HPhi_exercise.key
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- つねたけ いんそん
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1 laptop PC (TPQ ) OK
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3 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
4 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 = > HPhi -s SpinHalf.def, S=1, S=3/2 (2S=2 ) Emin=-S(S+1), Emax=S^2 3/17
5 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 = L = 12 Spin Canonical 2Sz z 2 Lanczos 1 > HPhi -s StdFace.def 6/17
6 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
7 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 = L = 12 Spin Canonical 2Sz z 2 Lanczos 1 > HPhi -s StdFace.def 6/17
8 2: S =1/2 Heisenbergchain output/zvo_lanczos_step.dat 4 1 > tail -n 3 output/zvo_lanczos_step.dat 2 stp= stp= stp= Lanczos step 2 4 7/17
9 2: S =1/2 Heisenbergchain tail awk 5 1 > tail -n 1 output/zvo_lanczos_step.dat awk {print $3-$2} L PC L = 18, 20 L 5 8/17
10 2: S =1/2 Heisenbergchain (StdFace.common) 1 model = "Spin" 2 lattice = "chain lattice" 3 method = "Lanczos" 4 2S = 1 5 2Sz = 0 6 J = 1.0 L 1 rm -f res.dat 2 for L in ; do 3 cp StdFace.common StdFace.def 4 echo "L=$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
11 2: S =1/2 Heisenbergchain S = 1/2 Heisenberg chain log L \Delta a + b*x Lanczos /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
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13 H = J 1 X S i S j + J 2 X hi,ji hhi,jii S i S j m s (k 0 ) m s (k x ) T S m s T, S Neel AFM QSL Stripe AFM J 2 /J
14 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
15 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 Ep
16 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 gapless J z =1, J x = J y = A z gapped J y J x =1, =1, = =0 J z A x B A y J y J x = =0 J z Annals of Physics 321, (2016)
17 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
18 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
19 FullDiag, TPQ, Lanczos Hubbard model, L=8, U/t=8, half filling, Sz=0 E/Ns TPQ FullDiag Lanczos D/Ns TPQ FullDiag Lanczos T/t T/t
20 HPhi/samples/Standard/ Hubbard Heisenberg Kitaev Standard mode StdFace.def StdFace.def - (PC spin 1/2 24site, Hubbard 12 ) -Lanczos ( ) -TPQ ( )
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22 #!/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
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26 H+ = X i,j,k,l X 1, 2, 3, 4 I ijkl c i 1 c j 2 c k 3 c l 4 i σ1 j σ2 k σ3 l σ4
27 - CoulombIntra H+ = i ================================= NCoulombintra 2 ================================= ===========Exchange============== ================================= U i n i n i -Exchange H+ = i,j J Ex ij (S + i S j + S i S+ j ) ================================= NExchange 2 ================================= ===========Exchange============== =================================
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[ ] (Ising model) 2 i S i S i = 1 (up spin : ) = 1 (down spin : ) (4.38) s z = ±1 4 H 0 = J zn/2 i,j S i S j (4.39) i, j z 5 2 z = 4 z = 6 3
![[ ] (Ising model) 2 i S i S i = 1 (up spin : ) = 1 (down spin : ) (4.38) s z = ±1 4 H 0 = J zn/2 i,j S i S j (4.39) i, j z 5 2 z = 4 z = 6 3](/thumbs/103/161261933.jpg "[ ] (Ising model) 2 i S i S i = 1 (up spin : ) = 1 (down spin : ) (4.38) s z = ±1 4 H 0 = J zn/2 i,j S i S j (4.39) i, j z 5 2 z = 4 z = 6 3")
4.2 4.2.1 [ ] (Ising model) 2 i S i S i = 1 (up spin : ) = 1 (down spin : ) (4.38) s z = ±1 4 H 0 = J zn/2 S i S j (4.39) i, j z 5 2 z = 4 z = 6 3 z = 6 z = 8 zn/2 1 2 N i z nearest neighbors of i j=1
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