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Register a new userMicroscopic studies of solid 4He with Path Integral Projector Monte Carlo
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Added by
Davide Emilio Galli
Publication date
2007
fields
Physics
and research's language is
English
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We have investigated the ground state properties of solid $^4$He with the Shadow Path Integral Ground State method. This exact T=0 K projector method allows to describes quantum solids without introducing any a priori equilibrium position. We have found that the efficiency in computing off-diagonal properties in the solid phase sensibly improves when the direct sampling of permutations, in principle not required, is introduced. We have computed the exact one-body density matrix (obdm) in large commensurate 4He crystal finding a decreasing condensate fraction with increasing imaginary time of projection, making our result not conclusive on the presence of Bose-Einstein condensation in bulk solid 4He. We can only give an upper bound of 2.5 times 10^-8 on the condensate fraction. We have exploited the SPIGS method to study also 4He crystal containing grain boundaries by computing the related surface energy and the obdm along these defects. We have found that also highly symmetrical grain boundaries have a finite condensate fraction. We have also derived a route for the estimation of the true equilibrium concentration of vacancies x_v in bulk T=0 K solid 4He, which is shown to be finite, x_v=0.0014(1) at the melting density, when computed with the variational shadow wave function technique.
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High order actions proposed by Chin have been used for the first time in path integral Monte Carlo simulations. Contrarily to the Takahashi-Imada action, which is accurate to fourth order only for the trace, the Chin action is fully fourth order, with the additional advantage that the leading fourth and sixth 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 ten. 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.
We study the elasticity of perfect 4He at zero-temperature using the diffusion Monte Carlo method and a realistic semi-empirical pairwise potential to describe the He-He interactions. Specifically, we calculate the value of the elastic constants of hcp helium C_{ij} as a function of pressure up to 110 bar. It is found that the pressure dependence of all five non-zero C_{ij} is linear and we provide accurate parametrization of each of them. Our elastic constants results are compared to previous variational calculations and low-temperature measurements and in general notably good agreement is found among them. Furthermore, we report T = 0 results for the Gruneisen parameters, sound velocities and Debye temperature of hcp 4He. This work represents the first of a series of computational studies aimed at thoroughly characterizing the response of solid helium to external stress-strain.
Fractional derivatives are nonlocal differential operators of real order that often appear in models of anomalous diffusion and a variety of nonlocal phenomena. Recently, a version of the Schrodinger Equation containing a fractional Laplacian has been proposed. In this work, we develop a Fractional Path Integral Monte Carlo algorithm that can be used to study the finite temperature behavior of the time-independent Fractional Schrodinger Equation for a variety of potentials. In so doing, we derive an analytic form for the finite temperature fractional free particle density matrix and demonstrate how it can be sampled to acquire new sets of particle positions. We employ this algorithm to simulate both the free particle and $^{4}$He (Aziz) Hamiltonians. We find that the fractional Laplacian strongly encourages particle delocalization, even in the presence of interactions, suggesting that fractional Hamiltonians may manifest atypical forms of condensation. Our work opens the door to studying fractional Hamiltonians with arbitrarily complex potentials that escape analytical solutions.
The changes that vacancies produce in the properties of hcp solid 4He are studied by means of quantum Monte Carlo methods. Our results show that the introduction of vacancies produces significant changes in the behavior of solid 4He, even when the vacancy concentration is very small. We show that there is an onset temperature where the properties of incommensurate 4He change significantly. Below this temperature, we observe the emergence of off-diagonal long range order and a complete spatial delocalization of the vacancies. This temperature is quite close to the temperature where non-classical rotational inertia has been experimentally observed. Finally, we report results on the influence of vacancies in the elastic properties of hcp 4He at zero temperature.
Quantum Monte Carlo belongs to the most accurate simulation techniques for quantum many-particle systems. However, for fermions, these simulations are hampered by the sign problem that prohibits simulations in the regime of strong degeneracy. The situation changed with the development of configuration path integral Monte Carlo (CPIMC) by Schoof textit{et al.} [T. Schoof textit{et al.}, Contrib. Plasma Phys. textbf{51}, 687 (2011)] that allowed for the first textit{ab initio} simulations for dense quantum plasmas. CPIMC also has a sign problem that occurs when the density is lowered, i.e. in a parameter range that is complementary to traditional QMC formulated in coordinate space. Thus, CPIMC simulations for the warm dense electron gas are limited to small values of the Brueckner parameter -- the ratio of the interparticle distance to the Bohr radius -- $r_s=bar{r}/a_B lesssim 1$. In order to reach the regime of stronger coupling (lower density) with CPIMC, here we investigate additional restrictions on the Monte Carlo procedure. In particular, we introduce two differe
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