Added scripts to generate results for the Hubbard dimer.
This commit is contained in:
parent
8095e7c9c5
commit
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cat >> final.tex << '%EOF%'
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\documentclass{article}
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\usepackage{color,graphics,inputenc,amsmath}
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\begin{document}
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\pagenumbering{gobble}
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\clearpage
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\thispagestyle{empty}
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\begin{figure}
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\begin{center}
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\input{texfile}
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\end{center}
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\end{figure}
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\end{document}
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%EOF%
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pdflatex final.tex ;
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rm final.tex | rm final.log | rm final.aux | rm texfile.tex | rm texfile.eps | rm texfile-eps-converted-to.pdf ;
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pdfcrop --margins 10 final.pdf ;
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mv -f final-crop.pdf final.pdf ;
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@ -0,0 +1,111 @@
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set terminal epslatex color
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set output "texfile.tex"
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set style data linespoints
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### line styles
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###
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set style line 1 lt 1 lc rgb "red" lw 4
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set style line 2 dt 3 lc rgb "red" lw 4
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set style line 3 lt 1 lc rgb "dark-green" lw 4
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set style line 4 dt 3 lc rgb "dark-green" lw 4
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set style line 5 lt 1 lc rgb "dark-yellow" lw 4
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set style line 6 dt 3 lc rgb "dark-yellow" lw 4
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set style line 7 lt 1 lc rgb "dark-violet" lw 4
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set style line 8 dt 3 lc rgb "dark-violet" lw 4
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set style line 9 lt 1 lc rgb "blue" lw 4
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set style line 10 dt 3 lc rgb "blue" lw 4
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set style line 11 lt 1 lc rgb "dark-orange" lw 4
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set style line 12 dt 3 lc rgb "dark-orange" lw 2
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set style line 13 lt 1 lc rgb "black" lw 4
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set style line 14 dt 3 lc rgb "black" lw 4
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set style line 15 lt 1 lc rgb "purple" lw 4
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set style line 16 dt 3 lc rgb "purple" lw 4
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set style line 17 lt 1 lc rgb "#483D8B" lw 4
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set style line 18 dt 3 lc rgb "#483D8B" lw 4
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set style line 19 lt 1 lc rgb "#2ECCFA" lw 4
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set style line 20 dt 3 lc rgb "#2ECCFA" lw 4
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set style line 21 lt 1 lc rgb "#58FA82" lw 4
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set style line 22 dt 3 lc rgb "#58FA82" lw 4
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set style line 23 lt 1 lc rgb "#F5BCA9" lw 4
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set style line 24 dt 3 lc rgb "#F5BCA9" lw 4
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set style line 25 lt 1 lc rgb "#8A0829" lw 4
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set style line 26 dt 3 lc rgb "#8A0829" lw 4
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set tmargin 3
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set bmargin 2
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set lmargin 3
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set rmargin 2
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set format x '\tiny {%g}'
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set format y '\tiny {%g}'
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set multiplot layout 2,3 title "$E_w = (1-w)E_0 + w E_1 = fct(\\Delta v)$"
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set title "$U/t = 1$" font "Helvetica,28"
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U=1
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set xrange [-2*U:2*U]
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set key font ",001"
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set key horizontal bmargin
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set key width 5
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plot "../Ew1_Ew2_fctdeltav_Usurt0.0_w0.0" u 1:2 smooth csplines with lines ls 1 title "\\tiny $w = 0$",\
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"../Ew1_Ew2_fctdeltav_Usurt1.0_w0.1" u 1:2 smooth csplines with lines ls 3 title "\\tiny $.1$",\
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"../Ew1_Ew2_fctdeltav_Usurt1.0_w0.2" u 1:2 smooth csplines with lines ls 5 title "\\tiny $.2$",\
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"../Ew1_Ew2_fctdeltav_Usurt1.0_w0.3" u 1:2 smooth csplines with lines ls 7 title "\\tiny $.3$",\
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"../Ew1_Ew2_fctdeltav_Usurt1.0_w0.4" u 1:2 smooth csplines with lines ls 9 title "\\tiny $.4$",\
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"../Ew1_Ew2_fctdeltav_Usurt1.0_w0.5" u 1:2 smooth csplines with lines ls 11 title "\\tiny $.5$";
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set title "$U/t = 2$" font "Helvetica,28"
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U=2
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set xrange [-2*U:2*U]
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unset key
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plot "../Ew1_Ew2_fctdeltav_Usurt0.0_w0.0" u 1:2 smooth csplines with lines ls 1 title "$w = 0$",\
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"../Ew1_Ew2_fctdeltav_Usurt2.0_w0.1" u 1:2 smooth csplines with lines ls 3 title "$w = 0.1$",\
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"../Ew1_Ew2_fctdeltav_Usurt2.0_w0.2" u 1:2 smooth csplines with lines ls 5 title "$w = 0.2$",\
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"../Ew1_Ew2_fctdeltav_Usurt2.0_w0.3" u 1:2 smooth csplines with lines ls 7 title "$w = 0.3$",\
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"../Ew1_Ew2_fctdeltav_Usurt2.0_w0.4" u 1:2 smooth csplines with lines ls 9 title "$w = 0.4$",\
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"../Ew1_Ew2_fctdeltav_Usurt2.0_w0.5" u 1:2 smooth csplines with lines ls 11 title "$w = 0.5$";
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set title "$U/t = 5$" font "Helvetica,28"
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unset key
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U=5
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set xrange [-2*U:2*U]
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plot "../Ew1_Ew2_fctdeltav_Usurt5.0_w0.0" u 1:2 smooth csplines with lines ls 1 title "$w = 0$",\
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"../Ew1_Ew2_fctdeltav_Usurt5.0_w0.1" u 1:2 smooth csplines with lines ls 3 title "$w = 0.1$",\
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"../Ew1_Ew2_fctdeltav_Usurt5.0_w0.2" u 1:2 smooth csplines with lines ls 5 title "$w = 0.2$",\
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"../Ew1_Ew2_fctdeltav_Usurt5.0_w0.3" u 1:2 smooth csplines with lines ls 7 title "$w = 0.3$",\
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"../Ew1_Ew2_fctdeltav_Usurt5.0_w0.4" u 1:2 smooth csplines with lines ls 9 title "$w = 0.4$",\
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"../Ew1_Ew2_fctdeltav_Usurt5.0_w0.5" u 1:2 smooth csplines with lines ls 11 title "$w = 0.5$";
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set title "$U/t = 10$" font "Helvetica,28"
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unset key
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U=10
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set xrange [-2*U:2*U]
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plot "../Ew1_Ew2_fctdeltav_Usurt10.0_w0.0" u 1:2 smooth csplines with lines ls 1 title "$w = 0$",\
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"../Ew1_Ew2_fctdeltav_Usurt10.0_w0.1" u 1:2 smooth csplines with lines ls 3 title "$w = 0.1$",\
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"../Ew1_Ew2_fctdeltav_Usurt10.0_w0.2" u 1:2 smooth csplines with lines ls 5 title "$w = 0.2$",\
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"../Ew1_Ew2_fctdeltav_Usurt10.0_w0.3" u 1:2 smooth csplines with lines ls 7 title "$w = 0.3$",\
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"../Ew1_Ew2_fctdeltav_Usurt10.0_w0.4" u 1:2 smooth csplines with lines ls 9 title "$w = 0.4$",\
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"../Ew1_Ew2_fctdeltav_Usurt10.0_w0.5" u 1:2 smooth csplines with lines ls 11 title "$w = 0.5$";
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set title "$U/t = 100$" font "Helvetica,28"
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unset key
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U = 100
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set xrange [-2*U:2*U]
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plot "../Ew1_Ew2_fctdeltav_Usurt100.0_w0.0" u 1:2 smooth csplines with lines ls 1 title "$w = 0$",\
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"../Ew1_Ew2_fctdeltav_Usurt100.0_w0.1" u 1:2 smooth csplines with lines ls 3 title "$w = 0.1$",\
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"../Ew1_Ew2_fctdeltav_Usurt100.0_w0.2" u 1:2 smooth csplines with lines ls 5 title "$w = 0.2$",\
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"../Ew1_Ew2_fctdeltav_Usurt100.0_w0.3" u 1:2 smooth csplines with lines ls 7 title "$w = 0.3$",\
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"../Ew1_Ew2_fctdeltav_Usurt100.0_w0.4" u 1:2 smooth csplines with lines ls 9 title "$w = 0.4$",\
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"../Ew1_Ew2_fctdeltav_Usurt100.0_w0.5" u 1:2 smooth csplines with lines ls 11 title "$w = 0.5$";
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set title "$U/t = 1000$" font "Helvetica,28"
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unset key
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U = 1000
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set xrange [-2*U:2*U]
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plot "../Ew1_Ew2_fctdeltav_Usurt1000.0_w0.0" u 1:2 smooth csplines with lines ls 1 title "$w = 0$",\
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"../Ew1_Ew2_fctdeltav_Usurt1000.0_w0.1" u 1:2 smooth csplines with lines ls 3 title "$w = 0.1$",\
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"../Ew1_Ew2_fctdeltav_Usurt1000.0_w0.2" u 1:2 smooth csplines with lines ls 5 title "$w = 0.2$",\
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"../Ew1_Ew2_fctdeltav_Usurt1000.0_w0.3" u 1:2 smooth csplines with lines ls 7 title "$w = 0.3$",\
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"../Ew1_Ew2_fctdeltav_Usurt1000.0_w0.4" u 1:2 smooth csplines with lines ls 9 title "$w = 0.4$",\
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"../Ew1_Ew2_fctdeltav_Usurt1000.0_w0.5" u 1:2 smooth csplines with lines ls 11 title "$w = 0.5$";
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unset multiplot
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@ -0,0 +1,111 @@
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set terminal epslatex color
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set output "texfile.tex"
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set style data linespoints
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### line styles
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###
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set style line 1 lt 1 lc rgb "red" lw 4
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set style line 2 dt 3 lc rgb "red" lw 4
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set style line 3 lt 1 lc rgb "dark-green" lw 4
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set style line 4 dt 3 lc rgb "dark-green" lw 4
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set style line 5 lt 1 lc rgb "dark-yellow" lw 4
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set style line 6 dt 3 lc rgb "dark-yellow" lw 4
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set style line 7 lt 1 lc rgb "dark-violet" lw 4
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set style line 8 dt 3 lc rgb "dark-violet" lw 4
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set style line 9 lt 1 lc rgb "blue" lw 4
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set style line 10 dt 3 lc rgb "blue" lw 4
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set style line 11 lt 1 lc rgb "dark-orange" lw 4
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set style line 12 dt 3 lc rgb "dark-orange" lw 2
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set style line 13 lt 1 lc rgb "black" lw 4
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set style line 14 dt 3 lc rgb "black" lw 4
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set style line 15 lt 1 lc rgb "purple" lw 4
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set style line 16 dt 3 lc rgb "purple" lw 4
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set style line 17 lt 1 lc rgb "#483D8B" lw 4
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set style line 18 dt 3 lc rgb "#483D8B" lw 4
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set style line 19 lt 1 lc rgb "#2ECCFA" lw 4
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set style line 20 dt 3 lc rgb "#2ECCFA" lw 4
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set style line 21 lt 1 lc rgb "#58FA82" lw 4
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set style line 22 dt 3 lc rgb "#58FA82" lw 4
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set style line 23 lt 1 lc rgb "#F5BCA9" lw 4
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set style line 24 dt 3 lc rgb "#F5BCA9" lw 4
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set style line 25 lt 1 lc rgb "#8A0829" lw 4
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set style line 26 dt 3 lc rgb "#8A0829" lw 4
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set tmargin 3
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set bmargin 2
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set lmargin 3
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set rmargin 2
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set format x '\tiny {%g}'
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set format y '\tiny {%g}'
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set multiplot layout 2,3 title "$E_w = (1-w)E_0 + w E_2 = fct(\\Delta v)$"
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set title "$U/t = 1$" font "Helvetica,28"
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U=1
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set xrange [-2*U:2*U]
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set key font ",001"
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set key horizontal bmargin
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set key width 5
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plot "../Ew1_Ew2_fctdeltav_Usurt0.0_w0.0" u 1:3 smooth csplines with lines ls 1 title "\\tiny $w = 0$",\
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"../Ew1_Ew2_fctdeltav_Usurt1.0_w0.1" u 1:3 smooth csplines with lines ls 3 title "\\tiny $.1$",\
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"../Ew1_Ew2_fctdeltav_Usurt1.0_w0.2" u 1:3 smooth csplines with lines ls 5 title "\\tiny $.2$",\
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"../Ew1_Ew2_fctdeltav_Usurt1.0_w0.3" u 1:3 smooth csplines with lines ls 7 title "\\tiny $.3$",\
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"../Ew1_Ew2_fctdeltav_Usurt1.0_w0.4" u 1:3 smooth csplines with lines ls 9 title "\\tiny $.4$",\
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"../Ew1_Ew2_fctdeltav_Usurt1.0_w0.5" u 1:3 smooth csplines with lines ls 11 title "\\tiny $.5$";
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set title "$U/t = 2$" font "Helvetica,28"
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U=2
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set xrange [-2*U:2*U]
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unset key
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plot "../Ew1_Ew2_fctdeltav_Usurt0.0_w0.0" u 1:3 smooth csplines with lines ls 1 title "$w = 0$",\
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"../Ew1_Ew2_fctdeltav_Usurt2.0_w0.1" u 1:3 smooth csplines with lines ls 3 title "$w = 0.1$",\
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"../Ew1_Ew2_fctdeltav_Usurt2.0_w0.2" u 1:3 smooth csplines with lines ls 5 title "$w = 0.2$",\
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"../Ew1_Ew2_fctdeltav_Usurt2.0_w0.3" u 1:3 smooth csplines with lines ls 7 title "$w = 0.3$",\
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"../Ew1_Ew2_fctdeltav_Usurt2.0_w0.4" u 1:3 smooth csplines with lines ls 9 title "$w = 0.4$",\
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"../Ew1_Ew2_fctdeltav_Usurt2.0_w0.5" u 1:3 smooth csplines with lines ls 11 title "$w = 0.5$";
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set title "$U/t = 5$" font "Helvetica,28"
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unset key
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U=5
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set xrange [-2*U:2*U]
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plot "../Ew1_Ew2_fctdeltav_Usurt5.0_w0.0" u 1:3 smooth csplines with lines ls 1 title "$w = 0$",\
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"../Ew1_Ew2_fctdeltav_Usurt5.0_w0.1" u 1:3 smooth csplines with lines ls 3 title "$w = 0.1$",\
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"../Ew1_Ew2_fctdeltav_Usurt5.0_w0.2" u 1:3 smooth csplines with lines ls 5 title "$w = 0.2$",\
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"../Ew1_Ew2_fctdeltav_Usurt5.0_w0.3" u 1:3 smooth csplines with lines ls 7 title "$w = 0.3$",\
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"../Ew1_Ew2_fctdeltav_Usurt5.0_w0.4" u 1:3 smooth csplines with lines ls 9 title "$w = 0.4$",\
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"../Ew1_Ew2_fctdeltav_Usurt5.0_w0.5" u 1:3 smooth csplines with lines ls 11 title "$w = 0.5$";
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set title "$U/t = 10$" font "Helvetica,28"
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unset key
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U=10
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set xrange [-2*U:2*U]
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plot "../Ew1_Ew2_fctdeltav_Usurt10.0_w0.0" u 1:3 smooth csplines with lines ls 1 title "$w = 0$",\
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"../Ew1_Ew2_fctdeltav_Usurt10.0_w0.1" u 1:3 smooth csplines with lines ls 3 title "$w = 0.1$",\
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"../Ew1_Ew2_fctdeltav_Usurt10.0_w0.2" u 1:3 smooth csplines with lines ls 5 title "$w = 0.2$",\
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"../Ew1_Ew2_fctdeltav_Usurt10.0_w0.3" u 1:3 smooth csplines with lines ls 7 title "$w = 0.3$",\
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"../Ew1_Ew2_fctdeltav_Usurt10.0_w0.4" u 1:3 smooth csplines with lines ls 9 title "$w = 0.4$",\
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"../Ew1_Ew2_fctdeltav_Usurt10.0_w0.5" u 1:3 smooth csplines with lines ls 11 title "$w = 0.5$";
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set title "$U/t = 100$" font "Helvetica,28"
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unset key
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U = 100
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set xrange [-2*U:2*U]
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plot "../Ew1_Ew2_fctdeltav_Usurt100.0_w0.0" u 1:3 smooth csplines with lines ls 1 title "$w = 0$",\
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"../Ew1_Ew2_fctdeltav_Usurt100.0_w0.1" u 1:3 smooth csplines with lines ls 3 title "$w = 0.1$",\
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"../Ew1_Ew2_fctdeltav_Usurt100.0_w0.2" u 1:3 smooth csplines with lines ls 5 title "$w = 0.2$",\
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"../Ew1_Ew2_fctdeltav_Usurt100.0_w0.3" u 1:3 smooth csplines with lines ls 7 title "$w = 0.3$",\
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"../Ew1_Ew2_fctdeltav_Usurt100.0_w0.4" u 1:3 smooth csplines with lines ls 9 title "$w = 0.4$",\
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"../Ew1_Ew2_fctdeltav_Usurt100.0_w0.5" u 1:3 smooth csplines with lines ls 11 title "$w = 0.5$";
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set title "$U/t = 1000$" font "Helvetica,28"
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unset key
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U = 1000
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set xrange [-2*U:2*U]
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plot "../Ew1_Ew2_fctdeltav_Usurt1000.0_w0.0" u 1:3 smooth csplines with lines ls 1 title "$w = 0$",\
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"../Ew1_Ew2_fctdeltav_Usurt1000.0_w0.1" u 1:3 smooth csplines with lines ls 3 title "$w = 0.1$",\
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"../Ew1_Ew2_fctdeltav_Usurt1000.0_w0.2" u 1:3 smooth csplines with lines ls 5 title "$w = 0.2$",\
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"../Ew1_Ew2_fctdeltav_Usurt1000.0_w0.3" u 1:3 smooth csplines with lines ls 7 title "$w = 0.3$",\
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"../Ew1_Ew2_fctdeltav_Usurt1000.0_w0.4" u 1:3 smooth csplines with lines ls 9 title "$w = 0.4$",\
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"../Ew1_Ew2_fctdeltav_Usurt1000.0_w0.5" u 1:3 smooth csplines with lines ls 11 title "$w = 0.5$";
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unset multiplot
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@ -0,0 +1,164 @@
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from __future__ import print_function
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import math
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import scipy
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import scipy.optimize as opt
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import sys
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import numpy as np
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import scipy.linalg as sl
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import subprocess
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def correlation_2L(U,t,occ,imp_model=False):
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"""
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Second parametrization for the Hubbard dimer,
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see Senjean et al. Theoretical Chemistry Accounts (2018) 137:169 (or Carrascal paper). Careful : both have a corrigendum...
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imp_model = True will set u = U/4t instead of U/2t.
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"""
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occ_tmp = 0
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if U == 0:
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U =0.000001
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if occ == 1:
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occ = 0.99999
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occ_tmp = 1
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sign = lambda x: x and (1, -1)[x<0]
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rho = abs(occ - 1)
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# For the impurity case, u = U/4t and not U/2t as in the fully-interacting dimer.
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if imp_model:
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u = U/(4*t)
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else:
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u = U/(2*t)
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# Impurity correlation energy
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a_12 = 0.5*(1 - rho)
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a_21 = 0.5*np.sqrt(rho*(1- rho)/2.0)
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a_11 = a_21*(1 + 1.0/rho)
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a_22 = a_12*0.5
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a_1 = a_11 + u*a_12
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a_2 = a_21 + u*a_22
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da12_drho = - 0.5
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da21_drho = (1 - 2*rho)/(8*np.sqrt((1 - rho)*rho/2))
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da11_drho = da21_drho*(1 + 1.0/rho) - a_21/rho**2
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da22_drho = - 0.25
|
||||
da1_drho = da11_drho + u*da12_drho
|
||||
da2_drho = da21_drho + u*da22_drho
|
||||
N = (1 - rho)*(1 + rho*(1 + (1 + rho)**3*u*a_1))
|
||||
D = 1 + (1 + rho)**3*u*a_2
|
||||
dN_drho = - 1 + (1 - 2*rho)*(1 + (1 + rho)**3*u*a_1) + rho*u*(1 - rho)*(1 + rho)**2*(3*a_1 + (1 + rho)*da1_drho)
|
||||
dD_drho = u*(1 + rho)**2*(3*a_2 + (1 + rho)*da2_drho)
|
||||
g0 = np.sqrt((1 - rho)*(1 + rho*(1 + (1 + rho)**3*u*a_1))/(1 + (1 + rho)**3*u*a_2))
|
||||
dg0_drho = (dN_drho - g0**2*dD_drho)/(2*g0*D)
|
||||
Y0 = np.sqrt(1 - g0**2 - rho**2)
|
||||
dh_dg0 = g0*(g0**4 + 3*g0**2*rho**2 + 2*rho**2*(rho**2 - 1 - Y0))/(2*(g0**2 + rho**2)**2*Y0)
|
||||
j = (1 - rho)*(1 + rho)**3*u**2
|
||||
k = (3*rho/2 - 1 + rho*(1 + rho)**3*u*a_2)*a_12 - rho*(1 + (1 + rho)**3*u*a_1)*a_22
|
||||
l = 2*g0*(1 + (1 + rho)**3*u*a_2)**2
|
||||
q = j*k/l
|
||||
g1 = g0 + (u*dh_dg0 - 1)*q
|
||||
Y1 = np.sqrt(1 - g1**2 - rho**2)
|
||||
h = (g1**2*(1 - Y1) + 2*rho**2)/(2*(g1**2 + rho**2))
|
||||
f = -2*t*(g1 - u*h)
|
||||
Ts = - 2*t*np.sqrt(occ*(2 - occ))
|
||||
EHx = (u*2*t)*(1.0+occ*((0.5*occ)-1.0))
|
||||
Ec = f - Ts - EHx
|
||||
|
||||
# Derivative with respect to U
|
||||
da1_du = a_12
|
||||
da2_du = a_22
|
||||
v = 2*Y0*(g0**2 + rho**2)**2
|
||||
w = g0*(g0**4 + 3*g0**2*rho**2 + 2*rho**2*(rho**2 - 1 - Y0))
|
||||
dj_du = 2*(1 - rho)*(1 + rho)**3*u
|
||||
G = N/D
|
||||
dN_du = (1 - rho)*rho*(1 + rho)**3*(a_1 + u*da1_du)
|
||||
dD_du = (1 + rho)**3*(a_2 + u*da2_du)
|
||||
dG_du = (dN_du*D - N*dD_du)/D**2
|
||||
dg0_du = dG_du/(2*np.sqrt(G))
|
||||
dk_du = a_12*(rho*(1 + rho)**3*(a_2 + u*da2_du)) - a_22*(rho*(1 + rho)**3*(a_1 + u*da1_du))
|
||||
dl_du = 4*g0*(1 + (1 + rho)**3*u*a_2)*(1 + rho)**3*(a_2 + u*da2_du) + 2*dg0_du*(1 + (1 + rho)**3*u*a_2)**2
|
||||
dw_du = dg0_du*(g0**4 + 3*g0**2*rho**2 + 2*rho**2*(rho**2 - 1 - Y0) + g0*(4*g0**3 + 6*g0*rho**2 + 2*rho**2*g0/Y0))
|
||||
dv_du = g0*(g0**2 + rho**2)*dg0_du*(-2*(g0**2 + rho**2)/Y0 + 8*Y0)
|
||||
dh_dg1 = g1*(g1**4 + 3*g1**2*rho**2 + 2*rho**2*(rho**2 - 1 - Y1))/(2*(g1**2 + rho**2)**2*Y1)
|
||||
dq_du = ( (dj_du*k + j*dk_du)*l - j*k*dl_du )/l**2
|
||||
ddh_ddug0 = (dw_du*v - w*dv_du)/v**2
|
||||
dg1_du = dg0_du + (dh_dg0 + u*ddh_ddug0)*q + (u*dh_dg0 - 1)*dq_du
|
||||
dh_du = dg1_du*dh_dg1
|
||||
df_du = -2*t*(dg1_du - h - u*dh_du)
|
||||
dEc_dU =(u/U)*df_du - (1 + occ*(0.5*occ - 1))*(u*2*t/U)
|
||||
|
||||
# Derivative with respect to t
|
||||
dEc_dt = Ec/t - U*dEc_dU/t
|
||||
|
||||
# Derivative with respect to n
|
||||
if occ_tmp == 1:
|
||||
dEc_dn = 0
|
||||
else:
|
||||
drho_dn = sign(occ - 1)
|
||||
dTs_dn = - 2*t*(1 - occ)/np.sqrt(occ*(2 - occ))
|
||||
# Note that P = j*k and Q = l in Eq. 155 of Ref. Senjean et al. Theoretical Chemistry Accounts (2018) 137:169
|
||||
dP_drho = (3*(1 - rho)*(1 + rho)**2 - (1 + rho)**3)*u**2*((3*rho/2 - 1 + rho*(1 + rho)**3*u*a_2)*a_12 \
|
||||
- rho*(1 + (1 + rho)**3*u*a_1)*a_22) \
|
||||
+ (1 - rho)*(1 + rho)**3*u**2*((3/2.0 + 3*u*(1 + rho)**2*rho*a_2 \
|
||||
+ u*(1 + rho)**3*(a_2 + rho*da2_drho))*a_12 \
|
||||
+ (3*rho/2 - 1 + rho*(1 + rho)**3*u*a_2)*da12_drho - (rho*da22_drho + a_22)*(1 + (1 + rho)**3*u*a_1) \
|
||||
- rho*a_22*(3*(1 + rho)**2*u*a_1 + (1 + rho)**3*u*da1_drho))
|
||||
dQ_drho = 2*dg0_drho*(1 + (1 + rho)**3*u*a_2)**2 + 4*g0*(1 + (1 + rho)**3*u*a_2)*u*(3.0*(1 + rho)**2*a_2 + (1 + rho)**3*da2_drho)
|
||||
dq_drho = (dP_drho*l - j*k*dQ_drho)/l**2
|
||||
ddh_ddrhog0 = (- dg0_drho*(g0**2 + rho**2) + 4*g0*(g0*dg0_drho + rho))*(2*rho**2 + g0**2*(1 - Y0))/(g0**2 + rho**2)**3 \
|
||||
- g0*(4*rho + 2*g0*dg0_drho*(1 - Y0) + g0**2*(g0*dg0_drho + rho)/Y0)/(g0**2 + rho**2)**2 \
|
||||
- (g0*dg0_drho + rho)*(2*g0*(1 - Y0) + g0**3/Y0)/(g0**2 + rho**2)**2 \
|
||||
+ (2*dg0_drho*(1 - Y0) + 2*g0*rho/Y0 + 5*g0**2*dg0_drho/Y0 + g0**3*(g0*dg0_drho + rho)/Y0**3)/(2*(g0**2 + rho**2))
|
||||
dg1_drho = dg0_drho + (u*dh_dg0 - 1)*dq_drho + u*ddh_ddrhog0*q
|
||||
dh1_drho = (1/(2*(g1**2 + rho**2)))*(4*rho + 2*g1*dg1_drho*(1 - Y1) + g1**2*(g1*dg1_drho + rho)/Y1) \
|
||||
- (g1*dg1_drho + rho)*(2*rho**2 + g1**2*(1 - Y1))/(g1**2 + rho**2)**2
|
||||
df_drho = -2*t*(dg1_drho - u*dh1_drho)
|
||||
dEHxc_dn = drho_dn*df_drho - dTs_dn
|
||||
dEc_dn = drho_dn*df_drho - dTs_dn - (u*2*t)*(occ - 1)
|
||||
return Ec, dEc_dU, dEc_dt, dEc_dn, f
|
||||
|
||||
def u(twot,bigu):
|
||||
return bigu/twot
|
||||
def nu(twot,deltav):
|
||||
return deltav/twot
|
||||
def omega(nu,u):
|
||||
return np.sqrt(3.0*(1.0+(nu**2))+(u**2))
|
||||
def theta(u,nu,w):
|
||||
return (1.0/3.0)*np.arccos((u/(w**3))*(9.0*(nu**2-0.5)-u**2))
|
||||
def r(twot,bigu,deltav):
|
||||
return np.sqrt(3.0*(twot**2 + deltav**2) + bigu**2)
|
||||
def thetatilde(twot,bigu,deltav):
|
||||
return (1.0/3.0)*np.arccos((9.0*bigu*(deltav**2-(twot**2)/2.0) - bigu**3)/(r(twot,bigu,deltav)**3))
|
||||
def E(twot,bigu,deltav,i): # i = 0 --> GS (should be same as above, not tested), i = 1 --> ES.
|
||||
return 2.0*bigu/3.0 + (2.0*r(twot,bigu,deltav)/3.0)*np.cos(thetatilde(twot,bigu,deltav) + 2.0*np.pi*(i+1.0)/3.0)
|
||||
def dE_dv(twot,bigu,deltav,i):
|
||||
return 2.0*deltav*(2.0*bigu/3.0 + (2.0*r(twot,bigu,deltav)/3.0)*np.cos(thetatilde(twot,bigu,deltav) + 2.0*np.pi*(i+1.0)/3.0))/(3.0*(2.0*bigu/3.0 + (2.0*r(twot,bigu,deltav)/3.0)*np.cos(thetatilde(twot,bigu,deltav) + 2.0*np.pi*(i+1.0)/3.0))**2 - 4.0*bigu*(2.0*bigu/3.0 + (2.0*r(twot,bigu,deltav)/3.0)*np.cos(thetatilde(twot,bigu,deltav) + 2.0*np.pi*(i+1.0)/3.0)) + bigu**2 - twot**2 - deltav**2)
|
||||
def Ebar(twot,bigu,deltavbar):
|
||||
return E(twot,bigu,deltavbar*bigu)
|
||||
def E0_1(twot,deltav):
|
||||
return - np.sqrt(twot**2/4.0 + (deltav**2/4.0))
|
||||
def Ts_func(n,twot):
|
||||
return -twot*np.sqrt(n*(2.0-n))
|
||||
def EHx_func(n,bigu):
|
||||
return bigu*(1.0+n*((0.5*n)-1.0))
|
||||
def EH_func(n,bigu):
|
||||
return bigu*(1.0+(n-1.0)**2)
|
||||
def dE0_1_dv(twot,deltav):
|
||||
return - deltav/(2*np.sqrt(twot**2 + deltav**2))
|
||||
# ensemble energy (ground and first excited state)
|
||||
def Eens_1(twot,bigu,deltav,w):
|
||||
return (1-w)*E(twot,bigu,deltav,0) + w*E(twot,bigu,deltav,1)
|
||||
# ensemble energy (ground and second excited state)
|
||||
def Eens_2(twot,bigu,deltav,w):
|
||||
return (1-w)*E(twot,bigu,deltav,0) + w*E(twot,bigu,deltav,2)
|
||||
|
||||
if __name__ == "__main__":
|
||||
t = 1
|
||||
twot = 2*t
|
||||
wlist = [0.0,0.1,0.2,0.3,0.4,0.5]
|
||||
Ulist = [1.0,2.0,5.0,10.0,100.0,1000.0]
|
||||
for w in wlist:
|
||||
for bigu in Ulist:
|
||||
LF_gs_gace_edft = open("Ew1_Ew2_fctdeltav_Usurt" + str(bigu) + "_w" + str(w), "w")
|
||||
v = range(int(-bigu-100),int(bigu+100))
|
||||
number_of_values = 3
|
||||
format_string_str = number_of_values*"{:>8} "
|
||||
format_string_real = number_of_values*"{:8.4f} "
|
||||
print(format_string_str.format("deltav","Ew_1","Ew_2"),file = LF_gs_gace_edft)
|
||||
for deltav in v:
|
||||
print(format_string_real.format(deltav,Eens_1(twot,bigu,deltav,w),Eens_2(twot,bigu,deltav,w)),file = LF_gs_gace_edft)
|
||||
Loading…
Reference in New Issue