Showing papers on "Quantum Monte Carlo published in 2004"

A new method for combining NLO QCD with shower Monte Carlo algorithms

Abstract: I show that with simple extensions of the shower algorithms in Monte Carlo programs, one can implement NLO corrections to the hardest emission that overcome the problems of negative weighted events found in previous implementations. Simple variants of the same method can be used for an improved treatment of matrix element corrections in Shower Monte Carlo programs.

Equation of State of a Fermi Gas in the BEC-BCS Crossover: A Quantum Monte Carlo Study

Abstract: We calculate the equation of state of a two-component Fermi gas with attractive short-range interspecies interactions using the fixed-node diffusion Monte Carlo method. The interaction strength is varied over a wide range by tuning the value $a$ of the $s$-wave scattering length of the two-body potential. For $ag0$ and $a$ smaller than the inverse Fermi wave vector our results show a molecular regime with repulsive interactions well described by the dimer-dimer scattering length ${a}_{m}=0.6a$. The pair correlation functions of parallel and opposite spins are also discussed as a function of the interaction strength.

Jastrow correlation factor for atoms, molecules, and solids

Abstract: A form of Jastrow factor is introduced for use in quantum Monte Carlo simulations of finite and periodic systems. Test data are presented for atoms, molecules, and solids, including both all-electron and pseudopotential atoms. We demonstrate that our Jastrow factor is able to retrieve a large fraction of the correlation energy.

Magnetic-field-induced condensation of triplons in Han Purple pigment BaCuSi2O6.

Abstract: Besides being an ancient pigment, BaCuSi2O6 is a quasi-2D magnetic insulator with a gapped spin dimer ground state. The application of strong magnetic fields closes this gap, creating a gas of bosonic spin triplet excitations. The topology of the spin lattice makes BaCuSi2O6 an ideal candidate for studying the Bose-Einstein condensation of triplet excitations as a function of the external magnetic field, which acts as a chemical potential. In agreement with quantum Monte Carlo numerical simulations, we observe a distinct lambda anomaly in the specific heat together with a maximum in the magnetic susceptibility upon cooling down to liquid helium temperatures.

Theoretical methods for strongly correlated electrons

Abstract: Contents Series Preface Preface C. Bourbonnais, D. Senechal, A. Ruckenstein, and A.-M.S. Tremblay I Numerical Methods 1 Density Matrix Renormalization Karen Hallberg 1 Introduction 2 The Method 3 Applications 4 Other Extensions to DMRG 4.1 Classical Systems 4.2 Finite-Temperature DMRG 4.3 Phonons, Bosons and Disorder 4.4 Molecules and Quantum Chemistry 5 Dynamical Correlation Functions 5.1 Lanczos and Correction Vector Techniques 5.2 Moment Expansion 5.3 Finite Temperature Dynamics 6 Conclusions 7 References 2 Quantum Monte Carlo Methods for Strongly Correlated Electron Systems Shiwei Zhang 1 Introduction 2 Preliminaries 2.1 Starting Point of Quantum Monte Carlo (QMC) 2.2 Basics of Monte Carlo Techniques 2.3 Slater Determinant Space 2.4 Hubbard-Stratonovich Transformation 3 Standard Auxiliary-Field Quantum Monte Carlo 3.1 Ground-State Method 3.2 Finite-Temperature Method 4 Constrained Path Monte Carlo Methods-Ground-State and Finite-Temperature 4.1 Why and How Does the Sign Problem Occur? 4.2 The Constrained-Path Approximation 4.3 Ground-State Constrained Path Monte Carlo (CPMC) Method 4.4 Finite-Temperature Method 4.5 Additional Technical Issues 5 Illustrative Results 6 Summary 7 References A Brief Review of Con.guration-Space Methods A.1 Variational Monte Carlo A.2 Green's Function Monte Carlo (GFMC) II Lagrangian, Functional Integral, Renormalization Group, Conformal and Bosonization Methods Renormalization Group Technique for Quasi-One-Dimensional Interacting Fermion Systems at Finite Temperature C. Bourbonnais, B. Guay and R. Wortis 1 Introduction 2 Scaling Ansatz for Fermions 2.1 One Dimension 2.2 Anisotropic Scaling and Crossover Phenomena 3 Free Fermion Limit 3.1 One Dimension 3.2 Interchain Coupling 4 The Kadano.-Wilson Renormalization Group 4.1 One-Dimensional Case 4.2 One-Loop Results 4.3 Two-Loop Results 4.4 Response Functions 5 Interchain Coupling: One-Particle Hopping 5.1 Interchain Pair Hopping and Long-Range Order 5.2 Long-Range Order in the Decon.ned Region 6 Kohn-Luttinger Mechanism in Quasi-One-Dimensional Metals 6.1 Generation of Interchain Pairing Channels 6.2 Possibility of Long-Range Order in the Interchain Pairing Channels 7 Summary and Concluding Remarks 8 References A One-Particle Self-Energy at the Two-Loop Level A.1 Backward and Forward Scattering Contributions A.2 Umklapp contribution 4 An Introduction to Bosonization D. Senechal 1 Quantum Field Theory in Condensed Matter 2 A Word on Conformal Symmetry 2.1 Scale and Conformal Invariance 2.2 Conformal Transformations 2.3 E.ect of Perturbations 2.4 The Central Charge 3 Interacting Electrons in One Dimension 3.1 Continuum Fields and Densities 3.2 Interactions 4 Bosonization: A Heuristic View 4.1 Why Is One-Dimension Special? 4.2 The Simple Boson 4.3 Bose Representation of the Fermion Field 5 Details of the Bosonization Procedure 5.1 Left and Right Boson Modes 5.2 Proof of the Bosonization Formulas: Vertex Operators 5.3 Bosonization of the Free-Electron Hamiltonian 5.4 Spectral Equivalence of Boson and Fermion 5.5 Case of Many Fermion Species: Klein Factors 5.6 Bosonization of Interactions 6 Exact Solution of the Tomonaga-Luttinger Model 6.1 Field and Velocity Renormalization 6.2 Left-Right Mixing 6.3 Correlation Functions 6.4 Spin or Charge Gap 7 Non-Abelian Bosonization 7.1 Symmetry Currents 7.2 Application to the Perturbed Tomonaga-Luttinger Model 8 Other Applications of Bosonization 8.1 The Spin- 12 Heisenberg Chain 8.2 Edge States in Quantum Hall Systems 8.3 And More

Quantum Monte Carlo calculations of excited states in A =6-8 nuclei

Abstract: A variational Monte Carlo method is used to generate sets of orthogonal trial functions, ${\ensuremath{\Psi}}_{T}({J}^{\ensuremath{\pi}};T)$, for given quantum numbers in various light $p$-shell nuclei. These ${\ensuremath{\Psi}}_{T}$ are then used as input to Green's function Monte Carlo (GFMC) calculations of first, second, and higher excited $({J}^{\ensuremath{\pi}};T)$ states. Realistic two- and three-nucleon interactions are used. We find that if the physical excited state is reasonably narrow, the GFMC energy converges to a stable result. With the combined Argonne ${\mathrm{v}}_{18}$ two-nucleon and Illinois-2 three-nucleon interactions, the results for many second and higher states in $A=6\char21{}8$ nuclei are close to the experimental values.

Quantum monte carlo simulations of confined bosonic atoms in optical lattices

Abstract: We study static properties of ultra-cold bosonic atoms in two-dimensional optical lattices by quantum Monte Carlo simulations of the bosonic Hubbard model in parabolic confinement potentials. Our focus is on local probes identifying Mott-insulating and superfluid regions, which can coexist in the inhomogenous environment of the trap. By proposing an effective ladder model for the boundary region between the two phases we can show clear evidence for the absence of true quantum critical behavior and explain the absence of critical slowing down at the quantum phase transition in a harmonic trap.

Computing induced charges in inhomogeneous dielectric media: application in a Monte Carlo simulation of complex ionic systems.

Abstract: The efficient calculation of induced charges in an inhomogeneous dielectric is important in simulations and coarse-grained models in molecular biology, chemical physics, and electrochemistry. We present the induced charge computation ~ICC! method for the calculation of the polarization charges based on the variational formulation of Allen et al. @Phys. Chem. Chem. Phys. 3, 4177 ~2001!#. We give a different solution for their extremum condition that produces a matrix formulation. The induced charges are directly calculated by solving the linear matrix equation Ah5c, where h contains the discretized induced charge density, c depends only on the source charges—the ions moved in the simulation—and the matrix A depends on the geometry of dielectrics, which is assumed to be unchanged during the simulation. Thus, the matrix need be inverted only once at the beginning of the simulation. We verify the efficiency and accuracy of the method by means of Monte Carlo simulations for two special cases. In the simplest case, a single sharp planar dielectric boundary is present, which allows comparison with exact results calculated using the method of electrostatic images. The other special case is a particularly simple case where the matrix A is not diagonal: a slab with two parallel flat boundaries. Our results for electrolyte solutions in these special cases show that the ICC method is both accurate and efficient.

Quantum annealing of the traveling-salesman problem.

Abstract: We propose a path-integral Monte Carlo quantum annealing scheme for the symmetric traveling-salesman problem, based on a highly constrained Ising-like representation, and we compare its performance against standard thermal simulated annealing. The Monte Carlo moves implemented are standard, and consist in restructuring a tour by exchanging two links (two-opt moves). The quantum annealing scheme, even with a drastically simple form of kinetic energy, appears definitely superior to the classical one, when tested on a 1002-city instance of the standard TSPLIB.

Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations.

Abstract: We present an adaptive algorithm which optimizes the statistical-mechanical ensemble in a generalized broad-histogram Monte Carlo simulation to maximize the system's rate of round trips in total energy. The scaling of the mean round-trip time from the ground state to the maximum entropy state for this local-update method is found to be O ( [N ln N](2) ) for both the ferromagnetic and the fully frustrated two-dimensional Ising model with N spins. Our algorithm thereby substantially outperforms flat-histogram methods such as the Wang-Landau algorithm.

Rejection-free geometric cluster algorithm for complex fluids.

Abstract: We present a novel, generally applicable Monte Carlo algorithm for the simulation of fluid systems. Geometric transformations are used to identify clusters of particles in such a manner that every cluster move is accepted, irrespective of the nature of the pair interactions. The rejection-free and nonlocal nature of the algorithm make it particularly suitable for the efficient simulation of complex fluids with components of widely varying size, such as colloidal mixtures. Compared to conventional simulation algorithms, typical efficiency improvements amount to several orders of magnitude.

Efficient localized basis set for quantum Monte Carlo calculations on condensed matter

Abstract: We present an efficient scheme for representing many-body wave functions in quantum Monte Carlo (QMC) calculations. The scheme is based on $B$ splines (blip functions), which consist of localized cubic splines centered on the points of a regular grid. We show that blip functions are unbiased, systematically improvable, and conveniently obtained from any standard plane-wave density functional theory (PW-DFT) code, and therefore provide a convenient and natural interface between PW-DFT and QMC calculations. We present tests on a 16-atom system of $\mathrm{Si}$ in the $\ensuremath{\beta}$-tin structure, and on 2- and 8-atom systems of $\mathrm{MgO}$ in the $\mathrm{NaCl}$ structure. We show that already with such small systems the speed-up of blip functions with respect to plane waves is between one and two order of magnitudes, without compromising the accuracy.

Variational cluster approach to spontaneous symmetry breaking: The itinerant antiferromagnet in two dimensions

Abstract: Based on the self-energy-functional approach proposed recently [M. Potthoff, Eur. Phys. J. B 32, 429 (2003)], we present an extension of the cluster-perturbation theory to systems with spontaneously broken symmetry. Our method applies to models with local interactions and accounts for both short-range correlations and long-range order. Short-range correlations are accurately taken into account via exact diagonalization of finite clusters. Long-range order is described by variational optimization of a ficticious symmetry-breaking field. In comparison with related cluster methods, our approach is more flexible and, for a given cluster size, less demanding numerically, especially at zero temperature. An application of the method to the antiferromagnetic phase of the Hubbard model at half-filling shows good agreement with results from quantum Monte Carlo calculations. We demonstrate that the variational extension of the cluster-perturbation theory is crucial to reproduce salient features of the single-particle spectrum.

The incomplete beta function law for parallel tempering sampling of classical canonical systems

Abstract: We show that the acceptance probability for swaps in the parallel tempering Monte Carlo method for classical canonical systems is given by a universal function that depends on the average statistical fluctuations of the potential and on the ratio of the temperatures. The law, called the incomplete beta function law, is valid in the limit that the two temperatures involved in swaps are close to one another. An empirical version of the law, which involves the heat capacity of the system, is developed and tested on a Lennard-Jones cluster. We argue that the best initial guess for the distribution of intermediate temperatures for parallel tempering is a geometric progression and we also propose a technique for the computation of optimal temperature schedules. Finally, we demonstrate that the swap efficiency of the parallel tempering method for condensed-phase systems decreases naturally to zero at least as fast as the inverse square root of the dimensionality of the physical system.

Quantitative comparison between theoretical predictions and experimental results for the BCS-BEC crossover.

Abstract: Theoretical predictions for the Bardeen-Cooper-Schrieffer–Bose-Einstein condensation crossover of trapped Fermi atoms are compared with recent experimental results for the density profiles of 6 Li .T he calculations rest on a single theoretical approach that includes pairing fluctuations beyond mean-field. Excellent agreement with experimental results is obtained. Theoretical predictions for the zerotemperature chemical potential and gap at the unitarity limit are also found to compare extremely well with Quantum Monte Carlo simulations and with recent experimental results.

The ground state tunneling splitting of malonaldehyde: accurate full dimensional quantum dynamics calculations.

Abstract: Benchmark calculations of the tunneling splitting in malonaldehyde using the full dimensional potential proposed by Yagi et al. are reported. Two exact quantum dynamics methods are used: the multiconfigurational time-dependent Hartree (MCTDH) approach and the diffusion Monte Carlo based projection operator imaginary time spectral evolution (POITSE) method. A ground state tunneling splitting of 25.7+/-0.3 cm(-1) is calculated using POITSE. The MCTDH computation yields 25 cm(-1) converged to about 10% accuracy. These rigorous results are used to evaluate the accuracy of approximate dynamical approaches, e.g., the instanton theory.

Bridging the Gap between Small Clusters and Nanodroplets: Spectroscopic Study and Computer Simulation of Carbon Dioxide Solvated with Helium Atoms

Abstract: High resolution infrared spectra of HeN–CO2 clusters with N up to about 20 have been studied in the region of the CO2 v3 fundamental band The B rotational constant initially drops as expected for a normal molecule, reaching a minimum for N = 5 Its subsequent rise for N = 6 to 11 can be interpreted as the transition from a normal (though floppy) molecule to a quantum solvation regime For N > 13, the B value becomes approximately constant with a value about 17% larger than that measured in much larger helium nanodroplets Quantum Monte Carlo calculations of pure rotational spectra are in excellent agreement with the measured B in this size range, and complement the experimental study with detailed structural information For larger cluster size (N = 30-50) the simulations show a clear sign of convergence towards the nanodroplet B value

Ground state phases of the Half-Filled One-Dimensional Extended Hubbard Model

Abstract: Using quantum Monte Carlo simulations, results of a strong-coupling expansion, and Luttinger liquid theory, we determine quantitatively the ground state phase diagram of the one-dimensional extended Hubbard model with on-site and nearest-neighbor repulsions U and V. We show that spin frustration stabilizes a bond-ordered (dimerized) state for U approximately V/2 up to U/t approximately 9, where t is the nearest-neighbor hopping. The transition from the dimerized state to the staggered charge-density-wave state for large V/U is continuous for U < or approximately 5.5 and first order for higher U.

Gaussian quantum Monte Carlo methods for fermions and bosons.

Abstract: We introduce a new class of quantum Monte Carlo methods, based on a Gaussian quantum operator representation of fermionic states. The methods enable first-principles dynamical or equilibrium calculations in many-body Fermi systems, and, combined with the existing Gaussian representation for bosons, provide a unified method of simulating Bose-Fermi systems. As an application relevant to the Fermi sign problem, we calculate finite-temperature properties of the two dimensional Hubbard model and the dynamics in a simple model of coherent molecular dissociation.

Spin susceptibility of two-dimensional electrons in narrow AlAs quantum wells.

Abstract: We report measurements of the spin susceptibility in dilute two-dimensional electrons confined to a 45 A wide AlAs quantum well. The electrons in this well occupy an out-of-plane conduction-band valley, rendering a system similar to two-dimensional electrons in Si-MOSFETs but with only one valley occupied. We observe an enhancement of the spin susceptibility over the band value that increases as the density is decreased, following closely the prediction of quantum Monte Carlo calculations and continuing at finite values through the metal-insulator transition.

Recent Developments of World-Line Monte Carlo Methods

Abstract: World-line quantum Monte Carlo methods are reviewed with an emphasis on breakthroughs made in recent years. In particular, three algorithms – the loop algorithm, the worm algorithm, and the directed-loop algorithm – for updating world-line configurations are presented in a unified perspective. Detailed descriptions of the algorithms in specific cases are also given.

Phase transitions for rock-scissors-paper game on different networks.

Abstract: Monte Carlo simulations and dynamical mean-field approximations are performed to study the phase transitions in the rock-scissors-paper game on different host networks. These graphs are originated from lattices by introducing quenched and annealed randomness simultaneously. In the resulting phase diagrams three different stationary states are identified for all structures. The comparison of results on different networks suggests that the value of the clustering coefficient plays an irrelevant role in the emergence of a global oscillating phase. The critical behavior of phase transitions seems to be universal and can be described by the same exponents.

Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals

Abstract: We report diffusion quantum Monte Carlo calculations of three-dimensional Wigner crystals in the density range rs=100–150. We have tested different types of orbital for use in the approximate wave functions but none improve upon the simple Gaussian form. The Gaussian exponents are optimized by directly minimizing the diffusion quantum Monte Carlo energy. We have carefully investigated and sought to minimize the potential biases in our Monte Carlo results. We conclude that the uniform electron gas undergoes a transition from a ferromagnetic fluid to a body-centered-cubic Wigner crystal at rs=106±1. The diffusion quantum Monte Carlo results are compared with those from Hartree-Fock and Hartree theory in order to understand the role played by exchange and correlation in Wigner crystals. We also study “floating” Wigner crystals and give results for their pair-correlation functions.

Global Analytical Potential Hypersurface for Large Amplitude Nuclear Motion and Reactions in Methane II. Characteristic Properties of the Potential and Comparison to Other Potentials and Experimental Information

Abstract: The global analytical potential surface for the electronic ground state of methane developed in paper I is analyzed and discussed in detail. A new determination of the experimental potential surface for the CH chromophorein CHD 3 , obtained from more recently measured line positions and integrated absorption coefficients, is also reported. The complete, nine-dimensional calculation of the vibrational ground state by diffusion quantum Monte Carlo on the fully anharmonic potential surface allows the determination of r e = (1.086 ′ 0.002) A with a high level of certainty from comparison with experimental values of rotational constants for methane and isotopomers. Other results regarding properties of the anharmonic potential surface close to the equilibrium configuration are theoretical values for the vibrationally induced electric dipole moments in CH 3 D, CH 2 D 2 , and CHD 3 , which are obtained in conjunction with a nine-dimensional, vector-valued representation of the electric dipole moment in this molecule and agree well with the experimental data. It is shown that, if equilibrium geometry and harmonic force field are fixed to experimental values, the overtone spectrum of the CH chromophore in CHD 3 can be described in an acceptable way ( 40 cm - 1 up to 18 000 cm - 1 (METPOT 3). The agreement can be improved to within 17 cm - 1 (METPOT 4), on the average, if the anharmonic part of the model potential is refined with data from the experimentally derived, three-dimensional CH chromophore potential surface from Lewerenz and Quack (J. Chem. Phys. 88). For this purpose, the analytical representation of the potential, mainly along the bending degrees of freedom, must be sufficiently flexible, as shown by the present calculations. The accuracy regarding the description of spectroscopic data pertaining to highly excited vibrational states and the global character of the proposed potential surface representation render it a powerful instrument for the theoretical treatment of chemical reaction dynamics. A relation to reaction kinetics can be established through calculation of the lowest adiabatic channel on the complete nine-dimensional potential hypersurface for methane using quasiadiabatic channel quantum Monte Carlo techniques. It is found that the behavior of this channel, corresponding approximately to an exponential interpolation with a parameter α 0.7-0.8 A - 1 in the adiabatic channel model, is consistent with empirical results obtained from experiment. Further refinements of the models are feasible and expected, when full dimensional calculations of the solution of the rovibrational Schrodinger equation will be performed.

Quantum Monte Carlo and variational approaches to the Holstein model

Abstract: Based on the canonical Lang-Firsov transformation of the Hamiltonian we develop a very efficient quantum Monte Carlo algorithm for the Holstein model with one electron. Separation of the fermionic degrees of freedom by a reweighting of the probability distribution leads to a dramatic reduction in computational effort. A principal component representation of the phonon degrees of freedom allows to sample completely uncorrelated phonon configurations. The combination of these elements enables us to perform efficient simulations for a wide range of temperature, phonon frequency, and electron-phonon coupling on clusters large enough to avoid finite-size effects. The algorithm is tested in one dimension and the data are compared with exact-diagonalization results and with existing work. Moreover, the ideas presented here can also be applied to the many-electron case. In the one-electron case considered here, the physics of the Holstein model can be described by a simple variational approach.

Continuous Time Quantum Monte Carlo Method for Fermions: Beyond Auxiliary Field Framework

Abstract: Numerically exact continuous-time Quantum Monte Carlo algorithm for finite fermionic systems with non-local interactions is proposed. The scheme is particularly applicable for general multi-band time-dependent correlations since it does not invoke Hubbard-Stratonovich transformation. The present determinantal grand-canonical method is based on a stochastic series expansion for the partition function in the interaction representation. The results for the Green function and for the time-dependent susceptibility of multi-orbital super-symmetric impurity model with a spin-flip interaction are presented.

Two-dimensional Hubbard-Holstein bipolaron

Abstract: We present a diagrammatic Monte Carlo study of the properties of the Hubbard-Holstein bipolaron on a two-dimensional square lattice. With a small Coulomb repulsion $U$ and with increasing electron-phonon interaction, and when reaching a value about two times smaller than the one corresponding to the transition of light polaron to heavy polaron, the system suffers a sharp transition from a state formed by two weakly bound light polarons to a heavy, strongly bound on-site bipolaron. Aside from this rather conventional bipolaron a new bipolaron state is found for large $U$ at intermediate and large electron-phonon coupling, corresponding to two polarons bound on nearest-neighbor sites. We discuss both the properties of the different bipolaron states and the transition from one state to another. We present a phase diagram in parameter space defined by the electron-phonon coupling and $U$. Our numerical method does not use any artificial approximation and can be easily modified to other bipolaron models with longer range electron-phonon and∕or electron-electron interaction.

Coupled Electron-Ion Monte Carlo Calculations of Dense Metallic Hydrogen

Abstract: We present an efficient new Monte Carlo method which couples path integrals for finite temperature protons with quantum Monte Carlo calculations 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 do Car-Parrinello molecular dynamics results. This method fills the gap between high temperature electron-proton path integral and ground state diffusion Monte Carlo methods and should have wide applicability.

Quantum Monte Carlo study of helium clusters doped with nitrous oxide: quantum solvation and rotational dynamics.

Abstract: Dynamical and structural properties of small 4HeN-N2O complexes have been analyzed using ground-state and finite-temperature Monte Carlo simulations. The effective rotational constants resulting from the ground-state calculations are in excellent agreement with the results of a recent spectroscopic study [Y. Xu et al., Phys. Rev. Lett. 91, 163401 (2003)]. After an initial decrease for cluster sizes up to N=8, the rotational constant increases, signaling a transition from a molecular complex to a quantum-solvated system. Such a turnaround is not present in the rotational constants extracted from the finite-temperature Monte Carlo calculations, performed for Boltzmann statistics, thus highlighting the importance of exchange effects to explain the decoupling between a solvated dopant and the helium motion.