Real space quantum cluster formulation for the typical medium theory of anderson localization

Ka Ming Tam; Hanna Terletska; Tom Berlijn; Liviu Chioncel; Juana Moreno

doi:10.3390/cryst11111282

Real space quantum cluster formulation for the typical medium theory of anderson localization

Ka Ming Tam, Hanna Terletska, Tom Berlijn, Liviu Chioncel, Juana Moreno

Nanomaterials Theory Institute

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

1 Scopus citations

Abstract

We develop a real space cluster extension of the typical medium theory (cluster-TMT) to study Anderson localization. By construction, the cluster-TMT approach is formally equivalent to the real space cluster extension of the dynamical mean field theory. Applying the developed method to the 3D Anderson model with a box disorder distribution, we demonstrate that cluster-TMT successfully captures the localization phenomena in all disorder regimes. As a function of the cluster size, our method obtains the correct critical disorder strength for the Anderson localization in 3D, and systematically recovers the re-entrance behavior of the mobility edge. From a general perspective, our developed methodology offers the potential to study Anderson localization at surfaces within quantum embedding theory. This opens the door to studying the interplay between topology and Anderson localization from first principles.

Original language	English
Article number	1282
Journal	Crystals
Volume	11
Issue number	11
DOIs	https://doi.org/10.3390/cryst11111282
State	Published - Nov 2021

Funding

This manuscript is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0017861. This work used the high performance computational resources provided by the Louisiana Optical Network Initiative http://www.loni.org, accessed on 16 September 2021, and HPC@LSU computing. This work also used the Extreme Science and Engineering Discovery Environment (XSEDE) through allocation DMR130036. K.-M.T. is partially supported by NSF DMR-1728457 and NSF OAC-1931445. H.T. has been supported by NSF OAC-1931367 and NSF DMR-1944974 grants. L.C. acknowledges the financial support by the Deutsche Forschungsgemeinschaft through TRR80 (project F6) project No. 107745057. A portion of this research was conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility (TB). The manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan, accessed on 16 September 2021).The authors would like to thank V. Dobrosavljevic and S. Iskakov for useful comments and discussions. Funding: This manuscript is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0017861. This work used the high performance computational resources provided by the Louisiana Optical Network Initiative http://www.loni.org, accessed on 16 September 2021, and HPC@LSU computing. This work also used the Extreme Science and Engineering Discovery Environment (XSEDE) through allocation DMR130036. K.-M.T. is partially supported by NSF DMR-1728457 and NSF OAC-1931445. H.T. has been supported by NSF OAC-1931367 and NSF DMR-1944974 grants. L.C. acknowledges the financial support by the Deutsche Forschungsgemeinschaft through TRR80 (project F6) project No. 107745057. A portion of this research was conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility (TB). The manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan, accessed on 16 September 2021).

Funders	Funder number
DOE Public Access Plan
United States Government
National Science Foundation	OAC-1931367, OAC-1931445, DMR-1728457, DMR-1944974
U.S. Department of Energy
Office of Science	DE-AC05-00OR22725
Basic Energy Sciences	DMR130036, DE-SC0017861
Deutsche Forschungsgemeinschaft	107745057, TRR80

Keywords

Anderson localization
Cellular dynamical mean field theory
Cluster mean field theory
Coherent potential approximation
Dynamical cluster approximation
Dynamical mean field theory
Metal insulator transition
Random disorder
Typical medium theory

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10.3390/cryst11111282

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title = "Real space quantum cluster formulation for the typical medium theory of anderson localization",

abstract = "We develop a real space cluster extension of the typical medium theory (cluster-TMT) to study Anderson localization. By construction, the cluster-TMT approach is formally equivalent to the real space cluster extension of the dynamical mean field theory. Applying the developed method to the 3D Anderson model with a box disorder distribution, we demonstrate that cluster-TMT successfully captures the localization phenomena in all disorder regimes. As a function of the cluster size, our method obtains the correct critical disorder strength for the Anderson localization in 3D, and systematically recovers the re-entrance behavior of the mobility edge. From a general perspective, our developed methodology offers the potential to study Anderson localization at surfaces within quantum embedding theory. This opens the door to studying the interplay between topology and Anderson localization from first principles.",

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author = "Tam, {Ka Ming} and Hanna Terletska and Tom Berlijn and Liviu Chioncel and Juana Moreno",

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AU - Tam, Ka Ming

AU - Terletska, Hanna

AU - Berlijn, Tom

AU - Chioncel, Liviu

AU - Moreno, Juana

N1 - Publisher Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

PY - 2021/11

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N2 - We develop a real space cluster extension of the typical medium theory (cluster-TMT) to study Anderson localization. By construction, the cluster-TMT approach is formally equivalent to the real space cluster extension of the dynamical mean field theory. Applying the developed method to the 3D Anderson model with a box disorder distribution, we demonstrate that cluster-TMT successfully captures the localization phenomena in all disorder regimes. As a function of the cluster size, our method obtains the correct critical disorder strength for the Anderson localization in 3D, and systematically recovers the re-entrance behavior of the mobility edge. From a general perspective, our developed methodology offers the potential to study Anderson localization at surfaces within quantum embedding theory. This opens the door to studying the interplay between topology and Anderson localization from first principles.

AB - We develop a real space cluster extension of the typical medium theory (cluster-TMT) to study Anderson localization. By construction, the cluster-TMT approach is formally equivalent to the real space cluster extension of the dynamical mean field theory. Applying the developed method to the 3D Anderson model with a box disorder distribution, we demonstrate that cluster-TMT successfully captures the localization phenomena in all disorder regimes. As a function of the cluster size, our method obtains the correct critical disorder strength for the Anderson localization in 3D, and systematically recovers the re-entrance behavior of the mobility edge. From a general perspective, our developed methodology offers the potential to study Anderson localization at surfaces within quantum embedding theory. This opens the door to studying the interplay between topology and Anderson localization from first principles.

KW - Anderson localization

KW - Cellular dynamical mean field theory

KW - Cluster mean field theory

KW - Coherent potential approximation

KW - Dynamical cluster approximation

KW - Dynamical mean field theory

KW - Metal insulator transition

KW - Random disorder

KW - Typical medium theory

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Real space quantum cluster formulation for the typical medium theory of anderson localization

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