Application of the locally self-consistent embedding approach to the Anderson model with non-uniform random distributions

Tam, Ka-Ming; Zhang, Y.; Terletska, Hanna; Wang, Y.; Eisenbach, Markus; Chioncel, Liviu; Moreno, Juana

doi:10.1016/j.aop.2021.168480

“…In addition, the locally self-consistent formulation opens up the possibility to formulate linear scaling methods. Unlike the previous typical medium cluster extensions of TMT, formulated in the momentum space (TMDCA) [54,67], or in a mixed representation (locally self-consistent approach) [66,68], here we propose an exclusively real space cluster extension of TMT (cluster-TMT). This construction is formally equivalent to the real space cluster extension of the dynamical mean field theory (DMFT) [69][70][71][72][73].…”

Section: Introductionmentioning

confidence: 99%

Real Space Quantum Cluster Formulation for the Typical Medium Theory of Anderson Localization

Tam

¹

,

Terletska

²

,

Berlijn

³

et al. 2021

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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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“…Besides, the locally self-consistent formulation it opens the possibility to formulate linear scaling methods. Unlike the previous typical medium cluster extensions of TMT, formulated in the momentum space (TMDCA) 28,41 , or in a mixed representation (locally self-consistent approach) 40,42 , here we propose an exclusively real space cluster extension of TMT (cluster-TMT). This construction is formally equivalent to the real space cluster extension of the dynamical mean field theory (DMFT) [43][44][45][46][47] .…”

Section: Introductionmentioning

confidence: 99%

Real Space Quantum Cluster Formulation for the Typical Medium Theory of Anderson Localization

Tam¹,

Terletska²,

Berlijn³

et al. 2021

Preprint

0

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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.

show abstract

Special Issue “Localisation 2020”: Editorial Summary

Bhatt

¹

,

Kettemann

²

2021

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Application of the locally self-consistent embedding approach to the Anderson model with non-uniform random distributions

Cited by 3 publications

References 40 publications

Real Space Quantum Cluster Formulation for the Typical Medium Theory of Anderson Localization

Real Space Quantum Cluster Formulation for the Typical Medium Theory of Anderson Localization

Real Space Quantum Cluster Formulation for the Typical Medium Theory of Anderson Localization

Special Issue “Localisation 2020”: Editorial Summary

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