Performance Impact Applying Compression Format to Sparse Matrix on Kernel Polynomial Method Using GPU

2011 ◽  
Author(s):  
Shixun Zhang ◽  
Shinichi Yamagiwa ◽  
Masahiko Okumura ◽  
Seiji Yunoki
Keyword(s):  
Sparse Matrix ◽  
Polynomial Method ◽  
Performance Impact ◽  
Kernel Polynomial Method

scholarly journals Electronic Properties of Twisted Bilayer Graphene in the Presence of a Magnetic Field

2020 ◽  
Vol 233 ◽  
pp. 03004
Author(s):  
M.F.C. Martins Quintela ◽  
J.C.C. Guerra ◽  
S.M. João
Keyword(s):  
Magnetic Field ◽  
Electronic Properties ◽  
Twist Angle ◽  
Bilayer Graphene ◽  
Polynomial Method ◽  
Zero Energy ◽  
Energy Bands ◽  
Optical And Electronic Properties ◽  
Twisted Bilayer Graphene ◽  
Kernel Polynomial Method

In AA-stacked twisted bilayer graphene, the lower energy bands become completely flat when the twist angle passes through certain specific values: the so-called “magic angles”. The Dirac peak appears at zero energy due to the flattening of these bands when the twist angle is sufficiently small [1-3]. When a constant perpendicular magnetic field is applied, Landau levels start appearing as expected [5]. We used the Kernel Polynomial Method (KPM) [6] as implemented in KITE [7] to study the optical and electronic properties of these systems. The aim of this work is to analyze how the features of these quantities change with the twist angle in the presence of an uniform magnetic field.

Kernel Polynomial Method on GPU

2012 ◽  
Vol 41 (1) ◽  
pp. 59-88 ◽  
Author(s):  
Shixun Zhang ◽  
Shinichi Yamagiwa ◽  
Masahiko Okumura ◽  
Seiji Yunoki
Keyword(s):  
Polynomial Method ◽  
Kernel Polynomial Method

scholarly journals Computation of topological phase diagram of disordered Pb1−xSnxTe using the kernel polynomial method

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Dániel Varjas ◽  
Michel Fruchart ◽  
Anton R. Akhmerov ◽  
Pablo M. Perez-Piskunow
Keyword(s):  
Phase Diagram ◽  
Polynomial Method ◽  
Topological Phase ◽  
Kernel Polynomial Method

scholarly journals Probing the Global Delocalization Transition in the de Moura-Lyra Model with the Kernel Polynomial Method

2020 ◽  
Vol 233 ◽  
pp. 05011
Author(s):  
N.A. Khan ◽  
J.P. Santos Pires ◽  
J.M. Viana Parente Lopes ◽  
J.M.B. Lopes dos Santos
Keyword(s):  
Nearest Neighbor ◽  
Tight Binding ◽  
Localization Length ◽  
Polynomial Method ◽  
Tight Binding Model ◽  
Weak Disorder ◽  
Binding Model ◽  
One Dimensional ◽  
Open Boundaries ◽  
Kernel Polynomial Method

In this paper, we report numerical calculations of the localization length in a non-interacting one-dimensional tight-binding model at zero tem¬perature, holding a correlated disorder model with an algebraic power-spectrum (de Moura-Lyra model). Our calculations were based on a Kernel Polynomial implementation of the Thouless formula for the inverse localization length of a general nearest-neighbor 1D tight-binding model with open boundaries. Our results confirm the delocalization of all eigenstates in de Moura-Lyra model for α > 1 and a localization length which diverges as ξ ∝ (1 – α)–1 for α → 1–, at all energies in the weak disorder limit (as previously seen in [12]).

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