laptop PC (TPQ ) OK
https://github.com/yomichi/hphi-samples
1: S =1/2 Heisenbergdimer 2 S =1/2 Heisenberg dimer model H = S 1 S 2 S tot =0 E = 3/4 S tot =1 E =1/4 HPhi 2 2/17
1: S =1/2 Heisenbergdimer SpinHalf.def 1 model = "SpinGC" 2 lattice = "chain lattice" 3 method = "FullDiag" 4 2S = 1 5 L = 2 6 J = 0.5 HPhi Standard SpinGC GC Grand Canonical J = 0.5 2 1 > HPhi -s SpinHalf.def, S=1, S=3/2 (2S=2 ) Emin=-S(S+1), Emax=S^2 3/17
2: S =1/2 Heisenbergchain StdFace.def 1 model = "Spin" 2 lattice = "chain lattice" 3 method = "Lanczos" 4 2S = 1 5 2Sz = 0 6 J = 1.0 7 L = 12 Spin Canonical 2Sz z 2 Lanczos 1 > HPhi -s StdFace.def 6/17
2-A: S =1/2 Heisenbergchain S = 1/2 Heisenberg chain H = L i=1 S i S i+1 S L+1 = S 1 Luttinger 1/L 3 HPhi 3 5/17
2: S =1/2 Heisenbergchain StdFace.def 1 model = "Spin" 2 lattice = "chain lattice" 3 method = "Lanczos" 4 2S = 1 5 2Sz = 0 6 J = 1.0 7 L = 12 Spin Canonical 2Sz z 2 Lanczos 1 > HPhi -s StdFace.def 6/17
2: S =1/2 Heisenbergchain output/zvo_lanczos_step.dat 4 1 > tail -n 3 output/zvo_lanczos_step.dat 2 stp=42-5.3873909174-5.0315434037-4.7773893336-4.5693744101 3 stp=44-5.3873909174-5.0315434037-4.7773893337-4.5693744108 4 stp=46-5.3873909174-5.0315434037-4.7773893337-4.5693744108 Lanczos step 2 4 7/17
2: S =1/2 Heisenbergchain tail awk 5 1 > tail -n 1 output/zvo_lanczos_step.dat awk {print $3-$2} 2 0.355848 L PC L = 18, 20 L 5 8/17
2: S =1/2 Heisenbergchain (StdFace.common) 1 model = "Spin" 2 lattice = "chain lattice" 3 method = "Lanczos" 4 2S = 1 5 2Sz = 0 6 J = 1.0 L 1 rm -f res.dat 2 for L in 10 12 14 16; do 3 cp StdFace.common StdFace.def 4 echo "L=$L" >> StdFace.def 5 HPhi -s StdFace.def 6 gap=$((tail -n1 \ 7 output/zvo_lanczos_step.dat \ 8 awk {print $3-$2} ) 9 echo $L $gap >> res.dat 10 done 9/17
2: S =1/2 Heisenbergchain S = 1/2 Heisenberg chain log L \Delta 0.5 0.4 0.3 0.2 0.1 0 a + b*x Lanczos 0 0.02 0.04 0.06 0.08 0.1 1/L S =1/2 XY chain (J z =0, J x =1.0) S=1 Heisenberg chain (Haldane gap) [input file 2S=2 ] 10 / 17
H = J 1 X S i S j + J 2 X hi,ji hhi,jii S i S j 3 0 1 2 3 0 15 12 13 14 15 12 0.3 m s (k 0 ) m s (k x ) T S 0.3 11 8 9 10 11 8 m s 0.2 0.2 T, S 7 4 5 6 7 4 0.1 Neel AFM QSL Stripe AFM 0.1 3 0 1 2 3 0 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 J 2 /J 1 15 12 13 14 15 12
H = J 1 X S i S j + J 2 X hi,ji hhi,jii S i S j L =4 W = 4 model = "Spin" method = "Lanczos" lattice = "square lattice" J = 2.0 J = 1.0 2Sz = 0
J1-J2 Heisenberg model, Ns=4 4, J1=2.0 E. Dagotto and A. Moreo, PRB (R) 39, 4744 (1989) TABLE I. Ground-state energy (Ep) and first excited-state energy (E~) per site (both singlets with zero momentum) of the 2D Heisenberg model with frustration as a function of J2 on a 4X41attice. The error is in the last digit. 0.950 1.100 1.150 1.200 1.325 1.400 1.500 1.600 1.750 Ep 1.065 978 1.047 189 1.047 183 1.051 792 1.089 305 1.127 716 1.188 546 1.254670 1.358437 1.0160 1.0254 1.0307 1.0380 1.0804 1.1169 1.1691 1.2233 1.3072
X X X H = J x Si x Sj x J y S y i Sy j J z Si z Sj z x bond y bond z bond 4 5 0 1 2 3 4 5 gapless J z =1, J x = J y =0 17 13 15 17 13 16 12 14 16 12 A z gapped 11 7 9 11 7 10 6 8 10 6 5 1 3 5 1 4 0 2 4 0 J y J x =1, =1, = =0 J z A x B A y J y J x = =0 J z 12 13 14 15 16 17 12 13 Annals of Physics 321, 2-111 (2016)
H = J x X x bond S x i S x j J y X y bond W = 3 L = 3 model = "SpinGC" method = "Lanczos" lattice = "Honeycomb" J0x = -1.0 J0y = 0.0 J0z = 0.0 J1x = 0.0 J1y = -1.0 J1z = 0.0 J2x = 0.0 J2y = 0.0 J2z = -1.0 S y i Sy j J z X z bond S z i S z j
H = t X hi,ji (c i c j +h.c.)+u X i n i" n i# L = 8 model = "FermionHubbard" method = "Lanczos" lattice = "chain" t = 1.0 U = 8.0 nelec = 8 2Sz = 0
FullDiag, TPQ, Lanczos Hubbard model, L=8, U/t=8, half filling, Sz=0 E/Ns 2.5 2 1.5 1 0.5 TPQ FullDiag Lanczos D/Ns 0.25 0.2 0.15 0.1 TPQ FullDiag Lanczos 0 0.05-0.5 10 10 10 10 10 T/t -2-1 0 1 2 0 10 10 10 10 10 T/t -2-1 0 1 2
HPhi/samples/Standard/ Hubbard Heisenberg Kitaev Standard mode StdFace.def StdFace.def - (PC spin 1/2 24site, Hubbard 12 ) -Lanczos ( ) -TPQ ( )
#!/bin/sh #QSUB -queue F144cpu #QSUB -node 128 #QSUB -mpi 128 #QSUB -omp 24 #QSUB -place pack #QSUB -over false #PBS -l walltime=24:00:00 #PBS -N HPhi cd ${PBS_O_WORKDIR} source /home/issp/materiapps/hphi/hphivars.sh mpijob HPhi -s StdFace.def
H+ = X i,j,k,l X 1, 2, 3, 4 I ijkl 1 2 3 4c i 1 c j 2 c k 3 c l 4 i σ1 j σ2 k σ3 l σ4
- CoulombIntra H+ = i ================================= NCoulombintra 2 ================================= ===========Exchange============== ================================= 0 4.0 1 4.0 U i n i n i -Exchange H+ = i,j J Ex ij (S + i S j + S i S+ j ) ================================= NExchange 2 ================================= ===========Exchange============== ================================= 0 1 0.5 1 2 0.5