diff options
Diffstat (limited to 'figs')
26 files changed, 802 insertions, 0 deletions
diff --git a/figs/bands.fig/Makefile b/figs/bands.fig/Makefile new file mode 100644 index 0000000..cb5ada5 --- /dev/null +++ b/figs/bands.fig/Makefile @@ -0,0 +1,25 @@ +PROJECTNAME=$(basename $(wildcard *.gnuplot)) + +PDFS=$(addsuffix .pdf, $(PROJECTNAME)) + +all: $(PDFS) + +$(PDFS): + gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@) + pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@) + +install: $(PDFS) + cp $^ $(INSTALLDIR)/ + +clean-aux: + rm -f $(addsuffix .tikz.tex, $(PROJECTNAME)) + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + +clean-dat: + rm -f $(DATS) + +clean-tex: + rm -f $(PDFS) + +clean: clean-aux clean-tex diff --git a/figs/bands.fig/bands.gnuplot b/figs/bands.fig/bands.gnuplot new file mode 100644 index 0000000..8922c00 --- /dev/null +++ b/figs/bands.fig/bands.gnuplot @@ -0,0 +1,33 @@ +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 8,6 standalone + +unset key + +unset xtics +unset ytics +unset ztics +unset border + +unset colorbox + +set pointsize 1 + +#set xrange [0:4*pi/3] +#set yrange [-2*pi/sqrt(3):2*pi/sqrt(3)] + +set pm3d depthorder + +# make this odd and divisible by 7 to get the Fermi points +set isosamples 49 + +# rescale x and y components to render the Fermi points better +# units of 2*pi/3 +set xrange [0:2] +# units of 2*pi/(3*sqrt(3)) +set yrange [-3:3] + +set view 80,35 + +splot sqrt(1+4*cos(pi*x)*cos(pi/3*y)+4*cos(pi/3*y)**2) w pm3d, -sqrt(1+4*cos(pi*x)*cos(pi/3*y)+4*cos(pi/3*y)**2) w pm3d + +#pause mouse close diff --git a/figs/bilayer.fig/Makefile b/figs/bilayer.fig/Makefile new file mode 100644 index 0000000..147037c --- /dev/null +++ b/figs/bilayer.fig/Makefile @@ -0,0 +1,23 @@ +PROJECTNAME=$(basename $(basename $(wildcard *.tikz.tex))) + +PDFS=$(addsuffix .pdf, $(PROJECTNAME)) + +all: $(PDFS) + +$(PDFS): + pdflatex -jobname $(basename $@) $(patsubst %.pdf, %.tikz.tex, $@) + + +install: $(PROJECTNAME) + cp $^.pdf $(INSTALLDIR)/ + + +clean-aux: + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + rm -f $(addsuffix .out, $(PROJECTNAME)) + +clean-tex: + rm -f $(PDFS) $(SYNCTEXS) + +clean: clean-aux clean-tex diff --git a/figs/bilayer.fig/bilayer.tikz.tex b/figs/bilayer.fig/bilayer.tikz.tex new file mode 100644 index 0000000..a35b039 --- /dev/null +++ b/figs/bilayer.fig/bilayer.tikz.tex @@ -0,0 +1,40 @@ +\documentclass{standalone} + +\usepackage{tikz} +\usepackage{graphene} + +% reflected graphene grid at #1 of width #2 and height #3 +\def\graphenereflected#1#2#3{ + \foreach \i in {0,...,#2}{ + \foreach \j in {0,...,#3}{ + \cellreflected{#1++(\i*3,-2*\j*\sqrtThOT)} + \cellreflected{#1++(\i*3+1.5,\sqrtThOT-2*\j*\sqrtThOT)} + } + } +} +\def\cellreflected#1{ + \draw[dotted]#1--++(0:-1); + \draw[dotted]#1--++(120:-1); + \draw[dotted]#1--++(240:-1); + \asite{#1} + \draw[dotted]#1++(-1,0)--++(0:1); + \draw[dotted]#1++(-1,0)--++(120:1); + \draw[dotted]#1++(-1,0)--++(240:1); + \bsite{#1++(-1,0)} +} +\def\square#1#2{\draw#1++(-#2,-#2)--++(#2,0)--++(#2,0)--++(0,#2)--++(0,#2)--++(-#2,0)--++(-#2,0)--++(0,-#2)--++(0,-#2);} + + +\begin{document} +\begin{tikzpicture} + % first layer + \graphene{(0,0)}{3}{3} + + % redefine sites for second layer + \def\bsite#1{\draw#1circle(.1);} + \def\asite#1{\square{#1}{.17}} + + % second layer + \graphenereflected{(0,0)}{3}{3} +\end{tikzpicture} +\end{document} diff --git a/figs/bilayer.fig/graphene.sty b/figs/bilayer.fig/graphene.sty new file mode 120000 index 0000000..477bbc1 --- /dev/null +++ b/figs/bilayer.fig/graphene.sty @@ -0,0 +1 @@ +../lib/graphene.sty
\ No newline at end of file diff --git a/figs/brillouin.fig/Makefile b/figs/brillouin.fig/Makefile new file mode 100644 index 0000000..147037c --- /dev/null +++ b/figs/brillouin.fig/Makefile @@ -0,0 +1,23 @@ +PROJECTNAME=$(basename $(basename $(wildcard *.tikz.tex))) + +PDFS=$(addsuffix .pdf, $(PROJECTNAME)) + +all: $(PDFS) + +$(PDFS): + pdflatex -jobname $(basename $@) $(patsubst %.pdf, %.tikz.tex, $@) + + +install: $(PROJECTNAME) + cp $^.pdf $(INSTALLDIR)/ + + +clean-aux: + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + rm -f $(addsuffix .out, $(PROJECTNAME)) + +clean-tex: + rm -f $(PDFS) $(SYNCTEXS) + +clean: clean-aux clean-tex diff --git a/figs/brillouin.fig/brillouin.tikz.tex b/figs/brillouin.fig/brillouin.tikz.tex new file mode 100644 index 0000000..6b392af --- /dev/null +++ b/figs/brillouin.fig/brillouin.tikz.tex @@ -0,0 +1,17 @@ +\documentclass{standalone} + +\usepackage{tikz} + +% sqrt(3) +\def\sqrtTh{1.732} +% pi +\def\pival{3.14159} + +\begin{document} +\begin{tikzpicture} + \draw(0,0)--(2*\pival/3,2*\pival/\sqrtTh)--(4*\pival/3,0)--(2*\pival/3,-2*\pival/\sqrtTh)--cycle; + + \fill(2*\pival/3,2*\pival/3/\sqrtTh)circle(0.05); + \fill(2*\pival/3,-2*\pival/3/\sqrtTh)circle(0.05); +\end{tikzpicture} +\end{document} diff --git a/figs/brillouin.fig/scales.tikz.tex b/figs/brillouin.fig/scales.tikz.tex new file mode 100644 index 0000000..ebafd14 --- /dev/null +++ b/figs/brillouin.fig/scales.tikz.tex @@ -0,0 +1,47 @@ +\documentclass{standalone} + +\usepackage{tikz} +\usepackage{xcolor} + +\definecolor{gray0}{HTML}{EEEEEE} +\definecolor{gray1}{HTML}{CCCCCC} +\definecolor{gray2}{HTML}{AAAAAA} +\definecolor{gray3}{HTML}{888888} +\definecolor{gray4}{HTML}{666666} +\definecolor{gray5}{HTML}{444444} +\definecolor{gray6}{HTML}{222222} +\definecolor{gray7}{HTML}{000000} + +% sqrt(3) +\def\sqrtTh{1.732} +% pi +\def\pival{3.14159} + +\begin{document} +\begin{tikzpicture} + \draw(0,0)--(2*\pival/3,2*\pival/\sqrtTh)--(4*\pival/3,0)--(2*\pival/3,-2*\pival/\sqrtTh)--cycle; + + \fill[color=gray0](0,0)--(2*\pival/3,2*\pival/\sqrtTh)--(4*\pival/3,0)--(2*\pival/3,-2*\pival/\sqrtTh)--cycle; + + \fill[color=gray1](2*\pival/3, 2*\pival/3/\sqrtTh)circle(1); + \fill[color=gray1](2*\pival/3,-2*\pival/3/\sqrtTh)circle(1); + + \fill[color=gray2](2*\pival/3, 2*\pival/3/\sqrtTh)circle(0.5); + \fill[color=gray2](2*\pival/3,-2*\pival/3/\sqrtTh)circle(0.5); + + \fill[color=gray3](2*\pival/3, 2*\pival/3/\sqrtTh)circle(0.25); + \fill[color=gray3](2*\pival/3,-2*\pival/3/\sqrtTh)circle(0.25); + + \fill[color=gray4](2*\pival/3, 2*\pival/3/\sqrtTh)circle(0.125); + \fill[color=gray4](2*\pival/3,-2*\pival/3/\sqrtTh)circle(0.125); + + \fill[color=gray5](2*\pival/3, 2*\pival/3/\sqrtTh)circle(0.0626); + \fill[color=gray5](2*\pival/3,-2*\pival/3/\sqrtTh)circle(0.0625); + + \fill[color=gray6](2*\pival/3, 2*\pival/3/\sqrtTh)circle(0.03125); + \fill[color=gray6](2*\pival/3,-2*\pival/3/\sqrtTh)circle(0.03125); + + \fill[color=gray7](2*\pival/3, 2*\pival/3/\sqrtTh)circle(0.015625); + \fill[color=gray7](2*\pival/3,-2*\pival/3/\sqrtTh)circle(0.015625); +\end{tikzpicture} +\end{document} diff --git a/figs/cell-coarse.fig/Makefile b/figs/cell-coarse.fig/Makefile new file mode 100644 index 0000000..147037c --- /dev/null +++ b/figs/cell-coarse.fig/Makefile @@ -0,0 +1,23 @@ +PROJECTNAME=$(basename $(basename $(wildcard *.tikz.tex))) + +PDFS=$(addsuffix .pdf, $(PROJECTNAME)) + +all: $(PDFS) + +$(PDFS): + pdflatex -jobname $(basename $@) $(patsubst %.pdf, %.tikz.tex, $@) + + +install: $(PROJECTNAME) + cp $^.pdf $(INSTALLDIR)/ + + +clean-aux: + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + rm -f $(addsuffix .out, $(PROJECTNAME)) + +clean-tex: + rm -f $(PDFS) $(SYNCTEXS) + +clean: clean-aux clean-tex diff --git a/figs/cell-coarse.fig/cell-coarse.tikz.tex b/figs/cell-coarse.fig/cell-coarse.tikz.tex new file mode 100644 index 0000000..f296cb5 --- /dev/null +++ b/figs/cell-coarse.fig/cell-coarse.tikz.tex @@ -0,0 +1,28 @@ +\documentclass{standalone} + +\usepackage{tikz} +\usepackage{graphene} + +% rescale cells by +\def\rr{4} + +\begin{document} +\begin{tikzpicture} + %\graphene{(0,0)}{12}{12} + \graphene{(-3,3*\sqrtTh)}{17}{16} + + \foreach \i in {0,...,3}{ + \draw[line width=1pt, color=blue](-1*\rr,-\i*\sqrtTh*\rr)--++(1.5*2*\i*\rr+3*\rr,\sqrtThOT*2*\i*\rr+\sqrtTh*\rr); + } + \foreach \i in {0,...,3}{ + \draw[line width=1pt, color=blue](0.5*\rr+3*\i*\rr,-3.5*\sqrtTh*\rr)--++(-1.5*2*\i*\rr+12*\rr,-\sqrtThOT*2*\i*\rr+4*\sqrtTh*\rr); + } + + \foreach \i in {0,...,3}{ + \draw[line width=1pt, color=blue](-1*\rr,-\i*\sqrtTh*\rr)--++(-1.5*2*\i*\rr+10.5*\rr,+\sqrtThOT*2*\i*\rr-3.5*\sqrtTh*\rr); + } + \foreach \i in {0,...,3}{ + \draw[line width=1pt, color=blue](-1*\rr+3*\i*\rr,\sqrtTh*\rr)--++(-1.5*2*\i*\rr+13.5*\rr,\sqrtThOT*2*\i*\rr-4.5*\sqrtTh*\rr); + } +\end{tikzpicture} +\end{document} diff --git a/figs/cell-coarse.fig/graphene.sty b/figs/cell-coarse.fig/graphene.sty new file mode 120000 index 0000000..477bbc1 --- /dev/null +++ b/figs/cell-coarse.fig/graphene.sty @@ -0,0 +1 @@ +../lib/graphene.sty
\ No newline at end of file diff --git a/figs/cell.fig/Makefile b/figs/cell.fig/Makefile new file mode 100644 index 0000000..147037c --- /dev/null +++ b/figs/cell.fig/Makefile @@ -0,0 +1,23 @@ +PROJECTNAME=$(basename $(basename $(wildcard *.tikz.tex))) + +PDFS=$(addsuffix .pdf, $(PROJECTNAME)) + +all: $(PDFS) + +$(PDFS): + pdflatex -jobname $(basename $@) $(patsubst %.pdf, %.tikz.tex, $@) + + +install: $(PROJECTNAME) + cp $^.pdf $(INSTALLDIR)/ + + +clean-aux: + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + rm -f $(addsuffix .out, $(PROJECTNAME)) + +clean-tex: + rm -f $(PDFS) $(SYNCTEXS) + +clean: clean-aux clean-tex diff --git a/figs/cell.fig/cell.tikz.tex b/figs/cell.fig/cell.tikz.tex new file mode 100644 index 0000000..ec66a7c --- /dev/null +++ b/figs/cell.fig/cell.tikz.tex @@ -0,0 +1,30 @@ +\documentclass{standalone} + +\usepackage{tikz} +\usepackage{graphene} + +\begin{document} +\begin{tikzpicture} + \graphene{(0,0)}{3}{3} + + \foreach \i in {0,...,3}{ + \draw[color=blue](-1,-\i*\sqrtTh)--++(1.5*2*\i+3,\sqrtThOT*2*\i+\sqrtTh); + } + \foreach \i in {0,...,3}{ + \draw[color=blue](0.5+3*\i,-3.5*\sqrtTh)--++(-1.5*2*\i+12,-\sqrtThOT*2*\i+4*\sqrtTh); + } + + \foreach \i in {0,...,3}{ + \draw[color=blue](-1,-\i*\sqrtTh)--++(-1.5*2*\i+10.5,+\sqrtThOT*2*\i-3.5*\sqrtTh); + } + \foreach \i in {0,...,3}{ + \draw[color=blue](-1+3*\i,\sqrtTh)--++(-1.5*2*\i+13.5,\sqrtThOT*2*\i-4.5*\sqrtTh); + } + + \draw[color=red] (6,-\sqrtTh)++(0.5,.6)node[rotate=30]{$l_1$}; + \draw[color=red](6,-\sqrtTh)++(0.5,-.6)node[rotate=-30]{$l_2$}; + \pgfsetarrowsend{latex}; + \draw[color=red,line width=1.5pt](6,-\sqrtTh)--++\Lo; + \draw[color=red,line width=1.5pt](6,-\sqrtTh)--++\Lt; +\end{tikzpicture} +\end{document} diff --git a/figs/cell.fig/graphene.sty b/figs/cell.fig/graphene.sty new file mode 120000 index 0000000..477bbc1 --- /dev/null +++ b/figs/cell.fig/graphene.sty @@ -0,0 +1 @@ +../lib/graphene.sty
\ No newline at end of file diff --git a/figs/graphene.fig/Makefile b/figs/graphene.fig/Makefile new file mode 100644 index 0000000..147037c --- /dev/null +++ b/figs/graphene.fig/Makefile @@ -0,0 +1,23 @@ +PROJECTNAME=$(basename $(basename $(wildcard *.tikz.tex))) + +PDFS=$(addsuffix .pdf, $(PROJECTNAME)) + +all: $(PDFS) + +$(PDFS): + pdflatex -jobname $(basename $@) $(patsubst %.pdf, %.tikz.tex, $@) + + +install: $(PROJECTNAME) + cp $^.pdf $(INSTALLDIR)/ + + +clean-aux: + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + rm -f $(addsuffix .out, $(PROJECTNAME)) + +clean-tex: + rm -f $(PDFS) $(SYNCTEXS) + +clean: clean-aux clean-tex diff --git a/figs/graphene.fig/graphene.sty b/figs/graphene.fig/graphene.sty new file mode 120000 index 0000000..477bbc1 --- /dev/null +++ b/figs/graphene.fig/graphene.sty @@ -0,0 +1 @@ +../lib/graphene.sty
\ No newline at end of file diff --git a/figs/graphene.fig/graphene.tikz.tex b/figs/graphene.fig/graphene.tikz.tex new file mode 100644 index 0000000..c78e3e9 --- /dev/null +++ b/figs/graphene.fig/graphene.tikz.tex @@ -0,0 +1,12 @@ +\documentclass{standalone} + +\usepackage{tikz} +\usepackage{graphene} + +\def\bsite#1{\fill#1circle(.1);} + +\begin{document} +\begin{tikzpicture} + \graphene{(0,0)}{3}{3} +\end{tikzpicture} +\end{document} diff --git a/figs/hierarchical_graphene.fig/Makefile b/figs/hierarchical_graphene.fig/Makefile new file mode 100644 index 0000000..e5e1f5d --- /dev/null +++ b/figs/hierarchical_graphene.fig/Makefile @@ -0,0 +1,32 @@ +PROJECTNAME=graphene_vector_field + +DATS=graphene_vector_field.dat +PDFS=$(addsuffix .pdf, $(PROJECTNAME)) +TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME)) + +all: $(PDFS) + +$(PDFS): $(DATS) + gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@) + pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@) + +graphene_vector_field.dat: + meankondo -C graphene.mk > graphene-numkondo.mk + ./gendat > $@ + +install: $(PDFS) + cp $^ $(INSTALLDIR)/ + +clean-aux: + rm -f $(addsuffix .tikz.tex, $(PROJECTNAME)) + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + +clean-dat: + rm -f $(DATS) + rm -f graphene-numkondo.mk + +clean-tex: + rm -f $(PDFS) + +clean: clean-aux clean-tex diff --git a/figs/hierarchical_graphene.fig/gendat b/figs/hierarchical_graphene.fig/gendat new file mode 100755 index 0000000..d905203 --- /dev/null +++ b/figs/hierarchical_graphene.fig/gendat @@ -0,0 +1,30 @@ +#!/bin/bash + +# location of numkondo config +config=$(dirname $0)/graphene-numkondo.mk + +# range and number of points in each direction +minx=-2 +maxx=2 +nx=20 + +miny=-1 +maxy=1 +ny=20 + +# compute each point +for i in $(seq $nx); do + # alpha_0 + alpha0=$(python -c "print($minx+($maxx-($minx))/($nx-1)*($i-1))") + for j in $(seq $ny); do + # alpha_1 + alpha1=$(python -c "print($miny+($maxy-($miny))/($ny-1)*($j-1))") + + # print alphas + echo -n "$alpha0 $alpha1 " + + # compute step and select the relevant lines + dat=$(numkondo -N 1 -F -I "0:$alpha0,1:$alpha1" "$config" | sed -r '/^[^01]/d;s/^[0-9]*://;s/,//' | tr '\n' ' ') + echo "$dat" + done +done diff --git a/figs/hierarchical_graphene.fig/graphene.mk b/figs/hierarchical_graphene.fig/graphene.mk new file mode 100644 index 0000000..7bd1cca --- /dev/null +++ b/figs/hierarchical_graphene.fig/graphene.mk @@ -0,0 +1,148 @@ +## This computes the logarithm of the flow equation + +#!fields +# extrenal fields: xy0 where x=alpha, y=sigma +x:110,120,210,220 +# internal fields: xy1 where x=alpha, y=sigma +i:111,121,211,221 +# all are Fermions +f:110,120,210,220,111,121,211,221 + +& +#!groups +# different spins are independent +(111,211) (121,221) + +& +#!preprocessor_variables + +# psi's with internal fields +psiAU=(1/2)[f110]+[f111], +psiAD=(1/2)[f120]+[f121], +psiBU=(1/2)[f210]+[f211], +psiBD=(1/2)[f220]+[f221], + +psiAU-=(1/2)[f-110]+[f-111], +psiAD-=(1/2)[f-120]+[f-121], +psiBU-=(1/2)[f-210]+[f-211], +psiBD-=(1/2)[f-220]+[f-221], + +# operators with internal fields +O0= +<<$psiAU>*<$psiBU->>+ +<<$psiBU>*<$psiAU->>+ +<<$psiAD>*<$psiBD->>+ +<<$psiBD>*<$psiAD->>, + +O1= +<<$psiAU>*<$psiAU->*<$psiAD>*<$psiAD->>+ +<<$psiBU>*<$psiBU->*<$psiBD>*<$psiBD->>, + +O2= +<<$psiAU>*<$psiAD->*<$psiBD>*<$psiBU->>+ +<<$psiBU>*<$psiBD->*<$psiAD>*<$psiAU->>+ +<<$psiAD>*<$psiAU->*<$psiBU>*<$psiBD->>+ +<<$psiBD>*<$psiBU->*<$psiAU>*<$psiAD->>, + +O3= +<<$psiAU>*<$psiAU->*<$psiBU>*<$psiBU->>+ +<<$psiAD>*<$psiAD->*<$psiBD>*<$psiBD->>, + +O4= +<<$psiAU>*<$psiBU->*<$psiAD>*<$psiBD->>+ +<<$psiBU>*<$psiAU->*<$psiBD>*<$psiAD->>, + +O5= +<<$psiAU>*<$psiAU->*<$psiAD>*<$psiBU->*<$psiBU>*<$psiBD->>+ +<<$psiAD>*<$psiAD->*<$psiAU>*<$psiBD->*<$psiBD>*<$psiBU->>+ +<<$psiBU>*<$psiBU->*<$psiBD>*<$psiAU->*<$psiAU>*<$psiAD->>+ +<<$psiBD>*<$psiBD->*<$psiBU>*<$psiAD->*<$psiAD>*<$psiAU->>, + +O6=<<$psiAU>*<$psiAU->*<$psiAD>*<$psiAD->*<$psiBU>*<$psiBU->*<$psiBD>*<$psiBD->>, + + +# psi's without internal fields +phiAU=[f110], +phiAD=[f120], +phiBU=[f210], +phiBD=[f220], + +phiAU-=[f-110], +phiAD-=[f-120], +phiBU-=[f-210], +phiBD-=[f-220], + +# operators without internal fields +E0= +<<$phiAU>*<$phiBU->>+ +<<$phiBU>*<$phiAU->>+ +<<$phiAD>*<$phiBD->>+ +<<$phiBD>*<$phiAD->>, + +E1= +<<$phiAU>*<$phiAU->*<$phiAD>*<$phiAD->>+ +<<$phiBU>*<$phiBU->*<$phiBD>*<$phiBD->>, + +E2= +<<$phiAU>*<$phiAD->*<$phiBD>*<$phiBU->>+ +<<$phiBU>*<$phiBD->*<$phiAD>*<$phiAU->>+ +<<$phiAD>*<$phiAU->*<$phiBU>*<$phiBD->>+ +<<$phiBD>*<$phiBU->*<$phiAU>*<$phiAD->>, + +E3= +<<$phiAU>*<$phiAU->*<$phiBU>*<$phiBU->>+ +<<$phiAD>*<$phiAD->*<$phiBD>*<$phiBD->>, + +E4= +<<$phiAU>*<$phiBU->*<$phiAD>*<$phiBD->>+ +<<$phiBU>*<$phiAU->*<$phiBD>*<$phiAD->>, + +E5= +<<$phiAU>*<$phiAU->*<$phiAD>*<$phiBU->*<$phiBU>*<$phiBD->>+ +<<$phiAD>*<$phiAD->*<$phiAU>*<$phiBD->*<$phiBD>*<$phiBU->>+ +<<$phiBU>*<$phiBU->*<$phiBD>*<$phiAU->*<$phiAU>*<$phiAD->>+ +<<$phiBD>*<$phiBD->*<$phiBU>*<$phiAD->*<$phiAD>*<$phiAU->>, + +E6=<<$phiAU>*<$phiAU->*<$phiAD>*<$phiAD->*<$phiBU>*<$phiBU->*<$phiBD>*<$phiBD->> + +& +#!propagator +111;211: 1 ,121;221: 1 , +211;111: 1 ,221;121: 1 + +& +#!input_polynomial +<%exp< + <<[l0]>*<$O0>>+ + <<[l1]>*<$O1>>+ + <<[l2]>*<$O2>>+ + <<[l3]>*<$O3>>+ + <<[l4]>*<$O4>>+ + <<[l5]>*<$O5>>+ + <<[l6]>*<$O6>> +>> + +& +#!postprocess_flow_equation +<<8>*<%log_1<$FLOW>>> + +& +#!id_table +0: <$E0>, +1: <$E1>, +2: <$E2>, +3: <$E3>, +4: <$E4>, +5: <$E5>, +6: <$E6> + +& +#!labels + +0:"O0" , +1:"O1" , +2:"O2" , +3:"O3" , +4:"O4" , +5:"O5" , +6:"O6" diff --git a/figs/hierarchical_graphene.fig/graphene_vector_field.gnuplot b/figs/hierarchical_graphene.fig/graphene_vector_field.gnuplot new file mode 100644 index 0000000..9eef976 --- /dev/null +++ b/figs/hierarchical_graphene.fig/graphene_vector_field.gnuplot @@ -0,0 +1,25 @@ +set ylabel "$\\alpha_1$" norotate +set xlabel "$\\alpha_0$" + +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 8,6 standalone + +unset key + +set pointsize 1 + +# color functions + +rgb(r,g,b) = 65536 * int(r) + 256 * int(g) + int(b) +color(x) = rgb(x*255, 0 , (1-x)*255) + +# get min/max +set yrange [-1000:1000] +stats "graphene_vector_field.dat" u (log10(sqrt(($3-$1)**2+($4-$2)**2))) + +set xrange [-2:2] +set yrange [-1:1] + +rescale=15 + +plot "graphene_vector_field.dat" u 1:2:(($3-$1)/sqrt(($3-$1)**2+($4-$2)**2)/rescale):(($4-$2)/sqrt(($3-$1)**2+($4-$2)**2)/rescale):(color((log10(sqrt(($3-$1)**2+($4-$2)**2))-STATS_min)/(STATS_max-STATS_min))) with vec filled head linecolor rgb variable diff --git a/figs/hierarchical_sd.fig/Makefile b/figs/hierarchical_sd.fig/Makefile new file mode 100644 index 0000000..175f61b --- /dev/null +++ b/figs/hierarchical_sd.fig/Makefile @@ -0,0 +1,32 @@ +PROJECTNAME=sd_vector_field + +DATS=sd_vector_field.dat +PDFS=$(addsuffix .pdf, $(PROJECTNAME)) +TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME)) + +all: $(PDFS) + +$(PDFS): $(DATS) + gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@) + pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@) + +sd_vector_field.dat: + meankondo -C sd.mk > sd-numkondo.mk + ./gendat > $@ + +install: $(PDFS) + cp $^ $(INSTALLDIR)/ + +clean-aux: + rm -f $(addsuffix .tikz.tex, $(PROJECTNAME)) + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + +clean-dat: + rm -f $(DATS) + rm -f sd-numkondo.mk + +clean-tex: + rm -f $(PDFS) + +clean: clean-aux clean-tex diff --git a/figs/hierarchical_sd.fig/gendat b/figs/hierarchical_sd.fig/gendat new file mode 100755 index 0000000..08bbdd9 --- /dev/null +++ b/figs/hierarchical_sd.fig/gendat @@ -0,0 +1,30 @@ +#!/bin/bash + +# location of numkondo config +config=$(dirname $0)/sd-numkondo.mk + +# range and number of points in each direction +minx=-1 +maxx=0.5 +nx=20 + +miny=-0.4 +maxy=0.4 +ny=20 + +# compute each point +for i in $(seq $nx); do + # alpha_0 + alpha0=$(python -c "print($minx+($maxx-($minx))/($nx-1)*($i-1))") + for j in $(seq $ny); do + # alpha_1 + alpha1=$(python -c "print($miny+($maxy-($miny))/($ny-1)*($j-1))") + + # print alphas + echo -n "$alpha0 $alpha1 " + + # compute step and select the relevant lines + dat=$(numkondo -N 1 -F -I "0:$alpha0,1:$alpha1" "$config" | sed -r '/^[^01]/d;s/^[0-9]*://;s/,//' | tr '\n' ' ') + echo "$dat" + done +done diff --git a/figs/hierarchical_sd.fig/sd.mk b/figs/hierarchical_sd.fig/sd.mk new file mode 100644 index 0000000..f0bd584 --- /dev/null +++ b/figs/hierarchical_sd.fig/sd.mk @@ -0,0 +1,81 @@ +#!fields +x:100,110 +i:101,102,111,112 +h:400,410,420 +f:100,110,101,102,111,112 +a:400,410,420 + +& +#!preprocessor_variables +psiAu1=[f100]+[f101], +psiAu2=[f100]+[f102], +psiAd1=[f110]+[f111], +psiAd2=[f110]+[f112], + +psiAu1-=[f-100]+[f-101], +psiAu2-=[f-100]+[f-102], +psiAd1-=[f-110]+[f-111], +psiAd2-=[f-110]+[f-112], + +A11=<<$psiAu1>*<$psiAd1->>+<<$psiAd1>*<$psiAu1->>, +A12=<<$psiAu2>*<$psiAd2->>+<<$psiAd2>*<$psiAu2->>, + +A21=<<(-1)s{-1}>*<$psiAu1>*<$psiAd1->>+<<s{-1}>*<$psiAd1>*<$psiAu1->>, +A22=<<(-1)s{-1}>*<$psiAu2>*<$psiAd2->>+<<s{-1}>*<$psiAd2>*<$psiAu2->>, + +A31=<<$psiAu1>*<$psiAu1->>+<<-1>*<$psiAd1>*<$psiAd1->>, +A32=<<$psiAu2>*<$psiAu2->>+<<-1>*<$psiAd2>*<$psiAd2->>, + +AB1=<<$A11>*<[f400]>>+<<$A21>*<[f410]>>+<<$A31>*<[f420]>>, +AA1=<<$A11>*<$A11>>+<<$A21>*<$A21>>+<<$A31>*<$A31>>, + +AB2=<<$A12>*<[f400]>>+<<$A22>*<[f410]>>+<<$A32>*<[f420]>>, +AA2=<<$A12>*<$A12>>+<<$A22>*<$A22>>+<<$A32>*<$A32>>, + + +A1=[f100][f-110] + [f110][f-100], +A2=((-1)s{-1})[f100][f-110] + (s{-1})[f110][f-100], +A3=[f100][f-100] + (-1)[f110][f-110], + +AB=<<$A1>*<[f400]>>+<<$A2>*<[f410]>>+<<$A3>*<[f420]>>, +AA=<<$A1>*<$A1>>+<<$A2>*<$A2>>+<<$A3>*<$A3>> + +& +#!identities +[f400][f400]=(1), +[f400][f410]=(s{-1})[f420], +[f420][f410]=((-1)s{-1})[f400], +[f410][f410]=(1), +[f410][f420]=(s{-1})[f400], +[f400][f420]=((-1)s{-1})[f410], +[f420][f420]=(1), +[f420][f400]=(s{-1})[f410], +[f410][f400]=((-1)s{-1})[f420] + +& +#!propagator +101;102: 1 ,111;112: 1 , +102;101: -1 ,112;111: -1 +& +#!input_polynomial +< + <1> + + <<(1/2)[l0]>*<$AB1>> + + <<(1/2)[l1]>*<$AA1>> +>*< + <1> + + <<(1/2)[l0]>*<$AB2>> + + <<(1/2)[l1]>*<$AA2>> +> + +& + +#!id_table +0: <$AB>, +1: <2>*<$AA> + +& + +#!labels +0:"at" , +1:"aa" , diff --git a/figs/hierarchical_sd.fig/sd_vector_field.gnuplot b/figs/hierarchical_sd.fig/sd_vector_field.gnuplot new file mode 100644 index 0000000..9952d15 --- /dev/null +++ b/figs/hierarchical_sd.fig/sd_vector_field.gnuplot @@ -0,0 +1,25 @@ +set ylabel "$\\ell_1$" norotate +set xlabel "$\\ell_0$" + +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 8,6 standalone + +unset key + +set pointsize 1 + +# color functions + +rgb(r,g,b) = 65536 * int(r) + 256 * int(g) + int(b) +color(x) = rgb(x*255, 0 , (1-x)*255) + +# get min/max +set yrange [-1000:1000] +stats "sd_vector_field.dat" u (log10(sqrt(($3-$1)**2+($4-$2)**2))) + +set xrange [-1:0.5] +set yrange [-0.4:0.4] + +rescale=40 + +plot "sd_vector_field.dat" u 1:2:(($3-$1)/sqrt(($3-$1)**2+($4-$2)**2)/rescale):(($4-$2)/sqrt(($3-$1)**2+($4-$2)**2)/rescale):(color((log10(sqrt(($3-$1)**2+($4-$2)**2))-STATS_min)/(STATS_max-STATS_min))) with vec filled head linecolor rgb variable diff --git a/figs/lib/graphene.sty b/figs/lib/graphene.sty new file mode 100644 index 0000000..4f044ae --- /dev/null +++ b/figs/lib/graphene.sty @@ -0,0 +1,48 @@ +% sqrt(3)/2 +\def\sqrtThOT{0.866} +% sqrt(3) +\def\sqrtTh{1.732} +% pi +\def\pival{3.14159} + +% base vectorsj +\def\Lo{(1.5,\sqrtThOT)} +\def\Lt{(1.5,-\sqrtThOT)} +\def\mLo{(-1.5,-\sqrtThOT)} +\def\mLt{(-1.5,\sqrtThOT)} + +% filled square at #1 of side-length #2 +\def\fullsquare#1#2{\fill#1++(-#2,-#2)--++(#2,0)--++(#2,0)--++(0,#2)--++(0,#2)--++(-#2,0)--++(-#2,0)--++(0,-#2)--++(0,-#2);} +% in color +\def\fullsquarecolor#1#2#3{\fill[color=#3]#1++(-#2,-#2)--++(#2,0)--++(#2,0)--++(0,#2)--++(0,#2)--++(-#2,0)--++(-#2,0)--++(0,-#2)--++(0,-#2);} + +% type-a site at #1 +\def\asite#1{\fill#1circle(.1);} +% in color +\def\asitec#1#2{\fill[color=#2]#1circle(.1);} +% type-b site at #1 +\def\bsite#1{\fullsquare{#1}{.1}} +% in color +\def\bsitec#1#2{\fullsquarecolor{#1}{.1}{#2}} + +% base cell with a site at #1 +\def\cell#1{ + \draw#1--++(0:1); + \draw#1--++(120:1); + \draw#1--++(240:1); + \asite{#1} + \draw#1++(1,0)--++(0:-1); + \draw#1++(1,0)--++(120:-1); + \draw#1++(1,0)--++(240:-1); + \bsite{#1++(1,0)} +} + +% grpahene grid at #1 of width #2 and height #3 +\def\graphene#1#2#3{ + \foreach \i in {0,...,#2}{ + \foreach \j in {0,...,#3}{ + \cell{#1++(\i*3,-2*\j*\sqrtThOT)} + \cell{#1++(\i*3+1.5,\sqrtThOT-2*\j*\sqrtThOT)} + } + } +} |