We present the first open access version of the QMeCha (Quantum MeCha /'mεkə/) code, a quantum Monte Carlo package developed to study many-body interactions between different types of quantum particles, with a modular and easy-to-expand structure. QMeCha is now available under a CC BY-NC-ND license through the repository github.com/QMeCha. The present code has been developed to solve the Hamiltonian of a system that can include nuclei and fermions of different mass and charge, e.g., electrons and positrons, embedded in an environment of classical charges and quantum Drude oscillators. To approximate the ground state of this many-particle operator, the code features different wavefunctions. For the fermionic particles, beyond the traditional Slater determinant, QMeCha also includes geminal functions, such as the Pfaffian, and presents different types of explicit correlation terms in Jastrow factors. The classical point charges and quantum Drude oscillators, described through different variational Ansätze, are used to model a molecular environment capable of explicitly describing dispersion, polarization, and electrostatic effects experienced by the nuclear and fermionic subsystems. To integrate these wavefunctions, efficient variational Monte Carlo and diffusion Monte Carlo protocols have been developed, together with a robust wavefunction optimization procedure that features correlated sampling.
We present the first open access version of the QMeCha (Quantum MeCha /'mεkə/) code, a quantum Monte Carlo package developed to study many-body interactions between different types of quantum particles, with a modular and easy-to-expand structure. QMeCha is now available under a CC BY-NC-ND license through the repository github.com/QMeCha. The present code has been developed to solve the Hamiltonian of a system that can include nuclei and fermions of different mass and charge, e.g., electrons and positrons, embedded in an environment of classical charges and quantum Drude oscillators. To approximate the ground state of this many-particle operator, the code features different wavefunctions. For the fermionic particles, beyond the traditional Slater determinant, QMeCha also includes geminal functions, such as the Pfaffian, and presents different types of explicit correlation terms in Jastrow factors. The classical point charges and quantum Drude oscillators, described through different variational Ansätze, are used to model a molecular environment capable of explicitly describing dispersion, polarization, and electrostatic effects experienced by the nuclear and fermionic subsystems. To integrate these wavefunctions, efficient variational Monte Carlo and diffusion Monte Carlo protocols have been developed, together with a robust wavefunction optimization procedure that features correlated sampling.
We present the first open access version of the QMeCha (Quantum MeCha) code, a quantum Monte Carlo (QMC) package developed to study many-body interactions between different types of quantum particles, with a modular and easy-to-expand structure. The present code has been built to solve the Hamiltonian of a system that can include nuclei and fermions of different mass and charge, e.g. electrons and positrons, embedded in an environment of classical charges and quantum Drude oscillators. To approximate the ground state of this many-particle operator, the code features different wavefunctions. For the fermionic particles, beyond the traditional Slater determinant, QMeCha also includes Geminal functions such as the Pfaffian, and presents different types of explicit correlation terms in the Jastrow factors. The classical point charges and quantum Drude oscillators, described through different variational ansätze, are used to model a molecular environment capable of explicitly describing dispersion, polarization, and electrostatic effects experienced by the nuclear and fermionic subsystem. To integrate these wavefunctions, efficient variational Monte Carlo and diffusion Monte Carlo protocols have been developed, together with a robust wavefunction optimization procedure that features correlated sampling.
QMCPACK is an open source quantum Monte Carlo package for ab initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wavefunctions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary-field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit and graphical processing unit systems. We detail the program's capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://qmcpack.org.
mVMC (many-variable Variational Monte Carlo) is an open-source software package based on the variational Monte Carlo method applicable for a wide range of Hamiltonians for interacting fermion systems. In mVMC, we introduce more than ten thousands variational parameters and simultaneously optimize them by using the stochastic reconfiguration (SR) method. In this paper, we explain basics and user interfaces of mVMC. By using mVMC, users can perform the calculation by preparing only one input file of about ten lines for widely studied quantum lattice models, and can also perform it for general Hamiltonians by preparing several additional input files. We show the benchmark results of mVMC for the Hubbard model, the Heisenberg model, and the Kondo-lattice model. These benchmark results demonstrate that mVMC provides ground-state and low-energy-excited-state wave functions for interacting fermion systems with high accuracy. Program title: mVMC Program Files doi: http://dx.doi.org/10.17632/xhgyp6ncvt.1 Licensing provisions: GNU General Public License version 3 Programming language: C External routines/libraries: MPI, BLAS, LAPACK, Pfapack, ScaLAPACK (optional) Nature of problem: Physical properties (such as the charge/spin structure factors) of strongly correlated electrons at zero temperature. Solution method: Application software based on the variational Monte Carlo method for quantum lattice model such as the Hubbard model, the Heisenberg model and the Kondo model. Unusual features: It is possible to perform the highly-accurate calculations for ground states in a wide range of theoretical Hamiltonians in quantum many-body systems. In addition to the conventional orders such as magnetic and/or charge orders, user can treat the anisotropic superconductivities within the same framework. This flexibility is the main advantage of mVMC.
Electronic structure quantum Monte Carlo Quantum Monte Carlo (QMC) is an advanced simulation methodology for studies of manybody quantum systems. The QMC approaches combine analytical insights with stochastic computational techniques for efficient solution of several classes of important many-body problems such as the stationary Schrödinger equation. QMC methods of various flavors have been applied to a great variety of systems spanning continuous and lattice quantum models, molecular and condensed systems, BEC-BCS ultracold condensates, nuclei, etc. In this review, we focus on the electronic structure QMC, i.e., methods relevant for systems described by the electron-ion Hamiltonians. Some of the key QMC achievements include direct treatment of electron correlation, accuracy in predicting energy differences and favorable scaling in the system size. Calculations of atoms, molecules, clusters and solids have demonstrated QMC applicability to real systems with hundreds of electrons while providing 90-95% of the correlation energy and energy differences typically within a few percent of experiments. Advances in accuracy beyond these limits are hampered by the so-called fixed-node approximation which is used to circumvent the notorious fermion sign problem. Many-body nodes of fermion states and their properties have therefore become one of the important topics for further progress in predictive power and efficiency of QMC calculations. Some of our recent results on the wave function nodes and related nodal domain topologies will be briefly reviewed. This includes analysis of few-electron systems and descriptions of exact and approximate nodes using transformations and projections of the highly-dimensional nodal hypersurfaces into the 3D space. Studies of fermion nodes offer new insights into topological properties of eigenstates such as explicit demonstrations that generic fermionic ground states exhibit the minimal number of two nodal domains. Recently proposed trial wave functions based on Pfaffians with pairing orbitals are presented and their nodal properties are tested in calculations of first row atoms and molecules. Finally, backflow "dressed" coordinates are introduced as another possibility for capturing correlation effects and for decreasing the fixed-node bias.
We introduce version 1.0 of the SmoQyElPhQMC.jl package, an open-source Julia code for performing scalable quantum Monte Carlo simulations of electron-phonon coupled model Hamiltonians. SmoQyElPhQMC.jl is built upon the SmoQyDQMC.jl codebase and implements improved versions of the algorithms presented in [B. Cohen-Stead \textit{et al}., Phys. Rev. E 105, 065302 (2022)] to enable (near-linear) scalable simulations of a broad class of uncorrelated e-ph models both in system size and inverse temperature. By extending the functionality of the flexible scripting interface introduced in SmoQyDQMC.jl, the SmoQyElPhQMC.jl package continues to allow users to adapt it to different workflows and interface with other software packages in the Julia ecosystem. The code for this package can be downloaded from our GitHub repository at https://github.com/SmoQySuite/SmoQyElPhQMC.jl or installed using the Julia package manager. The online documentation, including examples, can be obtained from our documentation page at https://smoqysuite.github.io/SmoQyElPhQMC.jl/stable/.
With the ability to solve the many-body Schrödinger equation accurately, in principle all physics and chemistry could be derived from first principles. However, exact wave functions of realistic and interesting systems are in general unavailable because they are non-deterministic polynomial-hard to compute (Troyer, 2005). This implies that we need to rely on approximations. The variational Monte Carlo (VMC) method is widely used for ground state studies, but requires a trial wave function ansatz which must trade off between efficiency and accuracy. The method also has many common features with machine learning algorithms, and as neural networks have shown impressive power as function approximators, the idea is to use a neural network as the trial wave function guess. For fermionic systems, like electronic structure systems, the wave function needs to obey Fermi-Dirac statistics. This is typically achieved using a Slater determinant. As a neural network hardly can model this feature, our approach is to replace the single-particle functions in the Slater determinant with restricted Boltzmann machines, getting the RBM ansatz. In addition, we add further correlations via so-called Jastrow factors (Drummond, 2004). The de facto standard trial wave function ansatz for electronic structure calculations is the Slater-Jastrow ansatz, which was implemented as a reference. Our primary focus is on closed-shell circular quantum dots, where we compute the ground state energy and electron density of two-dimensional systems with up to 90 electrons and three-dimensional systems with up to 70 electrons. The energy obtained by the RBM ansatz was reasonably close to experimental results, and it gradually became closer as we added more complex correlation factors. For our most complicated Jastrow factor, the energy was found to be lower than the energy provided by the Slater-Jastrow ansatz for small dots, but for larger dots it was slightly higher. However, the one-body density profile reveals that the RBM ansatz gives more distinctly located electrons compared to the Slater-Jastrow ansatz. This can be explained by the way the RBM ansatz models the correlations. From the two-body density profile, we also observe that the repulsive interactions get more significant as we add a Jastrow factor. Based on the electron densities and the energy distribution between kinetic and potential energy, it is certain that the various methods provide different electron configurations. For low-frequency dots, the electron density becomes more localized with an additional radial peak compared to high-frequency dots. This is reminiscent of what is known as Wigner localization (Ghosal, 2007). The computational time consumption was found to be favorable for the RBM ansatz for small systems and the Slater-Jastrow ansatz for large systems. This can be explained by the exploding number of variational parameters in the RBM ansatz as the system sizes increase. The RBM ansatz with Jastrow factors were notably more computationally intensive than the other ansätze, and evidently, there is no reason to use the simplest Jastrow factor when more complicated Jastrow factors are available.