Three-Body Interactions in Liquid and Solid Helium

Murphy, R. D.; Barker, John A.

doi:10.1103/physreva.3.1037

Cited by 46 publications

(17 citation statements)

References 14 publications

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“…The physical properties which we calculate are the ground state energy, defined by the lowest E satisfying HOo = E~o (1) and related to the binding energy e by e = -E/N (2) for an N-particle system, and the liquid structure function (at T = 0) S(k) = N-l<~,olPkP_kl~,o>/<0olOo> (3) which is measured (T # 0) by x-ray 4'5 and neutron scattering. 6…”

Section: Introductionmentioning

confidence: 99%

Test of interparticle potentials for liquid 4He

Whitney

Pinski

Campbell³

1981

J Low Temp Phys

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Euler-Lagrange calculations of the ground state properties of liquid 4He at several densities and for six different two-body potentials are compared to one another and to experiment. The trial ground state wave functions used are the Jastrow function and the triplet Feenberg function. Four recent potentials produce very good agreement with recent neutron and X-ray liquid structure function measurements. The experimental energy per particle lies about 0.3 K below two of the theoretical curves and 0.3 K above a third, all obtained using the triplet Feenberg function, though no fundamental three-body potentials are included.

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Section: Introductionmentioning

confidence: 99%

Test of interparticle potentials for liquid 4He

Whitney

Pinski

Campbell³

1981

J Low Temp Phys

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“…. (1) where V (r) describes the two-particle interaction depending only on the separation between the particles. The second term W (r i , r j , r k ) is the three-body interaction, which depends on the distance and orientation of three particles, and vanishes if one particle is far apart from the other two.…”

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confidence: 99%

Three-body interactions with cold polar molecules

Büchler¹,

Micheli²,

Zoller³

2007

Nature Phys

280

319

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We show that polar molecules driven by microwave fields give naturally rise to strong three-body interactions, while the two-particle interaction can be independently controlled and even switched off. The derivation of these effective interaction potentials is based on a microscopic understanding of the underlying molecular physics, and follows from a well controlled and systematic expansion into many-body interaction terms. For molecules trapped in an optical lattice, we show that these interaction potentials give rise to Hubbard models with strong nearest-neighbor two-body and three-body interaction. As an illustration, we study the one-dimensional Bose-Hubbard model with dominant three-body interaction and derive its phase diagram.Fundamental interactions between particles, such as the Coulomb law, involves pairs of particles, and our understanding of the plethora of phenomena in condensed matter physics rests on models involving effective twobody interactions. On the other hand, exotic quantum phases, such as topological phases or spin liquids, are often identified as ground states of Hamiltonians with three or more body terms. While the study of these phases and properties of their excitations is presently one of the most exciting developments in theoretical condensed matter physics, it is difficult to identify real physical systems exhibiting such properties -a noticeable exception being the Fractional Quantum Hall effect. Here we show that polar molecules in optical lattices driven by microwave fields give naturally rise to Hubbard models with strong nearest-neighbor three-body interactions, while the twobody terms can be tuned (even switched off) with external fields.The many-body Hamiltonians underlying condensed matter physics are derived within an effective low energy theory, obtained by integrating out the high energy excitations. In general, this gives rise to interaction termswhere V (r) describes the two-particle interaction depending only on the separation between the particles. The second term W (r i , r j , r k ) is the three-body interaction, which depends on the distance and orientation of three particles, and vanishes if one particle is far apart from the other two. The ellipsis denotes possible higher many-body term terms. While for Helium atoms in the context of superfluidity the two-particle interaction dominates and determines the ground state properties with the three-body interactions providing small corrections, 1 model Hamiltonians with strong three-body interactions have attracted a lot of interest in the search for microscopic Hamiltonians exhibiting exotic ground state properties. Well known examples are the fractional quantum Hall states described by the Pfaffian wave functions which appear as ground states of a Hamiltonian with three-body interaction. 2,3,4 These topological phases admit anyonic excitations with non-abelian braiding statistic. Of special interest are also spin systems and bosonic Hamiltonians with complex many-body interactions, such as ring exchange model, whic...

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“…No tail corrections were performed for the high-order interactions. This is justified because these corrections represent less than 10% of the high-order interaction energy, 25 and their inclusion would hardly modify our conclusions about the two-body potentials we are employing in our calculations. The solid phase was studied by imposing a fcc structure in the system.…”

Section: Simulationsmentioning

confidence: 96%

Ab initiotwo-body potentials and the properties of condensed phases of helium atoms

Ujevic

Vitiello

2005

Phys. Rev. B

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A careful comparison of some properties of systems of helium atoms in the liquid and solid phases is performed for several ab initio two-body potentials from the literature. Additional contributions from a threebody potential are considered as well. The multiweight diffusion Monte Carlo method is employed to quantitatively compute the small changes in the properties of the system as the different potentials are considered.

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Three-Body Interactions in Liquid and Solid Helium

Cited by 46 publications

References 14 publications

Test of interparticle potentials for liquid 4He

Test of interparticle potentials for liquid 4He

Three-body interactions with cold polar molecules

Ab initiotwo-body potentials and the properties of condensed phases of helium atoms

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