Path Integral Monte Carlo Simulation of Charged Particles in Traps

Filinov, A.; Böning, Jens; Bönitz, M.

doi:10.1007/978-3-540-74686-7_13

Cited by 4 publications

(6 citation statements)

References 41 publications

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“…To take advantage of the main benefits from the usual continuous space WA, we will temporarily construct artificial trajectories and sample new beads according to standard PIMC techniques, e.g. [43]. The initial situation for our considerations is illustrated in the left panel of figure 4, where a pre-existing trajectory (pink curve) with four missing beads in the middle is shown in the τ-x-plane.…”

Section: Sampling Schemementioning

confidence: 99%

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

et al. 2015

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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 PIMC approach allows us to obtain accurate results even for N = 20 electrons at low temperature and arbitrary coupling, where no other ab initio results have been reported, so far.

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Section: Sampling Schemementioning

confidence: 99%

“…(i) Deform: this update is similar to standard PIMC techniques, e.g. [43], and deforms a randomly constructed artificial trajectory.…”

Section: Appendix Monte Carlo Updatesmentioning

confidence: 99%

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

et al. 2015

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“…To simulate the system using the standard path integral Monte Carlo method, e.g. [3,4], we exploit a group property of the density matrix…”

Section: Standard Pimcmentioning

confidence: 99%

“…However, even simple models used to describe interacting quantum systems in the regime where strong Coulomb correlations and quantum exchange effects are present are computationally very demanding. Therefore, trapped few-particle systems such as electrons in quantum dots [2] ("artificial atoms") serve as a suitable laboratory for the investigation of fundamental many-body interaction phenomena without requiring undesirable (uncontrollable) simplifications of the fundamental physics.Path integral Monte Carlo (PIMC) is a finite temperature simulation technique for an ab-initio description of correlated quantum systems with arbitrarily strong Coulomb and quantum exchange (spin) effects [3,4]. Furthermore, it provides a high flexibility with respect to trap geometry or the inclusion of defects et cetera, and quasi exact simulations with up to N ∼ 10 4 bosons and boltzmannons are feasible [5,6].…”

mentioning

confidence: 99%

“…Path integral Monte Carlo (PIMC) is a finite temperature simulation technique for an ab-initio description of correlated quantum systems with arbitrarily strong Coulomb and quantum exchange (spin) effects [3,4]. Furthermore, it provides a high flexibility with respect to trap geometry or the inclusion of defects et cetera, and quasi exact simulations with up to N ∼ 10 4 bosons and boltzmannons are feasible [5,6].…”

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confidence: 99%

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Analyzing Quantum Correlations Made Simple

Dornheim

Thomsen

Ludwig

et al. 2016

Contrib. Plasma Phys.

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The understanding of correlations in degenerate nonideal many-particle systems is complex and theoretically challenging. Using the recently proposed permutation blocking path integral Monte Carlo (PB-PIMC) scheme, which allows for an exact treatment of many-body correlations, we study the influence of quantum statistics in a confined few-particle Coulomb (quantum dot) system. As a versatile tool to gain insight into the internal structure of correlated many-body systems, the application of triple correlation functions is extended to quantum systems.Self-organized structure formation of interacting particles is one of the most fundamental processes in nature [1]. The basic theoretical understanding and analysis of this cooperative phenomena requires (i) sophisticated simulation techniques that allow us to solve the basic equations of many-particle physics on first principles, and (ii) advanced tools for the analysis of the details of collective behaviour in these interacting systems such as structure formation, spatial correlations and melting (phase) transitions. However, even simple models used to describe interacting quantum systems in the regime where strong Coulomb correlations and quantum exchange effects are present are computationally very demanding. Therefore, trapped few-particle systems such as electrons in quantum dots [2] ("artificial atoms") serve as a suitable laboratory for the investigation of fundamental many-body interaction phenomena without requiring undesirable (uncontrollable) simplifications of the fundamental physics.Path integral Monte Carlo (PIMC) is a finite temperature simulation technique for an ab-initio description of correlated quantum systems with arbitrarily strong Coulomb and quantum exchange (spin) effects [3,4]. Furthermore, it provides a high flexibility with respect to trap geometry or the inclusion of defects et cetera, and quasi exact simulations with up to N ∼ 10 4 bosons and boltzmannons are feasible [5, 6]. However, a rigorous and exact treatment of fermionic quantum exchange with standard PIMC is strongly limited by the fermion sign problem [7,8]. For that reason, the permutation blocking path integral Monte Carlo (PB-PIMC) scheme [9,10] has been recently introduced which allows us to significantly reduce this issue and to extend the range of application of the PIMC method towards stronger degeneracy, i.e., lower temperature and higher densities. Therefore, we are able to obtain approximation-free data for Bose, Boltzmann and Fermi statistics on the footing of first principle quantum Monte Carlo simulations.Apart from an accurate computation, a central aspect of this contribution concerns the analysis of quantum correlations. To this end, we will extend the application of the recently derived triple-correlation functions [11][12][13] in order to resolve the influence of different quantum statistics on spatial correlations in degenerate 2D Coulomb (quantum dot) systems. While the (radial) pair distribution function-as a widely used tool for the structural analysis-is we...

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