我们提出了一种通用的量子蒙特卡罗算法，用于模拟任意高自旋（自旋大于1/2）哈密顿量，该算法基于最近发展的排列矩阵表示（PMR）框架。我们的方法扩展了之前为自旋-1/2哈密顿量开发的PMR-QMC方法[Phys. Rev. Research 6, 013281 (2024)]。由于该方法不依赖于局部键分解，它同样适用于具有任意连接性、长程和多自旋相互作用的模型，其闭合行走公式允许自然地分析符号问题条件，以循环权重为依据。为了证明其适用性和通用性，我们将其应用于正方形晶格上的自旋-1和自旋-3/2量子Heisenberg模型，以及随机生成的高自旋哈密顿量。此外，我们展示了该方法如何自然扩展到包含混合粒子种类的一般哈密顿量，包括玻色子和费米子。我们的程序代码已在GitHub上免费提供。
英文摘要：
We present a universal quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than 1/2) Hamiltonians, based on the recently developed permutation matrix representation (PMR) framework. Our approach extends a previously developed PMR-QMC method for spin-1/2 Hamiltonians [Phys. Rev. Research 6, 013281 (2024)]. Because it does not rely on a local bond decomposition, the method applies equally well to models with arbitrary connectivities, long-range and multi-spin interactions, and its closed-walk formulation allows a natural analysis of sign-problem conditions in terms of cycle weights. To demonstrate its applicability and versatility, we apply our method to spin-1 and spin-3/2 quantum Heisenberg models on the square lattice, as well as to randomly generated high-spin Hamiltonians. Additionally, we show how the approach naturally extends to general Hamiltonians involving mixtures of particle species, including bosons and fermions. We have made our program code freely accessible on GitHub.
We present a cross-language C++/Python program for simulations of quantum mechanical systems with the use of Quantum Monte Carlo (QMC) methods. We describe a system for which to apply QMC, the algorithms of variational Monte Carlo and diffusion Monte Carlo and we describe how to implement theses methods in pure C++ and C++/Python. Furthermore we check the efficiency of the implementations in serial and parallel cases to show that the overhead using Python can be negligible.
Starting from an exact lower bound on the imaginary-time propagator, we present a Path-Integral Quantum Monte Carlo method that can handle singular attractive potentials. We illustrate the basic ideas of this Quantum Monte Carlo algorithm by simulating the ground state of hydrogen and helium.
We present a simple approach to the fixed phase method in Quantum Monte Carlo. This applies to electrons in molecules and electron gas and is straightforwardly extended to the Schrödinger equation with magnetic field.
Quantum Monte Carlo (QMC) methods are some of the most accurate methods for simulating correlated electronic systems. We investigate the compatibility, strengths and weaknesses of two such methods, namely, diffusion Monte Carlo (DMC) and auxiliary-field quantum Monte Carlo (AFQMC). The multi-determinant trial wave functions employed in both approaches are generated using the configuration interaction using a perturbative selection made iteratively (CIPSI) technique. Complete basis set full configuration interaction (CBS-FCI) energies estimated with CIPSI are used as a reference in this compara…
We present a path integral Monte Carlo method which is the full quantum analogue of the Gibbs ensemble Monte Carlo method of Panagiotopoulos to study the gas-liquid coexistence line of a classical fluid. Unlike previous extensions of Gibbs ensemble Monte Carlo to include quantum effects, our scheme is viable even for systems with strong quantum delocalization in the degenerate regime of temperature. This is demonstrated by an illustrative application to the gas-superfluid transition of $^4$He in two dimensions.
Since its first description fifty years ago, the Metropolis Monte Carlo method has been used in a variety of different ways for the simulation of continuum quantum many-body systems. This paper will consider some of the generalizations of the Metropolis algorithm employed in quantum Monte Carlo: Variational Monte Carlo, dynamical methods for projector monte carlo ({\it i.e.} diffusion Monte Carlo with rejection), multilevel sampling in path integral Monte Carlo, the sampling of permutations, cluster methods for lattice models, the penalty method for coupled electron-ionic systems and the Bayes…
In this thesis, the properties of mixtures of Bose-Einstein condensates at $T = 0$ have been investigated using quantum Monte Carlo (QMC) methods and Density Functional Theory (DFT) with the aim of understanding physics beyond the mean-field theory in Bose-Bose mixtures.
Exchange Monte Carlo for continuous-space Path Integral Monte Carlo simulation
The University of Tokyo（东京大学）；Institute for Physics of Intelligence, The University of Tokyo（东京大学物理智能研究所）；Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）
We describe an open-source implementation of the continuous-time interaction-expansion quantum Monte Carlo method for cluster-type impurity models with onsite Coulomb interactions and complex Weiss functions. The code is based on the ALPS libraries.
We discuss a backward Monte-Carlo technique for muon transport problem, with emphasis on its application in muography. Backward Monte-Carlo allows exclusive sampling of a final state by reversing the simulation flow. In practice it can be made analogous to an adjoint Monte-Carlo, though it is more versatile for muon transport. A backward Monte-Carlo was implemented as a dedicated muon transport library: PUMAS. It is shown for case studies relevant for muography imaging that the implementations of forward and backward Monte-Carlo schemes agree to better than 1%.
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection method, and Markov chain Monte Carlo to sample a probability distribution function, and methods for variance reduction to evaluate numerical integrals using the Monte Carlo simulation. We will also briefly introduce the quasi-Monte Carlo sampling at the end of this lecture.
A scientometric analysis of Monte Carlo simulation and Monte Carlo codes has been performed over a set of representative scholarly journals related to radiation physics. The results of this study are reported and discussed. They document and quantitatively appraise the role of Monte Carlo methods and codes in scientific research and engineering applications.
Monte Carlo methods play an important role in scientific computation, especially when problems have a vast phase space. In this lecture an introduction to the Monte Carlo method is given. Concepts such as Markov chains, detailed balance, critical slowing down, and ergodicity, as well as the Metropolis algorithm are explained. The Monte Carlo method is illustrated by numerically studying the critical behavior of the two-dimensional Ising ferromagnet using finite-size scaling methods. In addition, advanced Monte Carlo methods are described (e.g., the Wolff cluster algorithm and parallel temperin…
This article reviews the basic computational techniques for carrying out multi-scale simulations using statistical methods, with the focus on simulations of epitaxial growth. First, the statistical-physics background behind Monte Carlo simulations is briefly described. The kinetic Monte Carlo (kMC) method is introduced as an extension of the more wide-spread thermodynamic Monte Carlo methods, and algorithms for kMC simulations, including parallel ones, are discussed in some detail. The step from the atomistic picture to the more coarse-grained description of Monte Carlo simulations is exemplif…
The kinetic Monte Carlo method is a standard approach for simulating physical systems whose dynamics are stochastic or that evolve in a probabilistic manner. Here we show how to calculate the system time for such simulations.
We introduce and discuss Monte Carlo methods in quantum field theories. Methods of independent Monte Carlo, such as random sampling and importance sampling, and methods of dependent Monte Carlo, such as Metropolis sampling and Hamiltonian Monte Carlo, are introduced. We review the underlying theoretical foundations of Markov chain Monte Carlo. We provide several examples of Monte Carlo simulations, including one-dimensional simple harmonic oscillator, unitary matrix model exhibiting Gross-Witten-Wadia transition and a supersymmetric model exhibiting dynamical supersymmetry breaking.
A preliminary version (v0.2.1) of the DANTON Monte-Carlo package is presented. DANTON allows the exclusive sampling of (decaying) $τ$ generated by $ν_τ$ interactions with the Earth. The particles interactions with matter are simulated in detail, including transverse scattering. Detailed topography data of the Earth can be used as well. Yet, high Monte-Carlo efficiency is achieved by using a Backward Monte-Carlo technique. Some validation results are provided.
We present a new Monte Carlo method which couples Path Integral for finite temperature protons with Quantum Monte Carlo for ground state electrons, and we apply it to metallic hydrogen for pressures beyond molecular dissociation. We report data for the equation of state for temperatures across the melting of the proton crystal. Our data exhibit more structure and higher melting temperatures of the proton crystal than Car-Parrinello Molecular Dynamics results. This method fills the gap between high temperature electron-proton Path Integral and ground state Diffusion Monte Carlo methods.
An alternative Monte Carlo estimator for the one-body density rho(r) is presented. This estimator has a simple form and can be readily used in any type of Monte Carlo simulation. Comparisons with the usual regularization of the delta-function on a grid show that the statistical errors are greatly reduced. Furthermore, our expression allows accurate calculations of the density at any point in space, even in the regions never visited during the Monte Carlo simulation. The method is illustrated with the computation of accurate Variational Monte Carlo electronic densities for the Helium atom (1D c…
We present a new, biased Monte Carlo scheme for simulating complex, cyclic peptides. Backbone atoms are equilibrated with a biased rebridging scheme, and side-chain atoms are equilibrated with a look-ahead configurational bias Monte Carlo. Parallel tempering is shown to be an important ingredient in the construction of an efficient approach.
New machine learning based algorithms have been developed and tested for Monte Carlo integration based on generative Boosted Decision Trees and Deep Neural Networks. Both of these algorithms exhibit substantial improvements compared to existing algorithms for non-factorizable integrands in terms of the achievable integration precision for a given number of target function evaluations. Large scale Monte Carlo generation of complex collider physics processes with improved efficiency can be achieved by implementing these algorithms into commonly used matrix element Monte Carlo generators once the…
We provide a description of a diagrammatic Monte Carlo algorithm for the resonant Fermi gas in the normal phase. Details are given on diagrammatic framework, Monte Carlo moves, and incorporation of ultraviolet asymptotics. Apart from the self-consistent bold scheme, we also describe a non-self-consistent scheme, for which the ultraviolet treatment is more involved.
We present an efficient method to find minimum energy structures using energy estimates from accurate quantum Monte Carlo calculations. This method involves a stochastic process formed from the stochastic energy estimates from Monte Carlo that can be averaged to find precise structural minima while using inexpensive calculations with moderate statistical uncertainty. We demonstrate the applicability of the algorithm by minimizing the energy of the H2O-OH- complex and showing that the structural minima from quantum Monte Carlo calculations affect the qualitative behavior of the potential energy…
A Monte Carlo algorithm for calculating the single-particle spin-echo small-angle neutron scattering (SESANS) correlation function is presented. It is argued that the algorithm provides a general and efficient way of calculating SESANS data for any given shape and structure.
We present a new adaptive Monte Carlo integration algorithm for ill-behaved integrands with non-factorizable singularities. The algorithm combines Vegas with multi channel sampling and performs significantly better than Vegas for a large class of integrals appearing in physics.
Several models for the Monte Carlo simulation of Compton scattering on electrons are quantitatively evaluated with respect to a large collection of experimental data retrieved from the literature. Some of these models are currently implemented in general purpose Monte Carlo systems; some have been implemented and evaluated for possible use in Monte Carlo particle transport for the first time in this study. Here we present first and preliminary results concerning total and differential Compton scattering cross sections.
We present a comparison of the kinetic Activation-Relaxation Technique (k-ART) and the Self-Evolving Atomistic Kinetic Monte Carlo (SEAKMC), two off-lattice, on-the-fly kinetic Monte Carlo (KMC) techniques that were recently used to solve several materials science problems. We show that if the initial displacements are localized the dimer method and the Activation-Relaxation Technique \emph{nouveau} provide similar performance. We also show that k-ART and SEAKMC, although based on different approximations, are in agreement with each other, as demonstrated by the examples of 50 vacancies in a 1…
We describe QWalk, a new computational package capable of performing Quantum Monte Carlo electronic structure calculations for molecules and solids with many electrons. We describe the structure of the program and its implementation of Quantum Monte Carlo methods. It is open-source, licensed under the GPL, and available at the web site http://www.qwalk.org
A binary format with lists of particle state information, for interchanging particles between various Monte Carlo simulation applications, is presented. Portable C code for file manipulation is made available to the scientific community, along with converters and plugins for several popular simulation packages.
