Variational quantum Monte Carlo study of twodimensional Wigner crystals: Exchange, correlation, and magneticfield effects
Abstract
The twodimensional Wigner crystals are studied with the variational quantum Monte Carlo method. The close relationship between the groundstate wave function and the collective excitations in the system is illustrated, and used to guide the construction of the groundstate wave function of the strongly correlated solid. Exchange, correlation, and magneticfield effects all give rise to distinct physical phenomena. In the absence of any external magnetic field, interesting spin orderings are observed in the ground state of the electron crystal in various twodimensional lattices. In particular, twodimensional bipartite lattices are shown not to lead necessarily to an antiferromagnetic ground state. In the quantum Hall effect regime, a strong magnetic field introduces energy and length scales. The magnetic field quenches the kinetic energy and poses constraints on how the electrons may correlate with each other. Care is taken to ensure the appropriate translational properties of the wave function when the system is in a uniform magnetic field. We have examined the exchange, intraLandaulevel correlation as well as Landaulevelmixing effects with various variational wave functions. We also determine their dependences on the experimental parameters such as the carrier effective mass at a modulationdoped semiconductor heterojunction. Our results, when combined with some recent calculationsmore »
 Authors:

 Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08855 (United States)
 Department of Physics, University of California, Berkeley, California 94720 (United States)
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Laboratory
 OSTI Identifier:
 122268
 DOE Contract Number:
 AC0376SF00098
 Resource Type:
 Journal Article
 Journal Name:
 Physical Review, B: Condensed Matter
 Additional Journal Information:
 Journal Volume: 52; Journal Issue: 8; Other Information: PBD: 15 Aug 1995
 Country of Publication:
 United States
 Language:
 English
 Subject:
 66 PHYSICS; CRYSTAL MODELS; GROUND STATES; COLLECTIVE EXCITATIONS; CORRELATEDPARTICLE MODELS; MONTE CARLO METHOD; TWODIMENSIONAL CALCULATIONS; TRANSPORT THEORY; WIGNER THEORY; QUANTIZATION; MAGNETORESISTANCE; LANDAU FLUCTUATIONS; EXCHANGE INTERACTIONS
Citation Formats
Zhu, X, Department of Physics, University of California, Berkeley, California 94720, Materials Science DIvision, Lawrence Livermore Laboratory, Berkeley, California 94720, Louie, S G, and Materials Science Division, Lawrence Livermore Laboratory, Berkeley, California 94720. Variational quantum Monte Carlo study of twodimensional Wigner crystals: Exchange, correlation, and magneticfield effects. United States: N. p., 1995.
Web. doi:10.1103/PhysRevB.52.5863.
Zhu, X, Department of Physics, University of California, Berkeley, California 94720, Materials Science DIvision, Lawrence Livermore Laboratory, Berkeley, California 94720, Louie, S G, & Materials Science Division, Lawrence Livermore Laboratory, Berkeley, California 94720. Variational quantum Monte Carlo study of twodimensional Wigner crystals: Exchange, correlation, and magneticfield effects. United States. doi:10.1103/PhysRevB.52.5863.
Zhu, X, Department of Physics, University of California, Berkeley, California 94720, Materials Science DIvision, Lawrence Livermore Laboratory, Berkeley, California 94720, Louie, S G, and Materials Science Division, Lawrence Livermore Laboratory, Berkeley, California 94720. Tue .
"Variational quantum Monte Carlo study of twodimensional Wigner crystals: Exchange, correlation, and magneticfield effects". United States. doi:10.1103/PhysRevB.52.5863.
@article{osti_122268,
title = {Variational quantum Monte Carlo study of twodimensional Wigner crystals: Exchange, correlation, and magneticfield effects},
author = {Zhu, X and Department of Physics, University of California, Berkeley, California 94720 and Materials Science DIvision, Lawrence Livermore Laboratory, Berkeley, California 94720 and Louie, S G and Materials Science Division, Lawrence Livermore Laboratory, Berkeley, California 94720},
abstractNote = {The twodimensional Wigner crystals are studied with the variational quantum Monte Carlo method. The close relationship between the groundstate wave function and the collective excitations in the system is illustrated, and used to guide the construction of the groundstate wave function of the strongly correlated solid. Exchange, correlation, and magneticfield effects all give rise to distinct physical phenomena. In the absence of any external magnetic field, interesting spin orderings are observed in the ground state of the electron crystal in various twodimensional lattices. In particular, twodimensional bipartite lattices are shown not to lead necessarily to an antiferromagnetic ground state. In the quantum Hall effect regime, a strong magnetic field introduces energy and length scales. The magnetic field quenches the kinetic energy and poses constraints on how the electrons may correlate with each other. Care is taken to ensure the appropriate translational properties of the wave function when the system is in a uniform magnetic field. We have examined the exchange, intraLandaulevel correlation as well as Landaulevelmixing effects with various variational wave functions. We also determine their dependences on the experimental parameters such as the carrier effective mass at a modulationdoped semiconductor heterojunction. Our results, when combined with some recent calculations for the energy of the fractional quantum Hall liquid including Landaulevelmixing, show quantitatively that in going from {ital n} doping to {ital p} doping in GaAs/Al{sub {ital x}}Ga{sub 1{minus}{ital x}}As heterojunction systems, the crossover filling factor from the fractional quantum Hall liquid to the Wigner crystal changes from filling factor {nu}{similar_to}1/5 to {nu}{similar_to}1/3.},
doi = {10.1103/PhysRevB.52.5863},
journal = {Physical Review, B: Condensed Matter},
number = 8,
volume = 52,
place = {United States},
year = {1995},
month = {8}
}