Quantum Monte Carlo Formalism Research Articles

Dense-sparse quantum Monte Carlo algebraic diagrammatic construction and importance ranking.

Quantum Monte Carlo Algebraic Diagrammatic Construction (QMCADC) has been proposed as a reformulation of the second-order ADC scheme for the polarization propagator within the projection quantum Monte Carlo formalism. Dense-sparse partitioning and importance ranking filtering strategies are now exploited to accelerate its convergence and to alleviate the signproblem inherent in such calculations. By splitting the configuration space into dense and sparse subsets, the corresponding projection operator is decomposed into four distinct blocks. Deterministic calculations handle the dense-to-dense and sparse-to-dense blocks, while the remaining blocks, dense-to-sparse and sparse-to-sparse, are stochastically evaluated. The dense set is efficiently stored in a fixed-size array, and the sparse set is represented through conventional floating random Monte Carlo walks. The stochastic projection is further refined through importance ranking criteria, enabling a reduction in the required number of walkers with a controllable bias. Our results demonstrate the integration of dense-sparse partitioning with importance ranking filtering to significantly enhance the efficiency of QMCADC, enabling large-scale molecular excited-state calculations. Furthermore, this novel approach maximizes the utilization of the sparsity of ADC(2), transforming QMCADC into a tailored framework for ADC calculations.

Amelioration for the Sign Problem: An Adiabatic Quantum MonteCarlo Algorithm.

We introduce the adiabatic quantum MonteCarlo (AQMC) method, where we gradually crank up the interaction strength, as an amelioration of the sign problem. It is motivated by the adiabatic theorem and will approach the true ground state if the evolution time is long enough. We demonstrate that the AQMC algorithm enhances the average sign exponentially such that low enough temperatures can be accessed and ground-state properties probed. It is a controlled approximation that satisfies the variational theorem and provides an upper bound for the ground-state energy. We first benchmark the AQMC algorithm vis-à-vis the undoped Hubbard model on the square lattice which is known to be sign-problem-free within the conventional quantum MonteCarlo formalism. Next, we test the AQMC algorithm against the density-matrix-renormalization-group approach for the doped four-leg ladder Hubbard model and demonstrate its remarkable accuracy. As a nontrivial example, we apply our method to the Hubbard model at p=1/8 doping for a 16×8 system and discuss its ground-state properties. We finally utilize our method and demonstrate the emergence of U(1)_{2}∼SU(2)_{1} topological order in a strongly correlated Chern insulator.

Quantum Monte Carlo formalism for dynamical pions and nucleons

In most simulations of nonrelativistic nuclear systems, the wave functions found solving the many-body Schr\"odinger equations describe the quantum-mechanical amplitudes of the nucleonic degrees of freedom. In those simulations the pionic contributions are encoded in nuclear potentials and electroweak currents, and they determine the low-momentum behavior. In this work we present an alternative quantum Monte Carlo formalism in which both relativistic pions and nonrelativistic nucleons are explicitly included in the quantum-mechanical states of the system. We report the renormalization of the nucleon mass as a function of the momentum cutoff, an Euclidean time density correlation function that deals with the short-time nucleon diffusion, and the pion cloud density and momentum distributions. In the two-nucleon sector we show that the interaction of two static nucleons at large distances reduces to the one-pion exchange potential, and we fit the low-energy constants of the contact interactions to reproduce the binding energy of the deuteron and two neutrons in finite volumes. We show that the method can be readily applied to light-nuclei.

Green's functions from real-time bold-line Monte Carlo calculations: spectral properties of the nonequilibrium Anderson impurity model.

The nonequilibrium spectral properties of the Anderson impurity model with a chemical potential bias are investigated within a numerically exact real-time quantum MonteCarlo formalism. The two-time correlation function is computed in a form suitable for nonequilibrium dynamical mean field calculations. Additionally, the evolution of the model's spectral properties are simulated in an alternative representation, defined by a hypothetical but experimentally realizable weakly coupled auxiliary lead. The voltage splitting of the Kondo peak is confirmed and the dynamics of its formation after a coupling or gate quench are studied. This representation is shown to contain additional information about the dot's population dynamics. Further, we show that the voltage-dependent differential conductance gives a reasonable qualitative estimate of the equilibrium spectral function, but significant qualitative differences are found including incorrect trends and spurious temperature dependent effects.

Dielectric Response of Periodic Systems from Quantum Monte Carlo Calculations

We present a novel approach that allows us to calculate the dielectric response of periodic systems in the quantum Monte Carlo formalism. We employ a many-body generalization for the electric-enthalpy functional, where the coupling with the field is expressed via the Berry-phase formulation for the macroscopic polarization. A self-consistent local Hamiltonian then determines the ground-state wave function, allowing for accurate diffusion quantum Monte Carlo calculations where the polarization's fixed point is estimated from the average on an iterative sequence, sampled via forward walking. This approach has been validated for the case of an isolated hydrogen atom and then applied to a periodic system, to calculate the dielectric susceptibility of molecular-hydrogen chains. The results found are in excellent agreement with the best estimates obtained from the extrapolation of quantum-chemistry calculations.

Nuclear degrees of freedom in calculated isotropic hyperfine coupling constants of the ethyl radical: a Feynman path integral – ab initio study

The Feynman path integral quantum Monte Carlo formalism has been combined with an electronic Hamiltonian of the B3LYP-EPRIII type to study the isotropic hyperfine coupling (hfs) constants of the ethyl radical in thermal equilibrium ( T=25 K). The nuclear vibrations and the intramolecular rotation around the C–C bond have a sizeable influence on the hfs parameters. The thermally averaged numbers differ from single-nuclear configuration values calculated at the minimum of the potential energy surface. The analysis of the distribution functions for the isotropic hfs constants of C 2H 5 offers insight into the strong coupling between calculated hfs parameters and the nuclear configuration adopted.

Isotope Effect in the Mott Transition; a Prediction on the Basis of Molecular All-Quantum Simulations

We have linked an ab initio Hartree-Fock Hamiltonian to the Feynman path integral quantum Monte Carlo formalism in order to derive electronic expectation values under consideration of nuclear degrees of freedom. This approach yields electronic expectation values which depend on the atomic masses. On the basis of combined path integral – ab initio calculations we predict an isotope effect in the correlation driven Mott transition. The nuclear degrees of freedom lead to an enhancement in the electronic correlation strength, an effect which supports the transition conditions. This enhancement is negatively correlated with the atomic masses. Implications of an isotope effect in the Mott transition for the explanation of the superconducting pairing are mentioned concisely.

Isotope Effect in the Mott Transition; a Prediction on the Basis of Molecular All-Quantum Simulations

We have linked an ab initio Hartree-Fock Hamiltonian to the Feynman path integral quantum Monte Carlo formalism in order to derive electronic expectation values under consideration of nuclear degrees of freedom. This approach yields electronic expectation values which depend on the atomic masses. On the basis of combined path integral – ab initio calculations we predict an isotope effect in the correlation driven Mott transition. The nuclear degrees of freedom lead to an enhancement in the electronic correlation strength, an effect which supports the transition conditions. This enhancement is negatively correlated with the atomic masses. Implications of an isotope effect in the Mott transition for the explanation of the superconducting pairing are mentioned concisely.

Wave‐function optimization by least‐squares fitting of the exact wave function sampled by quantum Monte Carlo

The sampling of the exact solution of the Schrödinger equation by quantum Monte Carlo methods allows one to solve the problem of the optimization of linear and nonlinear parameters of a trial wave function by minimization of the distance to the exact wave function in Hilbert space even for those systems whose exact wave function is unknown. The overlap integrals between the basis functions and the exact wave function can be easily estimated within the quantum Monte Carlo formalism. Several observables of the helium atom ground state, computed both within the orbital approximation and by an explicitly correlated basis set, evidence the overall goodness of the wave function optimized according to this criterion. © 1996 John Wiley & Sons, Inc.

Multidimensional vibrational quantum Monte Carlo technique using robust interpolation from static or growing sets of discrete potential energy points

A simple algorithm for the calculation of fully anharmonic vibrational ground states and their properties from clamped nucleus electronic energy calculations is presented. The method is based on the diffusion quantum Monte Carlo formalism but it does not require an analytical representation of the Born—Oppenheimer potential surface. Instead, it can be coupled to any electronic structure solver. In a static variant, the algorithm exploits a pre-existing data set of potential energy points, whereas in the dynamical formulation it iteratively samples arbitrarily sized batches of new optimal nuclear configurations, whose electronic energies can be evaluated in parallel on a network of processors. The method is well suited for molecular systems involving light nuclei and other applications where the classical nuclear motion of “ab initio molecular dynamics” methods is inadequate. Test calculations for (HF) 2 and (HF) 3 demonstrate accuracy and favourable dimensional scaling of the algorithm.

Comparative study of a model quantum solid using quantum Monte Carlo, the effective potential, and improved self-consistent theories.

We have used the quantum Monte Carlo formalism to calculate the volume, pressure, and energy at three temperatures for a nearest-neighbor Lennard-Jones solid, with parameters appropriate to solid neon. The purpose is to provide accurate test data for a system with substantial quantum effects. The results are compared with the predictions of the effective potential and improved self-consistent theories. The agreement of all three techniques is good. The effective-potential method results agree better with the quantum Monte Carlo results at high temperatures, and those of the improved self-consistent method agree better with the quantum Monte Carlo results at low temperatures. The relationship between the three theories is discussed. We show that at zero degrees the effective-potential method is equivalent to first-order self-consistent theory.