Exchange frequencies in the 2d Wigner crystal

B. Bernu; P. Gianinetti; Ladir Cândido; D. M. Ceperley

doi:10.1142/S0217979203020089

Exchange frequencies in the 2d Wigner crystal

B. Bernu, P. Gianinetti, Ladir Cândido, D. M. Ceperley

Research output: Contribution to journal › Article › peer-review

Abstract

Path Integral Monte Carlo is used to calculate exchange frequencies as electrons undergo ring exchanges in a "clean" 2d Wigner crystal as a function of density. Agreement with WKB calculations is found at very low density, but the results show an enhanced increase with density near melting. Remarkably, the exchange Hamiltonian closely resembles the measured exchanges in 2d ³He. Using the resulting multi-spin exchange model we find the spin Hamiltonian for r_s ≥ 175 ± 10 is a frustrated antiferromagnetic, with a spin liquid ground state. For lower density the ground state will be ferromagnetic. Some effects of a magnetic field are presented.

Original language	English (US)
Pages (from-to)	4965-4974
Number of pages	10
Journal	International Journal of Modern Physics B
Volume	17
Issue number	28 I
DOIs	https://doi.org/10.1142/S0217979203020089
State	Published - Nov 10 2003

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Condensed Matter Physics

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10.1142/S0217979203020089

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title = "Exchange frequencies in the 2d Wigner crystal",

abstract = "Path Integral Monte Carlo is used to calculate exchange frequencies as electrons undergo ring exchanges in a {"}clean{"} 2d Wigner crystal as a function of density. Agreement with WKB calculations is found at very low density, but the results show an enhanced increase with density near melting. Remarkably, the exchange Hamiltonian closely resembles the measured exchanges in 2d 3He. Using the resulting multi-spin exchange model we find the spin Hamiltonian for rs ≥ 175 ± 10 is a frustrated antiferromagnetic, with a spin liquid ground state. For lower density the ground state will be ferromagnetic. Some effects of a magnetic field are presented.",

author = "B. Bernu and P. Gianinetti and Ladir C{\^a}ndido and Ceperley, {D. M.}",

note = "Funding Information: This research was funded by NSF DMR 98-02373, the CNRS-University of Illinois exchange agreement, support by Funda¸c{\~a}o de Amparo {\`a} Pesquisa do Estado de S{\~a}o Paulo (FAPESP) and the Dept. of Physics at the University of Illinois. We used the computational facilities at the NCSA.",

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T1 - Exchange frequencies in the 2d Wigner crystal

AU - Bernu, B.

AU - Gianinetti, P.

AU - Cândido, Ladir

AU - Ceperley, D. M.

N1 - Funding Information: This research was funded by NSF DMR 98-02373, the CNRS-University of Illinois exchange agreement, support by Funda¸cão de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and the Dept. of Physics at the University of Illinois. We used the computational facilities at the NCSA.

PY - 2003/11/10

Y1 - 2003/11/10

N2 - Path Integral Monte Carlo is used to calculate exchange frequencies as electrons undergo ring exchanges in a "clean" 2d Wigner crystal as a function of density. Agreement with WKB calculations is found at very low density, but the results show an enhanced increase with density near melting. Remarkably, the exchange Hamiltonian closely resembles the measured exchanges in 2d 3He. Using the resulting multi-spin exchange model we find the spin Hamiltonian for rs ≥ 175 ± 10 is a frustrated antiferromagnetic, with a spin liquid ground state. For lower density the ground state will be ferromagnetic. Some effects of a magnetic field are presented.

AB - Path Integral Monte Carlo is used to calculate exchange frequencies as electrons undergo ring exchanges in a "clean" 2d Wigner crystal as a function of density. Agreement with WKB calculations is found at very low density, but the results show an enhanced increase with density near melting. Remarkably, the exchange Hamiltonian closely resembles the measured exchanges in 2d 3He. Using the resulting multi-spin exchange model we find the spin Hamiltonian for rs ≥ 175 ± 10 is a frustrated antiferromagnetic, with a spin liquid ground state. For lower density the ground state will be ferromagnetic. Some effects of a magnetic field are presented.

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Exchange frequencies in the 2d Wigner crystal

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