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Register a new userHigh order Chin actions in path integral Monte Carlo
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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.
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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.
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.
The feasibility of path integral Monte Carlo ground state calculations with very few beads using a high-order short-time Greens 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.
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
The local order around alkali (Li$^+$ and Na$^+$) and alkaline-eath (Be$^+$, Mg$^+$ and Ca$^+$) ions in $^4$He clusters has been studied using ground-state path integral Monte Carlo calculations. We apply a criterion based on multipole dynamical correlations to discriminate between solid-like versus liquid-like behavior of the $^4$He shells coating the ions. As it was earlier suggested by experimental measurements in bulk $^4$He, our findings indicate that Be$^+$ produces a solid-like (snowball) structure, similarly to alkali ions and in contrast to the more liquid-like $^4$He structure embedding heavier alkaline-earth ions.
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