Integral Monte Carlo Simulations Research Articles

Static and thermodynamic properties of low-density supercritical 4He—breakdown of the Feynman–Hibbs approximation

We study the applicability of the semiclassical Feynman and Hibbs (FH) (second-order or fourth-order) effective potentials to the description of the thermodynamic properties of quantum fluids at finite temperatures. First, we use path integral Monte Carlo (PIMC) simulations to estimate the thermodynamic/static properties of our model quantum fluid, i.e. low-density 4He at 10 K. With PIMC we obtain the experimental equation of state, the single-particle mean kinetic energy, the single-particle density matrix and the single-particle momentum distribution of this system at low densities. We show that our PIMC results are in full agreement with experimental data obtained with deep inelastic neutron scattering at high momentum transfers (D. Colognesi, C. Andreani, R. Senesi, Europhys. Lett., 2000, 50, 202). As expected, in this region of the 4He phase diagram, quantum effects modify the width of the single-particle momentum distribution but do not alter its Gaussian shape. Knowing the exact values of density, pressure and single-particle mean kinetic energy for our model quantum fluid, we investigate the limitations of the semiclassical FH effective potentials. We show that commonly used 'short-time' approximations to the high-temperature density matrix due to Feynman and Hibbs can only be applied in a very limited range of the 4He phase diagram. We found that FH effective potentials reproduce the experimental densities of 4He at 10 K for Lambda/a < 0.45 (Lambda = 2.73 A denotes the thermal de Broglie wavelength, a = rho(-1/3) is the mean nearest-neighbor distance in the fluid and rho denotes fluid density). Moreover, semiclassical FH effective potentials are able to correctly predict the single-particle mean kinetic energy of 4He at 10 K in a very limited range of fluid densities, i.e.Lambda/a < 0.17. We show that the ad hoc application of the semiclassical FH effective potentials for the calculation of the thermodynamic properties of dense liquid-like para-hydrogen (para-H2) adsorbed in nanoporous materials below 72 K is questionable.

Quantum sieving in organic frameworks

The isotopic separation factors for T 2/H 2 and D 2/H 2 mixtures adsorbed in various organic frameworks have been calculated using path integral Monte Carlo simulations. The results are in fair agreement with the available experimental data, and show a very strong dependence on temperature. The selectivity shows a less pronounced dependence on the external pressure, but different behaviours are found for different materials. They are analyzed from the point of view of the solid–fluid potential energy surface.

Population Inversion of a NAHS Mixture Adsorbed into a Cylindrical Pore

A cylindrical nanopore immersed in a non-additive hard sphere binary fluid is studied by means of integral equation theories and Monte Carlo simulations. It is found that at low and intermediate values of the bulk total number density the more concentrated bulk species is preferentially absorbed by the pore, as expected. However, further increments of the bulk number density lead to an abrupt population inversion in the confined fluid and an entropy driven prewetting transition at the outside wall of the pore. These phenomena are a function of the pore size, the non-additivity parameter, the bulk number density, and particles relative number fraction. We discuss our results in relation to the phase separation in the bulk.

Finite Size Effect in Path Integral Monte Carlo Simulations of 4 He Systems

Path integral Monte Carlo (PIMC) simulations are a powerful computational method to study interacting quantum systems at finite temperatures. In this work, PIMC has been applied to study the finite size effect of the simulated systems of 4 He. We determine the energy as a function of temperature at saturated-vapor-pressure (SVP) conditions in the temperature range of T ε [1.0 K,4.0 K], and the equation of state (EOS) in the ground state for systems consisted of 32, 64 and 128 4 He atoms, respectively. We find that the energy at SVP is influenced significantly by the size of the simulated system in the temperature range of T ε [2.1 K, 3.0 K] and the larger the system is, the better results are obtained in comparison with the experimental values; while the EOS appeared to be unrelated to it.

Cryogenic Separation of Hydrogen Isotopes in Single-Walled Carbon and Boron-Nitride Nanotubes: Insight into the Mechanism of Equilibrium Quantum Sieving in Quasi-One-Dimensional Pores

Quasi-one-dimensional cylindrical pores of single-walled boron nitride and carbon nanotubes efficiently differentiate adsorbed hydrogen isotopes at 33 K. Extensive path integral Monte Carlo simulations revealed that the mechanisms of quantum sieving for both types of nanotubes are quantitatively similar; however, the stronger and heterogeneous external solid-fluid potential generated from single-walled boron nitride nanotubes enhanced the selectivity of deuterium over hydrogen both at zero coverage and at finite pressures. We showed that this enhancement of the D(2)/H(2) equilibrium selectivity results from larger localization of hydrogen isotopes in the interior space of single-walled boron nitride nanotubes in comparison to that of equivalent single-walled carbon nanotubes. The operating pressures for efficient quantum sieving of hydrogen isotopes are strongly depending on both the type as well as the size of the nanotube. For all investigated nanotubes, we predicted the occurrence of the minima of the D(2)/H(2) equilibrium selectivity at finite pressure. Moreover, we showed that those well-defined minima are gradually shifted upon increasing of the nanotube pore diameter. We related the nonmonotonic shape of the D(2)/H(2) equilibrium selectivity at finite pressures to the variation of the difference between the average kinetic energy computed from single-component adsorption isotherms of H(2) and D(2). In the interior space of both kinds of nanotubes hydrogen isotopes formed solid-like structures (plastic crystals) at 33 K and 10 Pa with densities above the compressed bulk para-hydrogen at 30 K and 30 MPa.

Ordered structure formation in 2D mass asymmetric electron–hole plasmas

We study strong Coulomb correlations in dense two-dimensional electron–hole plasmas by means of direct path integral Monte Carlo simulations. In particular, the formation and dissociation of bound states, such as excitons, bi-excitons and many particle clusters, is analyzed and the density-temperature regions of their occurrence are identified. At high density, the Mott transition to the fully ionized state (electron–hole hexatic liquid) is detected. Particular attention is paid to the influence of the hole to electron mass ratio M on the properties of the plasma. For high enough values of M we observed the formation of Coulomb hole crystal-like structures.

Critical Temperature of Interacting Bose Gases in Two and Three Dimensions

We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=10;{5} particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3 < or approximately 10(-4). This value is different from the estimate na3 < or approximately 10(-6) for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |psi|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.

Anharmonic Effects in Neutron Scattering Studies of Lattice Excitations in BCC 4He

We report high resolution measurements of lattice excitations of bcc solid 4He using inelastic neutron scattering. The resulting dispersion relations of the phonons agree well with Path Integral Monte Carlo Simulations which we carried out in parallel with the experimental work. In addition, we studied the recently discovered two “optic-like” excitation branches. One of these branches is weakly dispersive, while the second one seems dispersionless. The dispersive optical branch interacts with the phonons. We suggest that this interaction may be responsible for some of the anharmonic effects reported in the past, such as phonon interference. We argue that the agreement of experimental results with the “Self Consistent Phonon Theory” may be improved if the coupling between the phonons and one of the “optic-like” excitation branches is included in the calculations.

Solvation Structure and Rotational Dynamics of LiH in 4He Clusters

We present results of path integral Monte Carlo simulations of LiH solvated in superfluid 4He clusters of size up to N = 100. Despite the light mass of LiH and the strongly anisotropic LiH-He potential with a large repulsion at the hydrogen end, LiH is solvated inside the cluster for sufficiently large N. Using path integral correlation function analysis, we have determined the dipole (J = 1) rotational excitations of the cluster and a corresponding effective rotational constant Beff of the solvated LiH. We predict that Beff is greatly reduced with respect to the gas-phase rotational constant B, to a value of only about 6% of B. This exceptionally large reduction of the rotational constant is due to the highly anisotropic 4He solvation structure around LiH. It does not follow the previously established trend of a relatively small B reduction for light molecules, showing the strongest reduction of all molecules in 4He to date. Comparison of the calculated rotational spectra of LiH in helium obeying Bose and Boltzmann statistics, respectively, demonstrates that the Bose statistics of helium is an essential requirement for obtaining well-defined molecule rotational spectra in helium-4.

Square-well mixtures: a study of their coexistence using theory and simulation

We study coexistence and thermodynamic properties of square-well monomeric mixtures using both continuum integral equation theory and Monte Carlo simulation. We focus most of our attention on a mixture which is slightly asymmetric, both in terms of size and energetics, and explore the liquid-vapour coexistence behaviour for both the pure components, and selected phase envelopes in the mixture. We find the theory to be in semi-quantitative agreement with the simulation results and expect to make use of the tools developed here as we move towards studies of chain mixtures.

Rovibrational Spectra for the HCCCN·HCN and HCN·HCCCN Binary Complexes in 4He Droplets

Rovibrational spectra are measured for the HCCCN*HCN and HCN*HCCCN binary complexes in helium droplets at low temperature. Though no Q-branch is observed in the infrared spectrum of the linear HCN*HCCCN dimer, which is consistent with previous experimental results obtained for other linear molecules, a prominent Q-branch is found in the corresponding infrared spectrum of the HCCCN*HCN complex. This Q-branch, which is reminiscent of the spectrum of a parallel band of a prolate symmetric top, implies that some component of the total angular momentum is parallel to the molecular axis. The appearance of this particular spectroscopic feature is analyzed here in terms of a nonsuperfluid helium density induced by the molecular interactions. Finite temperature path integral Monte Carlo simulations are performed using potential energy surfaces calculated with second-order Möller-Plesset perturbation theory, to investigate the structural and superfluid properties of both HCCCN*HCN(4He)N and HCN*HCCCN(4He)N clusters with N < or = 200. Explicit calculation of local and global nonsuperfluid densities demonstrates that this difference in the rovibrational spectra of the HCCCN*HCN and HCN*HCCCN binary complexes in helium can be accounted for by local differences in the superfluid response to rotations about the molecular axis, i.e., different parallel nonsuperfluid densities. The parallel and perpendicular nonsuperfluid densities are found to be correlated with the locations and strengths of extrema in the dimer interaction potentials with helium, differences between which derive from the variable extent of polarization of the CN bond in cyanoacetylene and the hydrogen-bonded CH unit in the two isomers. Calculation of the corresponding helium moments of inertia and effective rotational constants of the binary complexes yields overall good agreement with the experimental values.

Interacting electrons in one dimension: a path integral Monte Carlo study

Path integral Monte Carlo simulations have been carried out for a system of interacting fermionic particles in one dimension. Due to the fact that the sign problem can be completely eliminated for one-dimensional systems, such simulations allow one to obtain accurate energies and particle densities in arbitrary external potentials. Two cases were considered: electrons in the field of a uniform neutralizing background and in an effective field of atoms on a lattice. In the latter case, a clear asymmetry of the charge density distribution of conducting electrons and holes has been observed.

Structure, superfluidity, and quantum melting of hydrogen clusters

We present results of a theoretical study of para-hydrogen and ortho-deuterium clusters at low temperature (0.5 K < T < 3.5 K), based on Path Integral Monte Carlo simulations. Clusters of size up to N=21 para-hydrogen molecules are nearly entirely superfluid at T < 1 K. For 21 < N < 30, the superfluid response displays strong variations with N, reflecting structural changes that occur on adding or removing even a single molecule. Some clusters in this size range display quantum melting, going from solid- to liquid-like as T tends to 0. Melting is caused by quantum exchanges of molecules. The largest para-hydrogen cluster for which a significant superfluid response is observed comprises 27 molecules. Evidence of a finite superfluid response is presented for ortho-deuterium clusters of size up to 14 molecules. Magic numbers are observed, at which both types of clusters feature pronounced stability.

Correlation effects in partially ionized mass asymmetric electron-hole plasmas

The effects of strong Coulomb correlations in dense three-dimensional electron-hole plasmas are studied by means of unbiased direct path integral Monte Carlo simulations. The formation and dissociation of bound states, such as excitons and biexcitons, is analyzed and the density-temperature region of their appearance is identified. At high density, the Mott transition to the fully ionized metallic state (electron-hole liquid) is detected. Particular attention is paid to the influence of the hole to electron mass ratio M on the properties of the plasma. Above a critical value of about M=80 formation of a hole Coulomb crystal was recently verified [Bonitz, Phys. Rev. Lett. 95, 235006 (2005)] which is supported by additional results. Results are related to the excitonic phase diagram of intermediate valent Tm[Se,Te], where large values of M have been observed experimentally.

Voids, generic van der Waals equation of state, and transport coefficients of liquids

In this Perspective, we discuss the role of voids in transport processes in liquids and the manner in which the concept of voids enters the generic van der Waals equation of state and the modified free volume theory. The density fluctuation theory is then discussed and we show how the density fluctuation theory can be made a molecular theory with the help of the modified free volume theory and the generic van der Waals equation of state. The confluence of the aforementioned three theories makes it possible to calculate the transport coefficients of liquids by using the information on the equilibrium pair correlation function, which can be calculated either by an integral equation theory or Monte Carlo simulations. A number of relations between transport coefficients are also presented, which are derived on the basis of the density fluctuation theory. Since they can be used to obtain one transport coefficient from another they can be very useful in handling experimental and theoretical data. An application of the modified free volume theory to polymer melts is discussed as an example for a theory of transport properties of complex liquids.

Phase separation of model adsorbates in random matrices

The liquid-liquid phase behavior of binary mixtures in random pores is investigated with non-additive hard spheres using both ROZ (Replica Ornstein-Zernike) integral equations and cavity biased grand canonical Monte Carlo simulations. The critical densities of the coexistence phase envelopes are determined as function of the non-additivity parameter Delta, varying from Delta = 0.2, 0.4, 0.6, up to 0.8. The matrix is made of quenched hard spheres. Its porosity is varied to ascertain the effects of confinement, with packing densities rho(0) ranging from 0.1, 0.3, to 0.5. To obtain fiduciary results from ROZ, we use the accurate ZSEP closure relation proposed earlier with and without thermodynamic consistency. The ZSEP closure is known to enforce the zero-separation theorems via special adjustable parameters in the bridge function. Two versions of this closure are used to assess their accuracies (vis-à-vis the Monte Carlo data): first ZSEP-T, namely, the ZSEP closure with added thermodynamic consistency (the Gibbs-Duhem relation); and second purely ZSEP without adding thermodynamic consistency. It is found that both closures give correct qualitative trend, with errors of ZSEP falling within 8-9%, while ZSEP-T, being more accurate, to within 1-2%. As non-additivity is increased, both versions become more accurate. The critical density rho(c) is found to decrease with decreasing porosity. In addition, rho(c) also decreases with increasing Delta, in a non-monotone fashion.

Influence of nuclear fluctuations on the NMR parameters of bullvalene: A Feynman path integral – Ab initio study

The isotropic magnetic shieldings and chemical shifts in bullvalene have been determined by Feynman path integral Monte Carlo simulations which have been combined with the gauge-including atomic orbital formalism. This setup renders possible the treatment of the quantum and thermal nuclear degrees of freedom in the calculation of NMR quantities. Ab initio Hartree–Fock Hamiltonians have been employed in the present ensemble averaging of NMR parameters. The vibrational motions cause a nuclear deshielding which depends on the topology of the centre studied. The consideration of these corrections leads to a better agreement between measured and calculated chemical shifts.

First Principles Calculations of Shock Compressed Fluid Helium

The properties of hot dense helium at megabar pressures are studied with two first principles computer simulation techniques: path integral Monte Carlo simulation and density functional molecular dynamics. The simulations predict that the compressibility of helium is substantially increased by electronic excitations that are present in the hot fluid at thermodynamic equilibrium. A maximum compression ratio of 5.24(4)-fold the initial density was predicted for 360 GPa and 150,000 K. This result distinguishes helium from deuterium, for which simulations predicted a maximum compression ratio of 4.3(1). Hugoniot curves for statically precompressed samples are also discussed.

Rotational spectrum of cyanoacetylene solvated with helium atoms

The high resolution microwave spectra of He(N)-HCCCN clusters were studied in the size ranges of 1-18 and 25-31. In the absence of an accompanying infrared study, rotational excitation energies were computed by the reptation quantum Monte Carlo method and used to facilitate the search and assignment of R(0) transitions from N > 6, as well as R(1) transitions with N > 1. The assignments in the range of 25-31 are accurate to +/-2 cluster size units, with an essentially certain relative ordering. The rotational transition frequencies decrease with N = 1-6 and then show oscillatory behavior for larger cluster sizes, which is now recognized to be a manifestation of the onset and microscopic evolution of superfluidity. For cluster sizes beyond completion of the first solvation shell the rotational frequencies increase significantly above the large-droplet limit. This behavior, common to other linear molecules whose interaction with He features a strong nearly equatorial minimum, is analyzed using path integral Monte Carlo simulations. The He density in the incipient second solvation shell is shown to open a new channel for long permutation cycles, thus increasing the decoupling of the quantum solvent from the rotation of the dopant molecule.

Worm algorithm and diagrammatic Monte Carlo: A new approach to continuous-space path integral Monte Carlo simulations

A detailed description is provided of a new worm algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature. The algorithm is formulated within the general path integral Monte Carlo (PIMC) scheme, but also allows one to perform quantum simulations in the grand canonical ensemble, as well as to compute off-diagonal imaginary-time correlation functions, such as the Matsubara Green function, simultaneously with diagonal observables. Another important innovation consists of the expansion of the attractive part of the pairwise potential energy into elementary (diagrammatic) contributions, which are then statistically sampled. This affords a complete microscopic account of the long-range part of the potential energy, while keeping the computational complexity of all updates independent of the size of the simulated system. The computational scheme allows for efficient calculations of the superfluid fraction and off-diagonal correlations in space-time, for system sizes which are orders of magnitude larger than those accessible to conventional PIMC. We present illustrative results for the superfluid transition in bulk liquid 4He in two and three dimensions, as well as the calculation of the chemical potential of hcp 4He.