameter $b$ $(0.1\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*}\ensuremath{\leqslant}b\ensuremath{\leqslant}4\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*})$, we give a simple parametrization of the correlation energy, which provides an accurate local density energy functional for quasi-one-dimensional systems. Moreover, we show that static correlations are in qualitative agreement with those obtained for the Luttinger liquid model with long-range interactions.

arXiv:cond-mat/0607130Physical Review BDec 22, 200691 citations

Nonlinearity and Localization in One-Dimensional Random Media

Robert E. Knapp, George Papanicolaou, B. White

Springer proceedings in physicsJan 1, 198920 citations

Monte Carlo Study of Ising Critical Isotherms

J. G. García, Manuel I. Marqués, Julio A. Gonzalo

Monte Carlo investigations of magnetization versus field, Mc(H), at the critical temperature provide direct accurate results on the critical exponent δ−1 for one, two, three and four-dimensional lattices: δ−1 1D =0, δ−1 2D =0.0666(2)≈1/15, δ−1 3D =0.1997(4)≈1/5, δ−1 4D =0.332(5)≈1/3. This type of Monte Carlo data on δ, which is not easily found in studies of Ising lattices in the current literature, as far as we know, defines extremely well the numerical value of this exponent within very stringent limits.Monte Carlo investigations of magnetization versus field, Mc(H), at the critical temperature provide direct accurate results on the critical exponent δ−1 for one, two, three and four-dimensional lattices: δ−1 1D =0, δ−1 2D =0.0666(2)≈1/15, δ−1 3D =0.1997(4)≈1/5, δ−1 4D =0.332(5)≈1/3. This type of Monte Carlo data on δ, which is not easily found in studies of Ising lattices in the current literature, as far as we know, defines extremely well the numerical value of this exponent within very stringent limits.

FerroelectricsJan 1, 20120 citations

b

$(0.1\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*}\ensuremath{\leqslant}b\ensuremath{\leqslant}4\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*})$, we give a simple parametrization of the correlation energy, which provides an accurate local density energy functional for quasi-one-dimensional systems. Moreover, we show that static correlations are in qualitative agreement with those obtained for the Luttinger liquid model with long-range interactions.