set title "spin-1/2-AFM-Heisenberg-chain PBC groundstate, 2e0=1/4-ln(2), N=4..40" set key top left set xlabel "N^(-2)" set ylabel "e0(N)-e0" e0=0.5*(1/4.-log(2.)) set logscale xy # FS corrections: +2*e0/$1**2-4*e0/$1**4 ? plot -2*e0*x w l,\ "-" u (1./$1**2):(($2-e0)*0.5) t "0.5(e0(5,7,9,...)-e0)" w p,\ "-" u (1./$1**2):((e0-$2) ) t " -(e0(4,6,8,...)-e0)" w p # #til0 i0 odd ## kx(E0)=(N+1)/4 kx(E1)=(N+1)/4 - 1 + 2*((N+1)/2%2) ??? # E1/Nw is not always correct! sometimes it is E1 of E0-symspace! # N E0/Nw E1/Nw (s=1) SMag=m^2 # 3 -0.25000000 0.25000000 0.41666667 cx1 ea=2 5 -0.18680340 -0.05590170 0.32888540 cx1 ea=2 SMag?=0.22472140 wrong cx1 cx2 (c0,c1 gemittelt) 7 -0.20394138 -0.12901967 0.27537428 cx2 ea=2 9 -0.21096110 -0.16311893 0.23737171 cx2 ea=2 11 -0.21449711 -0.18145533 0.21012133 cx3 ea=2 13 -0.21652247 -0.19237983 0.18889346 cx3 ea=2(trivial +x10) 15 -0.21778892 -0.19939346 0.17222209 cx4 17 -0.21863295 -0.20415731 0.15849311 cx4 c0=c1 19 -0.21922338 -0.20753805 0.14713114 cx5 cx5=c0=c1 cx4 21 -0.21965245 -0.21002274 0.13743465 cx5 cx6 23 -0.21997399 -0.21190183 0.12913439 cx6 cx5 # -0.21997399 -0.21190183 0.12913439 cxx6 cxy 8*1comp2 1s,2s 2011-10 m_1d 25 -0.22022113 -0.21335709 0.12187402 cx6 cx7 27 -0.22041516 -0.21450695 0.11551121 cx7 cx6 12m,16m,18m (SiSj+SS 5h) # -0.22041516 -0.20821699 0.11551121 sisj=3zizj x7,x7 4*16comp2.flt=30s 29 -0.22057027 -0.20995251 0.10984443 cxx7 n1=2.7e6 nzx=16.00 8*1comp2=e26s,v54s 2011-10 31 -0.22069621 -.211370875 0.10479149 cxx8 n1=9.7e6 nzx=17.00(3..31) 8*1comp2=sh41s,e103s 33 -0.22079986 -.212544799 0.10022913 cxx8 n1=35e6 nzx=18.00(3..33) 8comp2:n39s,h161s,e8m,v16m 35 -0.22088618 -.213527323 0.09610662 cxx9 n1=130e6 nzx=19.00(3..35) 8comp2:n2m,h11m 4*8comp2:n2m,h5m,e13m 37 -0.22095883 -.214357862 0.09234394 cxx9 n1=478e6 nzx=20.00(3..37) 8comp2:n9m,h44m 4*8comp2:n9m,h21m,e53m,v130m xx11=-.21428843 39 -0.22102055 -.215066191 0.08890812 cxx10 n1=1.77e9 nzx=21.00(3..39) 8comp2:n35m,180m 4*16comp2=n35m,h79m,e230m,v6h,zz15h # 41 0 - 0 cxx10 n1=6.56e9 nzx=22(3..41) 16*16comp2.n138m,SH=37m,i100=ERR #inf -0.22157359 -0.22157359 0.00000001 # end of odd N e # #til0 i0 even n1=N!/(N/2)!**2/(2N) (SH=bandmatrix) N E0/Nw E1/Nw (s=1) SMag=m^2 4 -0.25 -0.125 0.5 6 -0.23356464 -0.176503 0.38867517 js 8 -0.22819334 -0.1955261 0.32266975 js 10 -0.22577232 -0.20461037 0.27814000 js E0=E !!! 12 -0.22447462 -0.2096476 0.24572716 js 14 -0.22369820 -0.21273014 0.22090875 js 16 -0.22319676 -0.21475333 0.20120173 ri E0=E/2 !!!??? 18 -0.22285414 -0.21615277 0.18511785 ri 20 -0.22260966 -0.21716102 0.17170570 ri 22 -0.22242911 -0.21791153 0.16054721 js 24 -0.22229197 -0.21848528 0.15053256 ri 26 -0.22218536 -0.21893378 0.14200261 28 -0.22210085 -0.21929103 0.13449742 30 -0.22203272 -0.21254371 0.12783583 js xx15_0- 32 -0.22197699 -0.2198176 0.12187783 n1=4.7e6 nzx=17.52 32meggie SH=0.12 Jan09 34 -0.22193083 -0.22001496 0.11651335 n1=17e6 nxz=18.52 32meggie SH=0.53 i100=0.77 q_17_0- Jan09 36 -0.22189216 -0.22018072 0.11165458 n1=63e6 nzx=19.51 32meggie SH=1.90 i100=3.06 q_0_0+ Jan09 H=11GB,v=1GB # 36 -0.221892164167 # dbl 38 -0.22185945 -0.22032133 0.10723050 n1=233e6 nzx=20.51 32meggie SH=7.90 i100=12.18 44GB q_19_0- 40 -0.22183153 -0.21641946 0.10318309 n1=862e6 nzx=21.51 8*1comp2:ns=143m,SH=149m,i100=236m,zz=194m 2011-10-23 AH=64 # 42 -0.22180752 -0.22054535 n1=3.2e9=2^31.6 nzx=22.51 900*1SC*550MB 704GB nsp=50m SH=50m i100=215m j290 hanging # 44 2.8TB need better balance to fit into memory #inf -0.22157359 -0.22157359 0.00000001 # e0=1./8-log(2)/2 # # B.-D. D"orfel J.Phys.A:Math.Gen.22(1989)L657: gap-formel wrong? or big O(N) # E0=1/4-ln(2) # PR128_2131cloizeaux Esw=pi/2 |sin q| (Achtung H-1/2) # PRB32_4703parkinson extensive numerical data # PRB42_6561lin S=1/2 Lancos+Sym+Trans+lintab e pause -1