From ceb579439241508459a85ad914304eaf15e1a9da Mon Sep 17 00:00:00 2001 From: Hugh Burton Date: Sat, 14 Nov 2020 22:08:02 +0000 Subject: [PATCH] added UMP data to notebook --- Notebooks/HughHubbarrdDimer.nb | 12874 ++++++++++++++++++++++++------- RapportStage/Rapport.tex | 12 +- 2 files changed, 10161 insertions(+), 2725 deletions(-) diff --git a/Notebooks/HughHubbarrdDimer.nb b/Notebooks/HughHubbarrdDimer.nb index 4474998..39d8d4d 100644 --- a/Notebooks/HughHubbarrdDimer.nb +++ b/Notebooks/HughHubbarrdDimer.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 3250287, 55092] -NotebookOptionsPosition[ 3241194, 54936] -NotebookOutlinePosition[ 3241531, 54951] -CellTagsIndexPosition[ 3241488, 54948] +NotebookDataLength[ 3618155, 62528] +NotebookOptionsPosition[ 3607264, 62341] +NotebookOutlinePosition[ 3607605, 62356] +CellTagsIndexPosition[ 3607562, 62353] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -31,10 +31,11 @@ Cell[TextData[{ "Hugh G. A. Burton\n", StyleBox["Last Updated: ", FontWeight->"Bold"], - "13-Nov-2020" + "14-Nov-2020 22:03:00" }], "Text", - CellChangeTimes->{{3.8142716881144743`*^9, - 3.814271731424687*^9}},ExpressionUUID->"52eada4f-59da-495f-bbb9-\ + CellChangeTimes->{{3.8142716881144743`*^9, 3.814271731424687*^9}, { + 3.814380222438754*^9, + 3.8143802392314262`*^9}},ExpressionUUID->"52eada4f-59da-495f-bbb9-\ 6b4f2346f7da"], Cell[TextData[StyleBox["We develop the Hubbard dimer as a consistent example \ @@ -68,8 +69,7 @@ Cell[BoxData[{ mhchem}\>\"", ",", "\"\<\\\\definecolor{darkgreen}{RGB}{0, 180, 0}\>\""}], "}"}]}]}], "]"}], ";"}]}], "Input", InitializationCell->True, - CellLabel-> - "In[102]:=",ExpressionUUID->"cdc91ebe-c467-43bc-a4ad-6f77ca683c02"], + CellLabel->"In[68]:=",ExpressionUUID->"cdc91ebe-c467-43bc-a4ad-6f77ca683c02"], Cell[BoxData[ RowBox[{ @@ -670,8 +670,7 @@ Cell[BoxData[ 3.814261294467675*^9}, {3.8142613321800632`*^9, 3.814261647731246*^9}, { 3.81426168692836*^9, 3.8142617778333073`*^9}, {3.814261816196641*^9, 3.814261858767838*^9}}, - CellLabel-> - "In[626]:=",ExpressionUUID->"1b78d52d-adad-46f9-a75a-0295b83375c5"] + CellLabel->"In[55]:=",ExpressionUUID->"1b78d52d-adad-46f9-a75a-0295b83375c5"] }, Closed]], Cell[CellGroupData[{ @@ -5026,9 +5025,10 @@ Cell[BoxData[ CellChangeTimes->{{3.814262171142853*^9, 3.814262175710464*^9}, { 3.814262304723651*^9, 3.8142623784769*^9}, {3.814262424175391*^9, 3.814262503549615*^9}, {3.814262549168585*^9, 3.814263045256138*^9}, { - 3.814263076416499*^9, 3.814263256323346*^9}}, + 3.814263076416499*^9, 3.814263256323346*^9}, {3.8143703426348248`*^9, + 3.8143703777699957`*^9}}, CellLabel-> - "In[735]:=",ExpressionUUID->"900c20e6-7495-4b35-b098-6a8279e0abef"], + "In[119]:=",ExpressionUUID->"900c20e6-7495-4b35-b098-6a8279e0abef"], Cell[BoxData[ TagBox[ @@ -6476,9 +6476,10 @@ iXs= SelectWithContents->False, Selectable->True]], "Output", CellChangeTimes->{{3.8142631301555758`*^9, 3.814263205459347*^9}, { - 3.814263242625832*^9, 3.814263256668569*^9}}, + 3.814263242625832*^9, 3.814263256668569*^9}, {3.814370344736964*^9, + 3.814370378438982*^9}}, CellLabel-> - "Out[735]=",ExpressionUUID->"92269758-93ad-48be-a56c-5c4817e568ad"] + "Out[119]=",ExpressionUUID->"ed5098d9-ab23-4f12-8133-681b147ec102"] }, Open ]], Cell[TextData[StyleBox["We can also plot the corresponding Riemann surface \ @@ -11190,18 +11191,19 @@ we have found so far...\n\nFCI: 1 = \[PlusMinus] i 4t / U\nRMP: \ FormBox[ RowBox[{ SubscriptBox["\[Lambda]", "c"], "="}], TraditionalForm]], - FormatType->"TraditionalForm", FontColor->RGBColor[1, 0, 0],ExpressionUUID-> "fab7bf44-655b-470d-bfc6-44777c73ed02"], - StyleBox[" \[PlusMinus] i 4t / U\n\nSo we see that the magnitudes of each \ -exceptional point are all the same... \nIs it possible that each of these \ -exceptional point is dictated by the fundamental exceptional point in the FCI \ -energy?\nOr is this an artefact of our incredible simple model?", + StyleBox[" \[PlusMinus] i 4t / U\nCFP: 1 = 2t / U\n\nSo we see \ +that the magnitudes of each exceptional point are all closely related.\nIs it \ +possible that each of these exceptional point is dictated by the fundamental \ +exceptional point in the FCI energy?\nOr is this an artefact of our \ +incredible simple model?", FontColor->RGBColor[1, 0, 0]] }], "Text", CellChangeTimes->{{3.814264982175564*^9, 3.8142651334405727`*^9}, { 3.814265279765139*^9, 3.814265402285018*^9}, {3.814266218490487*^9, - 3.814266218614222*^9}},ExpressionUUID->"07e56b25-3c15-4626-9e46-\ + 3.814266218614222*^9}, {3.814380174186116*^9, + 3.8143802102073708`*^9}},ExpressionUUID->"07e56b25-3c15-4626-9e46-\ 6c77981db19f"] }, Open ]] }, Closed]], @@ -11323,8 +11325,7 @@ Cell[BoxData[{ 3.814266464633909*^9, 3.81426650081355*^9}, {3.8142666096880283`*^9, 3.8142666243002987`*^9}, {3.814266737877754*^9, 3.814266753386414*^9}, { 3.814266789850511*^9, 3.814266825769374*^9}}, - CellLabel-> - "In[826]:=",ExpressionUUID->"69c5aaef-072f-4d84-bdc3-8a653dd87893"], + CellLabel->"In[33]:=",ExpressionUUID->"69c5aaef-072f-4d84-bdc3-8a653dd87893"], Cell[BoxData[ TagBox[ @@ -11413,249 +11414,1208 @@ Cell[BoxData[ MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{ 3.81426662457999*^9, {3.814266746284916*^9, 3.814266753803179*^9}, { - 3.814266792771175*^9, 3.814266826046225*^9}}, + 3.814266792771175*^9, 3.814266826046225*^9}, 3.81436633644205*^9, + 3.814366367497034*^9}, CellLabel-> - "Out[827]//MatrixForm=",ExpressionUUID->"67373b34-725b-49e2-9aa9-\ -0dadfbe26255"] + "Out[34]//MatrixForm=",ExpressionUUID->"46edaaf4-6210-4097-95e3-\ +9431990ac15a"] }, Open ]], Cell[TextData[StyleBox["As expected, the spatial and spin contamination makes \ the exact eigenvalues more difficult to work with and introduces many more\n\ -coupling elements into the expression.", +coupling elements into the expression. 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Alignment -> Left, AppearanceElements -> None, + ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> + "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { + FontFamily -> "Times"}, Background -> Automatic, StripOnInput -> + False], TraditionalForm]& ), + Editable->True, + InterpretationFunction:>(RowBox[{"PointLegend", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Directive", "[", + RowBox[{ + RowBox[{"PointSize", "[", "0.009166666666666668`", "]"}], + ",", + RowBox[{"CapForm", "[", "\"Butt\"", "]"}], ",", + RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0, + Rational[2, 3], 0], + RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> + "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, + FrameStyle -> RGBColor[0., 0.4444444444444444, 0.], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + 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\label{fig:RUMP_Gill} +%\end{wrapfigure} When one relies on MP perturbation theory (and more generally on any perturbative partitioning), it would be reasonable to ask for a systematic improvement of the energy with respect to the perturbative order, i.e., one would expect that the more terms of the perturbative series one can compute, the closer the result from the exact energy. %In other words, each time a higher-order term is computed, one would like to obtained an overall result closer to the exact energy. In other words, one would like a monotonic convergence of the MP series. Assuming this, the only limiting process to get the exact correlation energy (in a finite basis set) would be our ability to compute the terms of this perturbation series.