Effective cluster typical medium theory for the diagonal Anderson disorder model in one- and two-dimensions

Ekuma, Chinedu; Terletska, Hanna; Meng, Zi Yang; Moreno, Juana; Jarrell, Mark; Mahmoudian, Samiyeh; Dobrosavljević, Vladimir

doi:10.1088/0953-8984/26/27/274209

Cited by 18 publications

(32 citation statements)

References 60 publications

(141 reference statements)

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“…Recently, we extended the local TMT to a cluster version called the cluster typical medium theory (CTMT) [24]. Here, the diagonal cluster-momentum-resolved density of states is replaced by its typical value ρ c (K,ω) = exp( ln ρ c (K,ω) ).…”

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confidence: 99%

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Typical medium dynamical cluster approximation for the study of Anderson localization in three dimensions

et al. 2014

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We develop a systematic typical medium dynamical cluster approximation that provides a proper description of the Anderson localization transition in three dimensions (3D). Our method successfully captures the localization phenomenon both in the low and large disorder regimes, and allows us to study the localization in different momenta cells, which renders the discovery that the Anderson localization transition occurs in a cell-selective fashion. As a function of cluster size, our method systematically recovers the reentrance behavior of the mobility edge and obtains the correct critical disorder strength for Anderson localization in 3D.

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confidence: 99%

“…This is due to the fact that the "typical" value of a "random" variable corresponds to the most probable value of the PDF [21,24].…”

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confidence: 99%

Typical medium dynamical cluster approximation for the study of Anderson localization in three dimensions

et al. 2014

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“…In relevant cases, our results are found to be in excellent agreement with recent large-scale exact diagonalization results 37 , as well as with recent experiments 29 . Moreover, recently developed cluster refinements of TMT demonstrated [39][40][41] that significant corrections to (single site) TMT are only found very close to the Anderson transition. All these findings provide further evidence that TMT represents a flexible and practically useful tool for successfully describing the main qualitative trends for physical observables, in the vicinity of disorder-driven metal-insulator transitions.…”

Section: Discussionmentioning

confidence: 99%

Quantum criticality at the Anderson transition: A typical medium theory perspective

Mahmoudian¹,

Tang²,

Dobrosavljević³

2015

Phys. Rev. B

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We present a complete analytical and numerical solution of the Typical Medium Theory (TMT) for the Anderson metal-insulator transition. This approach self-consistently calculates the typical amplitude of the electronic wave-functions, thus representing the conceptually simplest order-parameter theory for the Anderson transition. We identify all possible universality classes for the critical behavior, which can be found within such a meanfield approach. This provides insights into how interaction-induced renormalizations of the disorder potential may produce qualitative modifications of the critical behavior. We also formulate a simplified description of the leading critical behavior, thus obtaining an effective Landau theory for Anderson localization.

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“…As noted above, our initial attempt to formulate a cluster version of the TMT reproduced the expected behavior in one and two dimensions as N c is increased. 33 However, in three dimensions, applying the algorithm directly will lead to an effective self-averaging for large clusters. This is due to the fact that close to criticality, there exist distinct localized and extended states above and below the localization edge given by the TDOS with an energy scale difference that can span an order of magnitude.…”

Section: Avoiding Self-averagingmentioning

confidence: 99%

Finite-cluster typical medium theory for disordered electronic systems

et al. 2015

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We use the recently developed typical medium dynamical cluster (TMDCA) approach [Ekuma et al., Phys. Rev. B 89, 081107 (2014)] to perform a detailed study of the Anderson localization transition in three dimensions for the Box, Gaussian, Lorentzian, and Binary disorder distributions, and benchmark them with exact numerical results. Utilizing the nonlocal hybridization function and the momentum resolved typical spectra to characterize the localization transition in three dimensions, we demonstrate the importance of both spatial correlations and a typical environment for the proper characterization of the localization transition in all the disorder distributions studied. As a function of increasing cluster size, the TMDCA systematically recovers the re-entrance behavior of the mobility edge for disorder distributions with finite variance, obtaining the correct critical disorder strengths, and shows that the order parameter critical exponent for the Anderson localization transition is universal. The TMDCA is computationally efficient, requiring only a small cluster to obtain qualitative and quantitative data in good agreement with numerical exact results at a fraction of the computational cost. Our results demonstrate that the TMDCA provides a consistent and systematic description of the Anderson localization transition.

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Effective cluster typical medium theory for the diagonal Anderson disorder model in one- and two-dimensions

Cited by 18 publications

References 60 publications

Typical medium dynamical cluster approximation for the study of Anderson localization in three dimensions

Typical medium dynamical cluster approximation for the study of Anderson localization in three dimensions

Quantum criticality at the Anderson transition: A typical medium theory perspective

Finite-cluster typical medium theory for disordered electronic systems

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