new fig with Hugh style

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Pierre-Francois Loos 2020-11-26 11:11:56 +01:00
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@ -1286,7 +1286,6 @@ and substituting $E(\lambda$) by its $n$th-order expansion and the polynomials b
A quadratic approximant, characterised by the label $[d_P/d_Q,d_R]$, generates, by construction, $n_\text{bp} = \max(2d_p,d_q+d_r)$ branch points at the roots of the polynomial $P^2(\lambda) - 4 Q(\lambda) R(\lambda)$.
The diagonal sequence of quadratic approximant, \ie, $[0/0,0]$, $[1/0,0]$, $[1/0,1]$, $[1/1,1]$, $[2/1,1]$, is of particular interest.
Note that, by construction, a quadratic approximant has only two branches which hampers the faithful description of more complicated singularity structures.
As shown in Ref.~\onlinecite{Goodson_2000}, quadratic approximants provide convergent results in the most divergent cases considered by Olsen and collaborators \cite{Christiansen_1996,Olsen_1996} and Leininger \etal \cite{Leininger_2000}
For the RMP series of the Hubbard dimer, the $[0/0,0]$ and $[1/0,0]$ quadratic approximant are quite poor approximation, but its $[1/0,1]$ version already model perfectly the RMP energy function by predicting a single pair of EPs at $\lambda_\text{EP} = \pm i 4t/U$.

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