Excitonic effect on the optical response in the one-dimensional two-band Hubbard model

Physical Review B - Condensed Matter and Materials Physics

Volumn 71, Issue 15, 2005, Pages

  Matsueda, H ^a   Tohyama, T ^a   Maekawa, S ^a  

^a TOHOKU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 28744434943     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.71.153106     Document Type: Article

References (22)

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22. G. S. Uhrig (private communications). By the Lorentz transformation, χγ (ω) can be decomposed into a set of Lorentzian components. The transformation is given by χγ (ω) = d ω′ γχ (ω′) π [(ω- ω′) 2 + γ2], with χ (ω′) denoting the intensity of the decomposed Lorentian. In actual numerical calculation, the integral is limited within a range where χγ (ω) is finite. The energies ω and ω′ are discretized equidistantly (ω1 < ω2 < < ωn and ωi+1 - ωi =δω for any i). In this case, the equation is rewritten by Xγ =XM, where Xγ = (χγ (ω1), χγ (ω2),..., χγ (ωn)), X= (χ (ω1), χ (ω2),..., χ (ωn)) and the (i,j) -component of the matrix M is defined by Mij = (δω π) γ [(ωi - ωj) 2 + γ2]. X is obtained by calculating Xγ M-1 with M-1 denoting the inverse matrix of M. It is noted that the numerically obtained χ (ωi) still has a finite broadening factor δω.