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

Mahmoudian, Samiyeh; Tang, Shao; Dobrosavljević, Vladimir

doi:10.1103/physrevb.92.144202

Cited by 9 publications

(9 citation statements)

References 43 publications

(88 reference statements)

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“…Motivated by disordered and correlated systems near a MIT, they consider a disordered Hubbard model, where Hubbard correlations are treated within static Hartree-Fock, giving rise to local moments, while disorder effects over and above HF are studied by exact diagonalization techniques. Their main findings are (i) a "soft" gap arises even with purely local interactions, in contrast to that in an Efros-Shklovskii picture, where it arises from long-range coulomb interactions and (ii) while the LDOS 3 ] provides a much better fit for |E − E F | < 0.1. In contrast, we find that the LDOS, ρ(ω) ≃ C|ω| 1/3 remains valid up to lowest energies at the QCP: this is similar to the situation found in single-site DMFT [13], where precisely the same behavior is found analytically.…”

Section: One-particle Spectral Responsementioning

confidence: 99%

Real-space cluster dynamical mean-field approach to the Falicov-Kimball model: An alloy-analogy approach

2017

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It is long known that the best single-site coherent potential approximation (CPA) falls short of describing Anderson localization (AL). Here, we study a binary alloy disorder (or equivalently, a spinless Falicov-Kimball (FK)) model and construct a dominantly analytic cluster extension that treats intra-cluster (1/d, d=spatial dimension) correlations exactly. We find that, in general, the irreducible two-particle vertex exhibits clear non-analyticities before the band-splitting transition of the Hubbard type occurs, signaling onset of an unusual type of localization at strong coupling. Using time-dependent response to a sudden local quench as a diagnostic, we find that the longtime wave function overlap changes from a power-law to an anomalous form at strong coupling, lending additional support to this idea. Our results also imply such novel "strong" localization in the equivalent FK model, the simplest interacting fermion system. Anderson's seminal paper [1] spawned the fertile field of localization in disordered systems. While all states in spatial dimension d = 1, 2 are long known to be localized for any arbitrary disorder in the "weak" localization sense, strong enough disorder is generally expected to lead to exponential localization in all d. In a distinct vein, the exact and otherwise successful mean-field theory of AL, the coherent potential approximation (CPA) cannot, by construction, describe AL, since it cannot account for coherent backscattering processes that underpin AL. Nevertheless, CPA has been used in the Vollhardt-Wölfle (VW) theory to obtain a phase diagram with AL and metallic phases [2]. Other schemes marry the CPA with typical medium theory (TMT) to study AL [3]. However, given the necessity of including non-local correlations, several heavily numeric-based cluster approaches [4][5][6] have also been devised with mixed success. In addition, the simplest model of correlated fermions on a lattice, the Falicov-Kimball model (FKM), is isomorphic to the binary-alloy Anderson disorder model, and exhibits a continuous metal-insulator transition of the Hubbard band splitting type [7]. One might thus expect the above issues to be relevant for the FKM as well. To our knowledge, a dominantly analytic approach to cluster-based techniques in such contexts remains to be attempted, and is potentially of great interest.Recent work on many-body localization [8] suggest that at strong disorder the localization length is of the order of lattice constant (ξ ≃ 1). In this limit, an exact treatment of inter-site "disorder" (1/d) correlations beyond DMFT may thus be adequate to describe "strong" localization. Non-local response to a sudden local quench (a suddenly switched-on localized hole) in this regime exhibits a statistical orthogonality catastrophe (sOC), also studied earlier in the context of correlated impurity potentials in a fermi gas [9]. Thus, qualitative change in the long-time response of a system to a sudden local quench, wherein the explicit long-time wave function overlap undergoes a qualitative ...

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Section: One-particle Spectral Responsementioning

confidence: 99%

Real-space cluster dynamical mean-field approach to the Falicov-Kimball model: An alloy-analogy approach

2017

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“…By considering the most probable or typical value over the ensemble, instead of the average one, TMT treatment of disorder has been proved capable of describing Anderson localization. 16,17 Here we use the combination of DMFT and TMT to solve the AHM (eq. 1) and describe the interplay between correlation and disorder induced localization.…”

Section: Model and Methodologymentioning

confidence: 99%

“…7 To circumvent this problem, a mean field treatment of disorder, the so-called Typical Medium Theory (TMT), has been proposed and proved capable of describing the disorderinduced localization. [16][17][18] The combination of TMT with DMFT has contributed to our understanding of the nontrivial interplay between correlation and disorder localization effects. [19][20][21][22][23] In previous works based on DMFT-TMT, an insulating phase which is a mixture of Mott and Anderson insulators has been observed at half-filling.…”

Section: Introductionmentioning

confidence: 99%

Anderson localization effects on doped Hubbard model

Giovanni,

Civelli,

Aguiar

2020

Preprint

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We derive the disorder vs. doping phase diagram of the doped Hubbard model via Dynamical Mean Field Theory combined with Typical Medium Theory, which allows the description of both Mott (correlation driven) and Anderson (disorder driven) metal-insulator transitions. We observe a metal-insulator transition to an Anderson-Mott insulator for increasing disorder strength at all interactions. In the weak correlation regime and rather small doping, the Anderson-Mott insulator displays properties which are alike to the ones found at half-filling. This is characterized by the presence of empty sites that give rise to a V-shaped electronic density of states. If we further increase either the doping or the correlation however, an Anderson-Mott phase of different kind arises for sharply weaker disorder strength. This phase occupies the largest part of the phase diagram in the strong correlation regime, and it has both Anderson and Mott character, but empty sites and the V-shaped density of states are absent.

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“…In the typical medium analysis, instead of using the arithmetically averaged disorder Green's function (as it is implemented in the CPA and the DCA), the geometrical averaging is used in the self-consistency loop. Such typical medium analysis has also been extended to interacting disordered systems [22,23,24,25,26,27,28,29,30,31,32,33]. However, by construction, the TMT is a local single-site approximation and, hence, it neglects the non-local spatial correlations.…”

Section: Introductionmentioning

confidence: 99%

Non-local corrections to the typical medium theory of Anderson localization

et al. 2021

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We use the recently developed finite cluster typical medium approach to study the Anderson localization transition in three dimensions. Applying our method to the box and binary alloy disorder distributions, we find a fast convergence with the cluster size. We demonstrate the importance of the typical medium environment and the non-local spatial correlations for the proper characterization of the localization transition. As the cluster size increases, our typical medium cluster method recovers the correct critical disorder strength for the transition. Our findings highlight the importance of the non-local cluster corrections for capturing the localization behavior of the mobility edge trajectories. Our results demonstrate that the typical medium cluster approach developed here provides a consistent and systematic description of the Anderson localization transition in the framework of the effective medium embedding schemes.

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

Cited by 9 publications

References 43 publications

Real-space cluster dynamical mean-field approach to the Falicov-Kimball model: An alloy-analogy approach

Real-space cluster dynamical mean-field approach to the Falicov-Kimball model: An alloy-analogy approach

Anderson localization effects on doped Hubbard model

Non-local corrections to the typical medium theory of Anderson localization

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