Worm algorithm and diagrammatic Monte Carlo: A new approach to continuous-space path integral Monte Carlo simulations (original) (raw)
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Worm Algorithm for Continuous-Space Path Integral Monte Carlo Simulations
Physical Review Letters, 2006
We present a new approach to path integral Monte Carlo (PIMC) simulations based on the worm algorithm, originally developed for lattice models and extended here to continuous-space manybody systems. The scheme allows for efficient computation of thermodynamic properties, including winding numbers and off-diagonal correlations, for systems of much greater size than that accessible to conventional PIMC. As an illustrative application of the method, we simulate the superfluid transition of 4 He in two dimensions. PACS numbers: 75.10.Jm, 05.30.Jp, 67.40.Kh, 74.25.Dw Over the past two decades, PIMC simulations have played a major role in the theoretical investigation of quantum many-body systems, not only by providing reliable quantitative results, but also by shaping our current conceptual understanding, e.g., of the relationship between superfluidity and Bose condensation. At least for Bose systems, PIMC is the only presently known method capable of furnishing in principle exact numerical estimates of physical quantities, including the superfluid density, and the condensate fraction[1].
Series on advances in quantum many-body theory, 2002
We review the use of the path integral Monte Carlo (PIMC) methodology to the study of finite-size quantum clusters, with particular emphasis on recent applications to pure and impurity-doped 4 He clusters. We describe the principles of PIMC, the use of the multilevel Metropolis method for sampling particle permutations, and the methods used to accurately incorporate anisotropic moleculehelium interactions into the path integral scheme. Applications to spectroscopic studies of embedded atoms and molecules are summarized, with discussion of the new concepts of local and nanoscale superfluidity that have been generated by recent PIMC studies of the impurity-doped 4 He clusters.
Quantum Gibbs ensemble Monte Carlo
The Journal of Chemical Physics, 2014
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.
Quantum Monte Carlo simulation in the canonical ensemble at finite temperature
Physical Review E, 2006
A quantum Monte Carlo method with a non-local update scheme is presented. The method is based on a pathintegral decomposition and a worm operator which is local in imaginary time. It generates states with a fixed number of particles and respects other exact symmetries. Observables like the equal-time Green's function can be evaluated in an efficient way. To demonstrate the versatility of the method, results for the one-dimensional Bose-Hubbard model and a nuclear pairing model are presented. Within the context of the Bose-Hubbard model the efficiency of the algorithm is discussed.
Calculating thermodynamics properties of quantum systems by a non-Markovian Monte Carlo procedure
We present a history-dependent Monte Carlo scheme for the efficient calculation of the freeenergy of quantum systems, inspired by the Wang-Landau sampling and metadynamics method. When embedded in a path integral formulation, it is of general applicability to a large variety of Hamiltonians. In the two-dimensional quantum Ising model, chosen here for illustration, the accuracy of free energy, critical temperature, and specific heat is demonstrated as a function of simulation time, and successfully compared with the best available approaches, particularly the Wang-Landau method over two different Monte Carlo procedures. PACS numbers: 02.70.Ss, 05.10.Ln, 05.30.-d
Molecular dynamics algorithms for quantum Monte Carlo methods
Chemical Physics Letters, 2009
In the present Letter, novel molecular dynamics methods compatible with corresponding quantum Monte Carlo methods are developed. One is a variational molecular dynamics method that is a molecular dynamics analog of quantum variational Monte Carlo method. The other is a variational path integral molecular dynamics method, which is based on the path integral molecular dynamics method for finite temperature systems by Tuckerman et al., J. Chem. Phys. 99, 2796 (1993). These methods are applied to model systems including the liquid helium-4, demonstrated to work satisfactorily for the tested ground state calculations.
Computational quantum mechanics: An underutilized tool in thermodynamics
Pure and Applied Chemistry, 2000
In this paper, we highlight the various ways computational quantum mechanics (QM) can be used in applied thermodynamics. We start with the most rigorous procedures of calculating the interactions between molecules that can then be used in simulation and progress, in steps, to less rigorous but easily used methods, including the very successful continuum solvation models.
The Journal of Chemical Physics, 2007
The numerical advantage of quantum Monte Carlo simulations of rigid bodies relative to the flexible simulations is investigated for some simple systems. The results show that if high frequency modes in molecular condensed matter are predominantly in the ground state, the convergence of path integral simulations becomes nonuniform. Rigid body quantum parallel tempering simulations are necessary to accurately capture thermodynamic phenomena in the temperature range where the dynamics are influenced by intermolecular degrees of freedom; the stereographic projection path integral adapted for quantum simulations of asymmetric tops is a significantly more efficient strategy compared with Cartesian coordinate simulations for molecular condensed matter under these conditions. The reweighted random series approach for stereographic path integral Monte Carlo is refined and implemented for the quantum simulation of water clusters treated as an assembly of rigid asymmetric tops.
The Journal of Chemical Physics, 2007
In this paper, we present a path integral hybrid Monte Carlo ͑PIHMC͒ method for rotating molecules in quantum fluids. This is an extension of our PIHMC for correlated Bose fluids ͓S. Miura and J. Tanaka, J. Chem. Phys. 120, 2160 ͑2004͔͒ to handle the molecular rotation quantum mechanically. A novel technique referred to be an effective potential of quantum rotation is introduced to incorporate the rotational degree of freedom in the path integral molecular dynamics or hybrid Monte Carlo algorithm. For a permutation move to satisfy Bose statistics, we devise a multilevel Metropolis method combined with a configurational-bias technique for efficiently sampling the permutation and the associated atomic coordinates. Then, we have applied the PIHMC to a helium-4 cluster doped with a carbonyl sulfide molecule. The effects of the quantum rotation on the solvation structure and energetics were examined. Translational and rotational fluctuations of the dopant in the superfluid cluster were also analyzed.
2005
We construct a quantum Monte Carlo algorithm for interacting fermions using the two-body density as the fundamental quantity. The central idea is mapping the interacting fermionic system onto an auxiliary system of interacting bosons. The correction term is approximated using correlated wave functions for the interacting system, resulting in an effective potential that represents the nodal surface. We calculate the properties of 3He and find good agreement with experiment and with other theoretical work. In particular, our results for the total energy agree well with other calculations where the same approximations were implemented but the standard quantum Monte Carlo algorithm was used