Quantum Monte Carlo estimation of complex-time correlations for the study of the ground-state dynamic structure function.

We present a method based on the path integral Monte Carlo formalism for the calculation of ground-state time correlation functions in quantum systems. The key point of the method is the consideration of time as a complex variable whose phase δ acts as an adjustable parameter. By using high-order approximations for the quantum propagator, it is possible to obtain Monte Carlo data all the way from purely imaginary time to δ values near the limit of real time. As a consequence, it is possible to infer accurately the spectral functions using simple inversion algorithms. We test this approach in the calculation of the dynamic structure function S(q, ω) of two one-dimensional model systems, harmonic and quartic oscillators, for which S(q, ω) can be exactly calculated. We notice a clear improvement in the calculation of the dynamic response with respect to the common approach based on the inverse Laplace transform of the imaginary-time correlation function.

High-order time expansion path integral ground state.

The feasibility of path integral Monte Carlo ground state calculations with very few beads using a high-order short-time Green's function expansion is discussed. An explicit expression of the evolution operator which provides dramatic enhancements in the quality of ground-state wave functions is examined. The efficiency of the method makes possible to remove the trial wave function and thus obtain completely model-independent results still with a very small number of beads. If a single iteration of the method is used to improve a given model wave function, the result is invariably a shadow-type wave function, whose precise content is provided by the high-order algorithm employed.

Ground-state properties and superfluidity of two- and quasi-two-dimensional solid 4He.

In a recent study we have reported a new type of trial wavefunction symmetric under the exchange of particles, which is able to describe a supersolid phase. In this work, we use the diffusion Monte Carlo method and this model wavefunction to study the properties of solid (4)He in two- and quasi-two-dimensional geometries. In the purely two-dimensional (2D) case, we obtain results for the total ground-state energy and freezing and melting densities which are in good agreement with previous exact Monte Carlo calculations performed with a slightly different interatomic potential model. We calculate the value of the zero-temperature superfluid fraction ρ(s)/ρ of 2D solid (4)He and find that it is negligible in all the considered cases, similarly to what is obtained in the perfect (free of defects) three-dimensional crystal using the same computational approach. Interestingly, by allowing the atoms to move locally in the direction perpendicular to the plane where they are confined to zero-point oscillations (quasi-2D crystal), we observe the emergence of a finite superfluid density that coexists with the periodicity of the system.

High order Chin actions in path integral Monte Carlo.

High order actions proposed by Chin have been used for the first time in path integral Monte Carlo simulations. Contrary to the Takahashi-Imada action, which is accurate to the fourth order only for the trace, the Chin action is fully fourth order, with the additional advantage that the leading fourth-order error coefficients are finely tunable. By optimizing two free parameters entering in the new action, we show that the time step error dependence achieved is best fitted with a sixth order law. The computational effort per bead is increased but the total number of beads is greatly reduced and the efficiency improvement with respect to the primitive approximation is approximately a factor of 10. The Chin action is tested in a one-dimensional harmonic oscillator, a H(2) drop, and bulk liquid (4)He. In all cases a sixth-order law is obtained with values of the number of beads that compare well with the pair action approximation in the stringent test of superfluid (4)He.

Ground-state properties of a one-dimensional system of hard rods.

A quantum Monte Carlo simulation of a system of bosonic hard rods in one dimension is presented and discussed. The calculation is exact since the analytical form of the wave function is known and is in excellent agreement with predictions obtained from asymptotic expansions valid at large distances. The analysis of the static structure factor and the pair distribution function indicates that a solidlike and a gaslike phases exist at high and low densities, respectively. The one-body density matrix decays following a power law at large distances and produces a divergence in the low density momentum distribution at k=0 which can be identified as a quasicondensate.

Beyond the Tonks-Girardeau gas: strongly correlated regime in quasi-one-dimensional Bose gases.

We consider a homogeneous 1D Bose gas with contact interactions and a large attractive coupling constant. This system can be realized in tight waveguides by exploiting a confinement induced resonance of the effective 1D scattering amplitude. By using the diffusion Monte Carlo method we show that, for small densities, the gaslike state is well described by a gas of hard rods. The critical density for cluster formation is estimated using the variational Monte Carlo method. The behavior of the correlation functions and of the frequency of the lowest breathing mode for harmonically trapped systems shows that the gas is more strongly correlated than in the Tonks-Girardeau regime.

Momentum distribution and condensate fraction of a fermion gas in the BCS-BEC crossover.

By using the diffusion Monte Carlo method we calculate the one- and two-body density matrix of an interacting Fermi gas at T = 0 in the BCS to Bose-Einstein condensate (BEC) crossover. Results for the momentum distribution of the atoms, as obtained from the Fourier transform of the one-body density matrix, are reported as a function of the interaction strength. Off-diagonal long-range order in the system is investigated through the asymptotic behavior of the two-body density matrix. The condensate fraction of pairs is calculated in the unitary limit and on both sides of the BCS-BEC crossover.

Quantum Monte Carlo simulation of overpressurized liquid 4He.

A diffusion Monte Carlo simulation of superfluid 4He at zero temperature and pressures up to 275 bar is presented. Increasing the pressure beyond freezing (approximately 25 bar), the liquid enters the overpressurized phase in a metastable state. In this regime, we report results of the equation of state and the pressure dependence of the static structure factor, the condensate fraction, and the excited-state energy corresponding to the roton. Along this large pressure range, both the condensate fraction and the roton energy decrease but do not become zero. The roton energies obtained are compared with recent experimental data in the overpressurized regime.

Equation of state of a Fermi gas in the BEC-BCS crossover: a quantum Monte Carlo study.

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 a>0 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.

Higher order and infinite Trotter-number extrapolations in path integral Monte Carlo.

Improvements beyond the primitive approximation in the path integral Monte Carlo method are explored both in a model problem and in real systems. Two different strategies are studied: The Richardson extrapolation on top of the path integral Monte Carlo data and the Takahashi-Imada action. The Richardson extrapolation, mainly combined with the primitive action, always reduces the number-of-beads dependence, helps in determining the approach to the dominant power law behavior, and all without additional computational cost. The Takahashi-Imada action has been tested in two hard-core interacting quantum liquids at low temperature. The results obtained show that the fourth-order behavior near the asymptote is conserved, and that the use of this improved action reduces the computing time with respect to the primitive approximation.

High-momentum response of liquid 3He.

A final-state-effects formalism suitable to analyze the high-momentum response of Fermi liquids is presented and used to study the dynamic structure function of liquid 3He. The theory, developed as a natural extension of the Gersch-Rodriguez formalism, incorporates the Fermi statistics explicitly through a new additive term which depends on the semidiagonal two-body density matrix. The use of a realistic momentum distribution, calculated using the diffusion Monte Carlo method, and the inclusion of this additive correction allows for good agreement with available deep-inelastic neutron scattering data.

Effective mass of two-dimensional 3He.

We use structural information from diffusion Monte Carlo calculations for two-dimensional 3He to calculate the effective mass. Static effective interactions are constructed from the density and spin-structure functions using sum rules. We find that both spin and density fluctuations contribute about equally to the effective mass. Our results show, in agreement with recent experiments, a flattening of the single-particle self-energy with increasing density, which eventually leads to a divergent effective mass.

Zero-temperature equation of state of two-dimensional 3He.

The equation of state of two-dimensional 3He at zero temperature has been calculated using the diffusion Monte Carlo method. By means of a combination of the fixed-node and released-node techniques, it is shown that backflow correlations provide a very accurate equation of state. The results prove unambiguously the non-self-bound character of two-dimensional 3He due to its Fermi statistics. We present solid evidence that the gas phase, predicted for the two-dimensional system, can be extrapolated to the case of 3He adsorbed on a strong substrate such as graphite.

Progress in monte carlo calculations of fermi systems: normal liquid 3He

The application of the diffusion Monte Carlo method to a strongly interacting Fermi system as normal liquid 3He is explored. We show that the fixed-node method together with the released-node technique and a systematic method to analytically improve the nodal surface constitute an efficient strategy to improve the calculation up to a desired accuracy. This methodology shows unambiguously that backflow correlations are enough to generate an equation of state of liquid 3He in excellent agreement with experimental data from equilibrium up to freezing.

Zero-temperature equation of state of quasi-one-dimensional H2

We have studied molecular hydrogen in a pure 1D geometry and inside a narrow carbon nanotube by means of the diffusion Monte Carlo method. The one dimensionality of H2 in the nanotube is well maintained in a large density range, this system being closer to an ideal 1D fluid than liquid 4He in the same setup. H2 shares with 4He the existence of a stable liquid phase and a quasicontinuous liquid-solid transition at very high linear densities.