Periodic ground states in the neutral Falicov-Kimball model in two dimensions

Karl Haller; Tom Kennedy

doi:10.1023/A:1026504524149

Periodic ground states in the neutral Falicov-Kimball model in two dimensions

Karl Haller, Tom Kennedy

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24 Scopus citations

Abstract

We consider the Falicov Kimball model in two dimensions in the neutral case, i.e., the number of mobile electrons is equal to the number of ions. For rational densities between 1/3 and 2/5 we prove that the ground state is periodic if the strength of the attraction between the ions and electrons is large enough. The periodic ground state is given by taking the one dimensional periodic ground state found by Lemberger and then extending it into two dimensions in such a way that the configuration is constant along lines at a 45 degree angle to the lattice directions.

Original language	English (US)
Pages (from-to)	15-34
Number of pages	20
Journal	Journal of Statistical Physics
Volume	102
Issue number	1-2
DOIs	https://doi.org/10.1023/A:1026504524149
State	Published - Jan 2001

Keywords

Falicov-Kimball model
Ground state
Periodic

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1023/A:1026504524149

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title = "Periodic ground states in the neutral Falicov-Kimball model in two dimensions",

abstract = "We consider the Falicov Kimball model in two dimensions in the neutral case, i.e., the number of mobile electrons is equal to the number of ions. For rational densities between 1/3 and 2/5 we prove that the ground state is periodic if the strength of the attraction between the ions and electrons is large enough. The periodic ground state is given by taking the one dimensional periodic ground state found by Lemberger and then extending it into two dimensions in such a way that the configuration is constant along lines at a 45 degree angle to the lattice directions.",

keywords = "Falicov-Kimball model, Ground state, Periodic",

author = "Karl Haller and Tom Kennedy",

note = "Funding Information: This work was supported by NSF Grant DMS-9623509. It was part of Karl Haller{\textquoteright}s Ph.D. dissertation.(6) We would like to thank the referee for several useful comments.",

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T1 - Periodic ground states in the neutral Falicov-Kimball model in two dimensions

AU - Haller, Karl

AU - Kennedy, Tom

N1 - Funding Information: This work was supported by NSF Grant DMS-9623509. It was part of Karl Haller’s Ph.D. dissertation.(6) We would like to thank the referee for several useful comments.

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Y1 - 2001/1

N2 - We consider the Falicov Kimball model in two dimensions in the neutral case, i.e., the number of mobile electrons is equal to the number of ions. For rational densities between 1/3 and 2/5 we prove that the ground state is periodic if the strength of the attraction between the ions and electrons is large enough. The periodic ground state is given by taking the one dimensional periodic ground state found by Lemberger and then extending it into two dimensions in such a way that the configuration is constant along lines at a 45 degree angle to the lattice directions.

AB - We consider the Falicov Kimball model in two dimensions in the neutral case, i.e., the number of mobile electrons is equal to the number of ions. For rational densities between 1/3 and 2/5 we prove that the ground state is periodic if the strength of the attraction between the ions and electrons is large enough. The periodic ground state is given by taking the one dimensional periodic ground state found by Lemberger and then extending it into two dimensions in such a way that the configuration is constant along lines at a 45 degree angle to the lattice directions.

KW - Falicov-Kimball model

KW - Ground state

KW - Periodic

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JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 1-2

ER -

Periodic ground states in the neutral Falicov-Kimball model in two dimensions

Abstract

Keywords

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