Scaling and renormalization in the modern theory of polarization: Application to disordered systems

Hetényi, Balázs; Parlak, Selçuk; Yahyavi, Mohammad

doi:10.1103/physrevb.104.214207

Cited by 11 publications

(1 citation statement)

References 53 publications

(97 reference statements)

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“…For comparison, we also used another method to locate the phase transition point. This method is an application of real-space renormalization to the polarization amplitude [38]. For a given value of V , Z 1 is calculated for some initial system size L. Then for L/2 the value of V is tuned to reproduce the same Z 1 as for the larger system.…”

Section: Correlated One-dimensional Modelmentioning

confidence: 99%

Geometric cumulants associated with adiabatic cycles crossing degeneracy points: Application to finite size scaling of metal-insulator transitions in crystalline electronic systems

Hetényi

Cengiz

2022

Phys. Rev. B

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In this work we focus on two questions. One, we complement the machinary to calculate geometric phases along adiabatic cycles as follows. The geometric phase is a line integral along an adiabatic cycle, and if the cycle encircles a degeneracy point, the phase becomes non-trivial. If the cycle crosses the degeneracy point the phase diverges. We construct quantities which are well-defined when the path crosses the degeneracy point. We do this by constructing a generalized Bargmann invariant, and noting that it can be interpreted as a cumulant generating function, with the geometric phase being the first cumulant. We show that particular ratios of cumulants remain finite for cycles crossing a set of isolated degeneracy points. The cumulant ratios take the form of the Binder cumulants known from the theory of finite size scaling in statistical mechanics (we name them geometric Binder cumulants). Two, we show that the machinery developed can be applied to perform finite size scaling in the context of the modern theory of polarization. The geometric Binder cumulants are size independent at gap closure points or regions with closed gap (Luttinger liquid). We demonstrate this by model calculations for a one-dimensional topological model, several two-dimensional models, and a one-dimensional correlated model. In the case of two dimensions we analyze to different situations, one in which the Fermi surface is one-dimensional (a line), and two cases in which it is zero dimensional (Dirac points). For the geometric Binder cumulants the gap closure points can be found by one dimensional scaling even in two dimensions. As a technical point we stress that only certain finite difference approximations for the cumulants are applicable, since not all approximation schemes are capable of extracting the size scaling information in the case of a closed gap system.

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Section: Correlated One-dimensional Modelmentioning

confidence: 99%

Geometric cumulants associated with adiabatic cycles crossing degeneracy points: Application to finite size scaling of metal-insulator transitions in crystalline electronic systems

Hetényi

Cengiz

2022

Phys. Rev. B

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Anderson transition and mobility edges on hyperbolic lattices with randomly connected boundaries

Li,

Peng,

Wang

et al. 2024

Commun Phys

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Regulating Anderson localization with structural defect disorder

Cheng 程,

Chen 陈,

Chen 陈

2024

Chinese Phys. B

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Localization due to disorder has been one of the most intriguing theoretical concepts evolved in condensed matter. Here, we expand the theory of localization by considering two types of disorder at the same time, namely the original Anderson’s disorder and the structural defect disorder, which has been suggested to be a key component in recently discovered two-dimensional amorphous materials. While increasing the degree of both disorders could induce localization of wavefunction in real space, we find that a small degree of structural defect disorder can significantly enhance the localization. As the degree of structural defect disorder increases, localized states quickly appear within the extended phase to enter a broad crossover region with mixed phases. We establish two-dimensional diagrams for the wavefunction localization and conductivity to highlight the interplay between the two types of disorder. Our theoretical model provides a comprehensive understanding of localization in two-dimensional amorphous materials and highlights the promising tunability of their transport properties.

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Scaling and renormalization in the modern theory of polarization: Application to disordered systems

Cited by 11 publications

References 53 publications

Geometric cumulants associated with adiabatic cycles crossing degeneracy points: Application to finite size scaling of metal-insulator transitions in crystalline electronic systems

Geometric cumulants associated with adiabatic cycles crossing degeneracy points: Application to finite size scaling of metal-insulator transitions in crystalline electronic systems

Anderson transition and mobility edges on hyperbolic lattices with randomly connected boundaries

Regulating Anderson localization with structural defect disorder

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