Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals

Drummond, Neil; Radnai, Z.; Trail, J. R.; Towler, M. D.; Needs, R. J.

doi:10.1103/physrevb.69.085116

Cited by 99 publications

(111 citation statements)

References 27 publications

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“…When V C further increases, these bisolitons form a Wigner "liquid" (Fig.10a) (with a short-range order of individual solitons -contrarily to a Wigner crystal with a long-range order). It is known that the groundstate distribution of charges must form a triangular lattice in 2D [45] and a body-centered cubic lattice in 3D [46]. However, for systems with finite discretization, the commensurateness effects become very important: even small incommensurateness destroys the long-range order, while the short-range order persists 47 .…”

Section: Strong Coulomb Interactionmentioning

confidence: 99%

Phase transitions in ensembles of solitons induced by an optical pumping or a strong electric field

Karpov

2016

Phys. Rev. B

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The latest trend in studies of modern electronically and/or optically active materials is to provoke phase transformations induced by high electric fields or by short (femtosecond) powerful optical pulses. The systems of choice are cooperative electronic states whose broken symmetries give rise to topological defects. For typical quasi-one-dimensional architectures, those are the microscopic solitons taking from electrons the major roles as carriers of charge or spin. Because of the longrange ordering, the solitons experience unusual super-long-range forces leading to a sequence of phase transitions in their ensembles: the higher-temperature transition of the confinement and the lower one of aggregation into macroscopic walls. Here we present results of an extensive numerical modeling for ensembles of both neutral and charged solitons in both two-and three-dimensional systems. We suggest a specific Monte Carlo algorithm preserving the number of solitons, which substantially facilitates the calculations, allows to extend them to the three-dimensional case and to include the important long-range Coulomb interactions. The results confirm the first confinement transition, except for a very strong Coulomb repulsion, and demonstrate a pattern formation at the second transition of aggregation.

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Section: Strong Coulomb Interactionmentioning

confidence: 99%

Phase transitions in ensembles of solitons induced by an optical pumping or a strong electric field

Karpov

2016

Phys. Rev. B

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“…Subsequently, it was employed to study solid hydrogen (Ceperley and Alder, 1987) and other crystals containing heavier atoms (Fahy et al, 1988(Fahy et al, , 1990Li et al, 1991). Wigner crystals in two and three dimensions have been also investigated thoroughly with eQMC methods (Tanatar and Ceperley, 1989;Drummond et al, 2004;Drummond and Needs, 2009). Important FN-DMC developments include the introduction of variance minimization techniques to optimize wave functions (Umrigar et al, 1988) and the use of nonlocal pseudopotentials (Hammond et al, 1987;Hurley and Christiansen, 1987;Fahy et al, 1988;Mitas et al, 1991;Trail and Needs, 2013;Lloyd-Williams, Needs, and Conduit, 2015;Trail and Needs, 2015).…”

Section: Electronic Quantum Monte Carlomentioning

confidence: 99%

“…Examples of quantum solids include, Wigner crystals (Wigner, 1934;Ceperley and Alder, 1980;Drummond et al, 2004;Militzer and Graham, 2006;Drummond and Needs, 2009), vortex lattices (Safar et al, 1992;Cooper, Wilkin, and Gunn, 2001;Abo-Shaeer et al, 2001), dipole systems (Astrakharchik et al, 2007;Matveeva and Giorgini, 2012;Boninsegni, 2013a;Moroni and Boninsegni, 2014), rare-gases, molecular solids, light metals, and many other similar systems (see the next paragraphs). For the sake of focus, however, in this review we will concentrate on quantum crystals formed by atoms and small molecules.…”

Section: Introduction a Quantum Crystals: Definition And Interestsmentioning

confidence: 99%

Simulation and understanding of atomic and molecular quantum crystals

2017

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Quantum crystals abound in the whole range of solid-state species. Below a certain threshold temperature the physical behavior of rare gases ( 4 He and Ne), molecular solids (H 2 and CH 4 ), and some ionic (LiH), covalent (graphite), and metallic (Li) crystals can be only explained in terms of quantum nuclear effects (QNE). A detailed comprehension of the nature of quantum solids is critical for achieving progress in a number of fundamental and applied scientific fields like, for instance, planetary sciences, hydrogen storage, nuclear energy, quantum computing, and nanoelectronics. This review describes the current physical understanding of quantum crystals formed by atoms and small molecules, as well as the wide palette of simulation techniques that are used to investigate them. Relevant aspects in these materials such as phase transformations, structural properties, elasticity, crystalline defects and the effects of reduced dimensionality, are discussed thoroughly. An introduction to quantum Monte Carlo techniques, which in the present context are the simulation methods of choice, and other quantum simulation approaches (e. g., path-integral molecular dynamics and quantum thermal baths) is provided. The overarching objective of this article is twofold. First, to clarify in which crystals and physical situations the disregard of QNE may incur in important bias and erroneous interpretations. And second, to promote the study and appreciation of QNE, a topic that traditionally has been treated in the context of condensed matter physics, within the broad and interdisciplinary areas of materials science.

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“…The physics at intermediate r s continues to offer puzzles, both from theory and experiments. There has been numerical evidence in bulk two 3,4,5 and three 6,7 dimensional (2D and 3D) systems that a single transition takes place at r c,2D s ≈ 30-35 and r c,3D s ∼ 100. However, recent work in 2D has predicted more complex phases and associated transitions or crossovers around these critical values.…”

Section: Introductionmentioning

confidence: 99%

Incipient Wigner localization in circular quantum dots

et al. 2007

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We study the development of electron-electron correlations in circular quantum dots as the density is decreased. We consider a wide range of both electron number, N ≤ 20, and electron gas parameter, rs < ∼ 18, using the diffusion quantum Monte Carlo technique. Features associated with correlation appear to develop very differently in quantum dots than in bulk. The main reason is that translational symmetry is necessarily broken in a dot, leading to density modulation and inhomogeneity. Electron-electron interactions act to enhance this modulation ultimately leading to localization. This process appears to be completely smooth and occurs over a wide range of density. Thus there is a broad regime of "incipient" Wigner crystallization in these quantum dots. Our specific conclusions are: (i) The density develops sharp rings while the pair density shows both radial and angular inhomogeneity. (ii) The spin of the ground state is consistent with Hund's (first) rule throughout our entire range of rs for all 4 ≤ N ≤ 20. (iii) The addition energy curve first becomes smoother as interactions strengthen -the mesoscopic fluctuations are damped by correlation -and then starts to show features characteristic of the classical addition energy. (iv) Localization effects are stronger for a smaller number of electrons. (v) Finally, the gap to certain spin excitations becomes small at the strong interaction (large rs) side of our regime.

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Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals

Cited by 99 publications

References 27 publications

Phase transitions in ensembles of solitons induced by an optical pumping or a strong electric field

Phase transitions in ensembles of solitons induced by an optical pumping or a strong electric field

Simulation and understanding of atomic and molecular quantum crystals

Incipient Wigner localization in circular quantum dots

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