From a5c2a2fc7ba292b81c5567c5351fcb63c3fd614c Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Wed, 25 Nov 2020 11:02:48 +0100 Subject: [PATCH] new fig for Pade --- Manuscript/EPAWTFT.tex | 9 +++++++++ Manuscript/PadeRMP.pdf | Bin 0 -> 31272 bytes 2 files changed, 9 insertions(+) create mode 100644 Manuscript/PadeRMP.pdf diff --git a/Manuscript/EPAWTFT.tex b/Manuscript/EPAWTFT.tex index b39db11..8c0c8bf 100644 --- a/Manuscript/EPAWTFT.tex +++ b/Manuscript/EPAWTFT.tex @@ -1185,6 +1185,15 @@ A $[d_A/d_B]$ Pad\'e approximant is defined as (with $b_0 = 1$), where the coefficients of the polynomials $A(\lambda)$ and $B(\lambda)$ are determined by collecting terms according to power of $\lambda$. Pad\'e approximants are extremely useful in many areas of physics and chemistry \cite{Loos_2013,Gluzman_2020} as they can model poles, which appears at the roots of the polynomial $B(\lambda)$. However, they are unable to model functions with square-root branch points, which are ubiquitous in the singularity structure of a typical perturbative treatment. +Figure \ref{fig:PadeRMP} illustrates the improvement brought by Pad\'e approximants as compared to the usual Taylor expansion in the case of the RMP series of the Hubbard dimer for $U/t = 4.5$. + +%%%%%%%%%%%%%%%%% +\begin{figure} + \includegraphics[width=\linewidth]{PadeRMP} + \caption{\label{fig:PadeRMP} + RMP ground-state energy as a function of $\lambda$ obtained with various approximations for $U/t = 4.5$.} +\end{figure} +%%%%%%%%%%%%%%%%% %==========================================% \subsection{Quadratic approximant} diff --git a/Manuscript/PadeRMP.pdf b/Manuscript/PadeRMP.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e90f635206a16c7630f68c9e6bc64dd2106f4447 GIT binary patch literal 31272 zcmV(_K-9k_P((&8F)lR4?5av(28Y+-a|L}g=dWMv9IJ_>Vma%Ev{3V58|y-lliJ(49h-@oDvZA0GP`j()n zfx#FGJZM*f2SpFeaaSkJ^BB53sK0MTtQDcy=iaQ!EIdhP^1km~v32&=XDGBHB&FBA z|Nn=y|CL*Py?uKV@(`=9@I{o{Y$&+pg&b(OE&UjN&x)~`B>zN)nL`fY;yE6vxh*FWg@ zzP&m9C2!uZsPom+*KB#eIJf44U%O=gaxn|({#tV)ORcn5N?&*C z`-g(pR9pw}$U|_tGcX?K)Gop8tFA19T9e@Z)ox8NmlU$jueM*5^4Hw?`}JyBt2OP{ z-15CPzV6wtmsEF=1iJ_+uUDF1Ye|CMzFNw=62FROu&=Lvw^uG-txJYR-8tQr+`sNo zU)L7Qud;T6`PH-JXy&il#;fcS=?`ZAn!UVA`5IH6uU!?pM#`?iSp>JQ`>xlkOs%3V zSYKtVSKUP#ZR2zoedDeQd?DTAYwq9H@zu5V(=Kk#<<;)5KKiAS{+0Jv+Rk>BucW-6 z_4(Qj*O$H|@0#xY)pq%Yz9g@&e2-V(HC7}aX=k~O>(%@2KUD?$gS*yum1Lx-`Ri`! 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