Tobias Dornheim

Permutation blocking path integral Monte Carlo: a highly efficient approach to the simulation of strongly degenerate non-ideal fermions

Correlated fermions are of high interest in condensed matter (Fermi liquids, Wigner molecules), cold atomic gases and dense plasmas. Here we propose a novel approach to path integral Monte Carlo (PIMC) simulations of strongly degenerate non-ideal fermions at finite temperature by combining a fourth-order factorization of the density matrix with antisymmetric propagators, i.e., determinants, between all imaginary time slices. To efficiently run through the modified configuration space, we introduce a modification of the widely used continuous space worm algorithm, which allows for an efficient sampling at arbitrary system parameters. We demonstrate how the application of determinants achieves an effective blocking of permutations with opposite signs, leading to a significant relieve of the fermion sign problem. To benchmark the capability of our method regarding the simulation of degenerate fermions, we consider multiple electrons in a quantum dot and compare our results with other ab initio techniques, where they are available. The present permutation blocking path integral Monte Carlo approach allows us to obtain accurate results even for

Permutation blocking path integral Monte Carlo approach to the uniform electron gas at finite temperature

N=20

Ab initioquantum Monte Carlo simulations of the uniform electron gas without fixed nodes

electrons at low temperature and arbitrary coupling, where no other ab initio results have been reported, so far.

Ab initio quantum Monte Carlo simulations of the uniform electron gas without fixed nodes: The unpolarized case

The uniform electron gas (UEG) at finite temperature is of high current interest due to its key relevance for many applications including dense plasmas and laser excited solids. In particular, density functional theory heavily relies on accurate thermodynamic data for the UEG. Until recently, the only existing first-principle results had been obtained for N = 33 electrons with restricted path integral Monte Carlo (RPIMC), for low to moderate density, rs=r¯/aB≳1. These data have been complemented by configuration path integral Monte Carlo (CPIMC) simulations for rs ≤ 1 that substantially deviate from RPIMC towards smaller rs and low temperature. In this work, we present results from an independent third method-the recently developed permutation blocking path integral Monte Carlo (PB-PIMC) approach [T. Dornheim et al., New J. Phys. 17, 073017 (2015)] which we extend to the UEG. Interestingly, PB-PIMC allows us to perform simulations over the entire density range down to half the Fermi temperature (θ = kBT/EF = 0.5) and, therefore, to compare our results to both aforementioned methods. While we find excellent agreement with CPIMC, where results are available, we observe deviations from RPIMC that are beyond the statistical errors and increase with density.

Free energy of the uniform electron gas: Testing analytical models against first-principles results†

The uniform electron gas (UEG) at finite temperature is of key relevance for many applications in the warm dense matter regime, e.g. dense plasmas and laser excited solids. Also, the quality of density functional theory calculations crucially relies on the availability of accurate data for the exchange-correlation energy. Recently, new benchmark results for the N = 33 spin-polarized electrons at high density, r_s = r/a_B <= 4 and low temperature, have been obtained with the configuration path integral Monte Carlo (CPIMC) method [T. Schoof et al., Phys. Rev. Lett. 115, 130402 (2015)]. To achieve these results, the original CPIMC algorithm [T. Schoof et al., Contrib. Plasma Phys. 51, 687 (2011)] had to be further optimized to cope with the fermion sign problem (FSP). It is the purpose of this paper to give detailed information on the manifestation of the FSP in CPIMC simulations of the UEG and to demonstrate how it can be turned into a controllable convergence problem. In addition, we present new thermodynamic results for higher temperatures. Finally, to overcome the limitations of CPIMC towards strong coupling, we invoke an independent method|the recently developed permutation blocking path integral Monte Carlo approach [T. Dornheim et al., accepted for publication in J. Chem Phys., arXiv:1508.03221]. The combination of both approaches is able to yield ab initio data for the UEG over the entire density range, above a temperature of about one half of the Fermi temperature. Comparison with restricted path integral Monte Carlo data [E. W. Brown et al., Phys. Rev. Lett. 110, 146405 (2013)] allows us to quantify the systematic error arising from the free particle nodes.

Superfluidity of strongly correlated bosons in two- and three-dimensional traps

In a recent publication [S. Groth et al., Phys. Rev. B 93, 085102 (2016)], we have shown that the combination of two complementary quantum Monte Carlo approaches, namely configuration path integral Monte Carlo [T. Schoof et al., Phys. Rev. Lett. 115, 130402 (2015)] and permutation blocking path integral Monte Carlo [T. Dornheim et al., New J. Phys. 17, 073017 (2015)], allows for the accurate computation of thermodynamic properties of the spin-polarized uniform electron gas over a wide range of temperatures and densities without the fixed-node approximation. In the present work, we extend this concept to the unpolarized case, which requires nontrivial enhancements that we describe in detail. We compare our simulation results with recent restricted path integral Monte Carlo data [E. W. Brown et al., Phys. Rev. Lett. 110, 146405 (2013)] for different energy contributions and pair distribution functions and find, for the exchange correlation energy, overall better agreement than for the spin-polarized case, while the separate kinetic and potential contributions substantially deviate.

Ab initio quantum Monte Carlo simulation of the warm dense electron gas

The uniform electron gas is a key model system in the description of matter, including dense plasmas and solid-state systems. However, the simultaneous occurrence of quantum, correlation, and thermal effects makes the theoretical description challenging. For these reasons, over the last half century, many analytical approaches have been developed, the accuracy of which has remained unclear. We have recently obtained the first ab initio data for the exchange correlation free energy of the uniform electron gas, which now provides the opportunity to assess the quality of the mentioned approaches and parameterizations. Particular emphasis is placed on the warm, dense matter regime, where we find significant discrepancies between the different approaches.

Configuration path integral Monte Carlo approach to the static density response of the warm dense electron gas

We analyze the superfluid phase transition of harmonically confined bosons with long-range interaction in both two and three dimensions in a broad parameter range from weak to strong coupling. We observe that the onset of superfluidity occurs in

Permutation-blocking path-integral Monte Carlo approach to the static density response of the warm dense electron gas

3D

Ab initio results for the static structure factor of the warm dense electron gas

at significantly lower temperatures compared to