asked by Hebatalla Elnaggar (2019/01/31 20:45)
Hi Maurits,
I am trying to plot the GS density matrix for a d5 HS cubic system however I think something goes wrong. Here I compare four calculations (the problem occurs in the fourth case ):
1- Jex parallel to the X axis with no spin-orbit coupling. The first 3 ground-states are:
# <E> <S^2> <L^2> <J^2> <Sx> <Lx> <Np> <Nd> <NL> 1 -5.6576 8.7500 -0.0000 8.7500 -2.5000 0.0000 6.0000 5.0000 10.0000 2 -5.5676 8.7500 -0.0000 8.7500 -1.5000 0.0000 6.0000 5.0000 10.0000 3 -5.4776 8.7500 -0.0000 8.7500 -0.5000 0.0000 6.0000 5.0000 10.0000
plotting the 1st GS I get a spherical state fully red as expected projecting along the x-axis
2- Jex parallel to the X axis with 100% spin-orbit coupling. The first 3 ground-states are:
# <E> <S^2> <L^2> <J^2> <Sx> <Lx> <Np> <Nd> <NL> 1 -5.6621 8.7439 0.0030 8.7505 -2.4988 -0.0012 6.0000 5.0000 10.0000 2 -5.5722 8.7437 0.0031 8.7505 -1.4993 -0.0007 6.0000 5.0000 10.0000 3 -5.4822 8.7436 0.0032 8.7506 -0.4998 -0.0002 6.0000 5.0000 10.0000
plotting the 1st GS I get an almost spherical state fully red as expected projecting along the x-axis
3- Jex aligned 30 degrees from the Y axis (rotation about the Z-axis) with no spin-orbit coupling. The first 3 ground-states are:
# <E> <S^2> <L^2> <J^2> <S||> <L||> <Np> <Nd> <NL> 1 -5.6576 8.7500 -0.0000 8.7500 -2.5000 0.0000 6.0000 5.0000 10.0000 2 -5.5676 8.7500 -0.0000 8.7500 -1.5000 0.0000 6.0000 5.0000 10.0000 3 -5.4776 8.7500 -0.0000 8.7500 -0.5000 0.0000 6.0000 5.0000 10.0000
plotting the 1st GS I get an almost spherical state nearly blue as expected for projecting along the || axis
4- Jex aligned 30 degrees from the Y axis (rotation about the Z-axis) with 100% spin-orbit coupling. The first 3 ground-states are:
# <E> <S^2> <L^2> <J^2> <S||> <L||> <Np> <Nd> <NL> 1 -5.6621 8.7439 0.0030 8.7505 -2.4988 -0.0012 6.0000 5.0000 10.0000 2 -5.5722 8.7437 0.0031 8.7505 -1.4993 -0.0007 6.0000 5.0000 10.0000 3 -5.4822 8.7436 0.0032 8.7506 -0.4998 -0.0002 6.0000 5.0000 10.0000
plotting the 1st GS I get a very strange non-spherical state with a mixed spin. I do not understand why the plot fails here. The GS is almost identical to the case of 2 but the resulting density matrix is very different.
Below is the script I used:
function TableToMathematica(t)
Chop(t)
local ret = "{ "
for k,v in pairs(t) do
if k~=1 then
ret = ret.." , "
end
if (type(v) == "table") then
ret = ret..TableToMathematica(v)
else
ret = ret..string.format("+ %18.15f ",Complex.Re(v))
ret = ret..string.format("+ I %18.15f ",Complex.Im(v))
end
end
ret = ret.." }"
return ret
end
NBosons = 0
NFermions = 26
NElectrons_2p = 6
NElectrons_3d = 5
NElectrons_Ld = 10
IndexDn_2p = {0, 2, 4}
IndexUp_2p = {1, 3, 5}
IndexDn_3d = {6, 8, 10, 12, 14}
IndexUp_3d = {7, 9, 11, 13, 15}
IndexDn_Ld = {16, 18, 20, 22, 24}
IndexUp_Ld = {17, 19, 21, 23, 25}
--------------------------------------------------------------------------------
-- Define the Coulomb term.
--------------------------------------------------------------------------------
OppF0_3d_3d = NewOperator('U', NFermions, IndexUp_3d, IndexDn_3d, {1, 0, 0})
OppF2_3d_3d = NewOperator('U', NFermions, IndexUp_3d, IndexDn_3d, {0, 1, 0})
OppF4_3d_3d = NewOperator('U', NFermions, IndexUp_3d, IndexDn_3d, {0, 0, 1})
OppF0_2p_3d = NewOperator('U', NFermions, IndexUp_2p, IndexDn_2p, IndexUp_3d, IndexDn_3d, {1, 0}, {0, 0})
OppF2_2p_3d = NewOperator('U', NFermions, IndexUp_2p, IndexDn_2p, IndexUp_3d, IndexDn_3d, {0, 1}, {0, 0})
OppG1_2p_3d = NewOperator('U', NFermions, IndexUp_2p, IndexDn_2p, IndexUp_3d, IndexDn_3d, {0, 0}, {1, 0})
OppG3_2p_3d = NewOperator('U', NFermions, IndexUp_2p, IndexDn_2p, IndexUp_3d, IndexDn_3d, {0, 0}, {0, 1})
OppNUp_2p = NewOperator('Number', NFermions, IndexUp_2p, IndexUp_2p, {1, 1, 1})
OppNDn_2p = NewOperator('Number', NFermions, IndexDn_2p, IndexDn_2p, {1, 1, 1})
OppN_2p = OppNUp_2p + OppNDn_2p
OppNUp_3d = NewOperator('Number', NFermions, IndexUp_3d, IndexUp_3d, {1, 1, 1, 1, 1})
OppNDn_3d = NewOperator('Number', NFermions, IndexDn_3d, IndexDn_3d, {1, 1, 1, 1, 1})
OppN_3d = OppNUp_3d + OppNDn_3d
OppNUp_Ld = NewOperator('Number', NFermions, IndexUp_Ld, IndexUp_Ld, {1, 1, 1, 1, 1})
OppNDn_Ld = NewOperator('Number', NFermions, IndexDn_Ld, IndexDn_Ld, {1, 1, 1, 1, 1})
OppN_Ld = OppNUp_Ld + OppNDn_Ld
OppConfNd={}
for i=0,10 do
OppConfNd[i] = NewOperator("Identity", NFermions)
OppConfNd[i].Restrictions = {NFermions,NBosons,{"000000 1111111111 0000000000",i,i}}
end
-- Fe3+ --
Delta_sc = 1.5*1
U_3d_3d_sc = 6.5*1
F2_3d_3d_sc = 10.965*0.74
F4_3d_3d_sc = 7.5351*0.74
F0_3d_3d_sc = U_3d_3d_sc + 2 / 63 * F2_3d_3d_sc + 2 / 63 * F4_3d_3d_sc
e_3d_sc = (10 * Delta_sc - NElectrons_3d * (19 + NElectrons_3d) * U_3d_3d_sc / 2) / (10 + NElectrons_3d)
e_Ld_sc = NElectrons_3d * ((1 + NElectrons_3d) * U_3d_3d_sc / 2 - Delta_sc) / (10 + NElectrons_3d)
Delta_ic = 1.5*1
U_3d_3d_ic = 6.5*1
F2_3d_3d_ic = 12.736*0.74 -- 0.74
F4_3d_3d_ic = 7.963*0.74 -- 0.74
F0_3d_3d_ic = U_3d_3d_ic + 2 / 63 * F2_3d_3d_ic + 2 / 63 * F4_3d_3d_ic
U_2p_3d_ic = 7.5*1
F2_2p_3d_ic = 5.957*0.75 -- 0.75
G1_2p_3d_ic = 4.453*0.75 -- 0.75
G3_2p_3d_ic = 2.533*0.75 -- 0.75
F0_2p_3d_ic = U_2p_3d_ic + 1 / 15 * G1_2p_3d_ic + 3 / 70 * G3_2p_3d_ic
e_2p_ic = (10 * Delta_ic + (1 + NElectrons_3d) * (NElectrons_3d * U_3d_3d_ic / 2 - (10 + NElectrons_3d) * U_2p_3d_ic)) / (16 + NElectrons_3d)
e_3d_ic = (10 * Delta_ic - NElectrons_3d * (31 + NElectrons_3d) * U_3d_3d_ic / 2 - 90 * U_2p_3d_ic) / (16 + NElectrons_3d)
e_Ld_ic = ((1 + NElectrons_3d) * (NElectrons_3d * U_3d_3d_ic / 2 + 6 * U_2p_3d_ic) - (6 + NElectrons_3d) * Delta_ic) / (16 + NElectrons_3d)
Delta_fc = 1.5*1
U_3d_3d_fc = 6.5*1
F2_3d_3d_fc = 10.965*0.74
F4_3d_3d_fc = 7.5351*0.74
F0_3d_3d_fc = U_3d_3d_fc + 2 / 63 * F2_3d_3d_fc + 2 / 63 * F4_3d_3d_fc
e_3d_fc = (10 * Delta_fc - NElectrons_3d * (19 + NElectrons_3d) * U_3d_3d_fc / 2) / (10 + NElectrons_3d)
e_Ld_fc = NElectrons_3d * ((1 + NElectrons_3d) * U_3d_3d_fc / 2 - Delta_fc) / (10 + NElectrons_3d)
H_coulomb_sc = F0_3d_3d_sc * OppF0_3d_3d
+ F2_3d_3d_sc * OppF2_3d_3d
+ F4_3d_3d_sc * OppF4_3d_3d
+ e_3d_sc * OppN_3d
+ e_Ld_sc * OppN_Ld
H_coulomb_ic = F0_3d_3d_ic * OppF0_3d_3d
+ F2_3d_3d_ic * OppF2_3d_3d
+ F4_3d_3d_ic * OppF4_3d_3d
+ F0_2p_3d_ic * OppF0_2p_3d
+ F2_2p_3d_ic * OppF2_2p_3d
+ G1_2p_3d_ic * OppG1_2p_3d
+ G3_2p_3d_ic * OppG3_2p_3d
+ e_2p_ic * OppN_2p
+ e_3d_ic * OppN_3d
+ e_Ld_ic * OppN_Ld
H_coulomb_fc = F0_3d_3d_fc * OppF0_3d_3d
+ F2_3d_3d_fc * OppF2_3d_3d
+ F4_3d_3d_fc * OppF4_3d_3d
+ e_3d_fc * OppN_3d
+ e_Ld_fc * OppN_Ld
--------------------------------------------------------------------------------
-- Define the spin-orbit coupling term.
--------------------------------------------------------------------------------
Oppldots_3d = NewOperator('ldots', NFermions, IndexUp_3d, IndexDn_3d)
Oppldots_2p = NewOperator('ldots', NFermions, IndexUp_2p, IndexDn_2p)
zeta_3d_sc = 0.059*1
zeta_3d_ic = 0.075*1
zeta_2p_ic = 8.199
zeta_3d_fc = zeta_3d_sc
H_soc_sc = zeta_3d_sc * Oppldots_3d
H_soc_ic = zeta_3d_ic * Oppldots_3d
+ zeta_2p_ic * Oppldots_2p
H_soc_fc = zeta_3d_fc * Oppldots_3d
--------------------------------------------------------------------------------
-- Define the ligand field term.
Akm = {{4, 0,(21/10)},{4,-4,21/10*math.sqrt(5/14)},{4, 4,21/10*math.sqrt(5/14)}}
OpptenDq_3d = NewOperator("CF", NFermions, IndexUp_3d, IndexDn_3d, Akm)
OpptenDq_Ld = NewOperator("CF", NFermions, IndexUp_Ld, IndexDn_Ld, Akm)
Akm = {{2, 0,-7}}
OppDs_3d = NewOperator("CF", NFermions, IndexUp_3d, IndexDn_3d, Akm)
OppDs_Ld = NewOperator("CF", NFermions, IndexUp_Ld, IndexDn_Ld, Akm)
Akm = {{4, 0,-21}}
OppDt_3d = NewOperator("CF", NFermions, IndexUp_3d, IndexDn_3d, Akm)
OppDt_Ld = NewOperator("CF", NFermions, IndexUp_Ld, IndexDn_Ld, Akm)
Akm = PotentialExpandedOnClm('D4h', 2, {0,0,0,1})
OppVe = NewOperator("CF", NFermions, IndexUp_3d, IndexDn_3d, IndexUp_Ld, IndexDn_Ld,Akm) + NewOperator("CF", NFermions, IndexUp_Ld, IndexDn_Ld, IndexUp_3d, IndexDn_3d, Akm)
Akm = PotentialExpandedOnClm('D4h', 2, {0,0,1,0})
OppVb2 = NewOperator("CF", NFermions, IndexUp_3d, IndexDn_3d, IndexUp_Ld, IndexDn_Ld,Akm) + NewOperator("CF", NFermions, IndexUp_Ld, IndexDn_Ld, IndexUp_3d, IndexDn_3d, Akm)
Akm = PotentialExpandedOnClm('D4h', 2, {1,0,0,0})
OppVa1 = NewOperator("CF", NFermions, IndexUp_3d, IndexDn_3d, IndexUp_Ld, IndexDn_Ld,Akm) + NewOperator("CF", NFermions, IndexUp_Ld, IndexDn_Ld, IndexUp_3d, IndexDn_3d, Akm)
Akm = PotentialExpandedOnClm('D4h', 2, {0,1,0,0})
OppVb1 = NewOperator("CF", NFermions, IndexUp_3d, IndexDn_3d, IndexUp_Ld, IndexDn_Ld,Akm) + NewOperator("CF", NFermions, IndexUp_Ld, IndexDn_Ld, IndexUp_3d, IndexDn_3d, Akm)
Akm = PotentialExpandedOnClm('D4h', 2, {0,0,0,1})
OppNe = NewOperator("CF", NFermions, IndexUp_3d, IndexDn_3d, Akm)
Akm = PotentialExpandedOnClm('D4h', 2, {0,0,1,0})
OppNb2 = NewOperator("CF", NFermions, IndexUp_3d, IndexDn_3d,Akm)
Akm = PotentialExpandedOnClm('D4h', 2, {1,0,0,0})
OppNa1 = NewOperator("CF", NFermions, IndexUp_3d, IndexDn_3d,Akm)
Akm = PotentialExpandedOnClm('D4h', 2, {0,1,0,0})
OppNb1 = NewOperator("CF", NFermions, IndexUp_3d, IndexDn_3d, Akm)
Ds_3d = 0.0
Dt_3d = Ds_3d*0.15
tenDq_3d_sc = -0.6 + Dt_3d*10*7/12
tenDq_Ld_sc = tenDq_3d_sc/3--0.0
Veg_sc = 3.2*0
Vt2g_sc = 1.705 *0
Ve = Vt2g_sc
Vb2 = Vt2g_sc
Va1 = Veg_sc /1000
Vb1 = Veg_sc
tenDq_3d_ic = tenDq_3d_sc
tenDq_Ld_ic = tenDq_Ld_sc
Veg_ic = Veg_sc
Vt2g_ic = Vt2g_sc
tenDq_3d_fc = tenDq_3d_sc
tenDq_Ld_fc = tenDq_Ld_sc
Veg_fc = Veg_sc
Vt2g_fc = Vt2g_sc
H_lf_sc = tenDq_3d_sc * OpptenDq_3d
+ tenDq_Ld_sc * OpptenDq_Ld
+ Ds_3d * OppDs_3d
+ Dt_3d * OppDt_3d
+ Ve * OppVe
+ Vb2 * OppVb2
+ Va1 * OppVa1
+ Vb1 * OppVb1
-- + Veg_sc * OppVeg
-- + Vt2g_sc * OppVt2g
H_lf_ic = tenDq_3d_ic * OpptenDq_3d
+ tenDq_Ld_ic * OpptenDq_Ld
+ Ds_3d * OppDs_3d
+ Dt_3d * OppDt_3d
+ Ve * OppVe
+ Vb2 * OppVb2
+ Va1 * OppVa1
+ Vb1 * OppVb1
-- + Veg_ic * OppVeg
-- + Vt2g_ic * OppVt2g
H_lf_fc = tenDq_3d_fc * OpptenDq_3d
+ tenDq_Ld_fc * OpptenDq_Ld
+ Ds_3d * OppDs_3d
+ Dt_3d * OppDt_3d
+ Ve * OppVe
+ Vb2 * OppVb2
+ Va1 * OppVa1
+ Vb1 * OppVb1
-- + Veg_fc * OppVeg
-- + Vt2g_fc * OppVt2g
--------------------------------------------------------------------------------
-- Define the magnetic field term.
--------------------------------------------------------------------------------
OppSx_3d = NewOperator('Sx' , NFermions, IndexUp_3d, IndexDn_3d)
OppSy_3d = NewOperator('Sy' , NFermions, IndexUp_3d, IndexDn_3d)
OppSz_3d = NewOperator('Sz' , NFermions, IndexUp_3d, IndexDn_3d)
OppSsqr_3d = NewOperator('Ssqr' , NFermions, IndexUp_3d, IndexDn_3d)
OppSplus_3d = NewOperator('Splus', NFermions, IndexUp_3d, IndexDn_3d)
OppSmin_3d = NewOperator('Smin' , NFermions, IndexUp_3d, IndexDn_3d)
OppLx_3d = NewOperator('Lx' , NFermions, IndexUp_3d, IndexDn_3d)
OppLy_3d = NewOperator('Ly' , NFermions, IndexUp_3d, IndexDn_3d)
OppLz_3d = NewOperator('Lz' , NFermions, IndexUp_3d, IndexDn_3d)
OppLsqr_3d = NewOperator('Lsqr' , NFermions, IndexUp_3d, IndexDn_3d)
OppLplus_3d = NewOperator('Lplus', NFermions, IndexUp_3d, IndexDn_3d)
OppLmin_3d = NewOperator('Lmin' , NFermions, IndexUp_3d, IndexDn_3d)
OppJx_3d = NewOperator('Jx' , NFermions, IndexUp_3d, IndexDn_3d)
OppJy_3d = NewOperator('Jy' , NFermions, IndexUp_3d, IndexDn_3d)
OppJz_3d = NewOperator('Jz' , NFermions, IndexUp_3d, IndexDn_3d)
OppJsqr_3d = NewOperator('Jsqr' , NFermions, IndexUp_3d, IndexDn_3d)
OppJplus_3d = NewOperator('Jplus', NFermions, IndexUp_3d, IndexDn_3d)
OppJmin_3d = NewOperator('Jmin' , NFermions, IndexUp_3d, IndexDn_3d)
OppSx_Ld = NewOperator('Sx' , NFermions, IndexUp_Ld, IndexDn_Ld)
OppSy_Ld = NewOperator('Sy' , NFermions, IndexUp_Ld, IndexDn_Ld)
OppSz_Ld = NewOperator('Sz' , NFermions, IndexUp_Ld, IndexDn_Ld)
OppSsqr_Ld = NewOperator('Ssqr' , NFermions, IndexUp_Ld, IndexDn_Ld)
OppSplus_Ld = NewOperator('Splus', NFermions, IndexUp_Ld, IndexDn_Ld)
OppSmin_Ld = NewOperator('Smin' , NFermions, IndexUp_Ld, IndexDn_Ld)
OppLx_Ld = NewOperator('Lx' , NFermions, IndexUp_Ld, IndexDn_Ld)
OppLy_Ld = NewOperator('Ly' , NFermions, IndexUp_Ld, IndexDn_Ld)
OppLz_Ld = NewOperator('Lz' , NFermions, IndexUp_Ld, IndexDn_Ld)
OppLsqr_Ld = NewOperator('Lsqr' , NFermions, IndexUp_Ld, IndexDn_Ld)
OppLplus_Ld = NewOperator('Lplus', NFermions, IndexUp_Ld, IndexDn_Ld)
OppLmin_Ld = NewOperator('Lmin' , NFermions, IndexUp_Ld, IndexDn_Ld)
OppJx_Ld = NewOperator('Jx' , NFermions, IndexUp_Ld, IndexDn_Ld)
OppJy_Ld = NewOperator('Jy' , NFermions, IndexUp_Ld, IndexDn_Ld)
OppJz_Ld = NewOperator('Jz' , NFermions, IndexUp_Ld, IndexDn_Ld)
OppJsqr_Ld = NewOperator('Jsqr' , NFermions, IndexUp_Ld, IndexDn_Ld)
OppJplus_Ld = NewOperator('Jplus', NFermions, IndexUp_Ld, IndexDn_Ld)
OppJmin_Ld = NewOperator('Jmin' , NFermions, IndexUp_Ld, IndexDn_Ld)
OppSx = OppSx_3d + OppSx_Ld
OppSy = OppSy_3d + OppSy_Ld
OppSz = OppSz_3d + OppSz_Ld
OppSsqr = OppSx * OppSx + OppSy * OppSy + OppSz * OppSz
OppLx = OppLx_3d + OppLx_Ld
OppLy = OppLy_3d + OppLy_Ld
OppLz = OppLz_3d + OppLz_Ld
OppLsqr = OppLx * OppLx + OppLy * OppLy + OppLz * OppLz
OppJx = OppJx_3d + OppJx_Ld
OppJy = OppJy_3d + OppJy_Ld
OppJz = OppJz_3d + OppJz_Ld
OppJsqr = OppJx * OppJx + OppJy * OppJy + OppJz * OppJz
Jvec= {1,0,0}
J0 = 1e-3 * 90
B0 = 1e-4
Bx = Jvec[1]*B0
By = Jvec[2]*B0
Bz = Jvec[3]*B0
Jx = Jvec[1]*J0
Jy = Jvec[2]*J0
Jz = Jvec[3]*J0
Jex = Jx * OppSx
+ Jy * OppSy
+ Jz * OppSz
B = Bx * ( OppLx)
+ By * ( OppLy)
+ Bz * ( OppLz)
--------------------------------------------------------------------------------
-- Compose the total Hamiltonian.
--------------------------------------------------------------------------------
H_sc = 1 * H_coulomb_sc + 1 * H_soc_sc + 1 * H_lf_sc + B + Jex
H_ic = 1 * H_coulomb_ic + 1 * H_soc_ic + 1 * H_lf_ic + B + Jex
H_fc = 1 * H_coulomb_fc + 1 * H_soc_fc + 1 * H_lf_fc + B + Jex
H_sc.Chop()
H_ic.Chop()
H_fc.Chop()
--------------------------------------------------------------------------------
-- Define the starting restrictions and set the number of initial states.
--------------------------------------------------------------------------------
StartingRestrictions = {NFermions, NBosons, {'111111 0000000000 0000000000', NElectrons_2p, NElectrons_2p},
{'000000 1111111111 0000000000', NElectrons_3d, NElectrons_3d},
{'000000 0000000000 1111111111', NElectrons_Ld, NElectrons_Ld}}
NPsis = 6
Restrictions = {NFermions, NBosons, {"000000 0000000000 1111111111",10,10}}
Psis = Eigensystem(H_sc, StartingRestrictions, NPsis,{{"restrictions",Restrictions}})
if not (type(Psis) == 'table') then
Psis = {Psis}
end
-- Plotting
mathematicaInput = [[
Needs["Quanty`PlotTools`"];
rho=%s;
pl = Table[ Rasterize[ DensityMatrixPlot[ rho[ [i] ],QuantizationAxes->"x", PlotRange -> {{-1, 1}, {-1, 1}, {-1, 1}}] ], {i, 1, Length[rho]}];
For[i = 1, i <= Length[pl], i++,
Export[",." <> ToString[i] <> ".png", pl[ [i] ] ];
];
Quit[];
]]
-- Plotting density plots:
rhoList1 = DensityMatrix(Psis, {6,7,8,9,10,11,12,13,14,15})
rhoListMathematicaForm1 = TableToMathematica(rhoList1)
file = io.open("./Densitymatrix2.nb", "w")
file:write( mathematicaInput:format(rhoListMathematicaForm1 ) )
file:close()
--os.execute("/Applications/Mathematica.app/Contents/MacOS/MathKernel -run '<<".."Densitymatrix1.nb'")
print('Finished the density matrix')
-- Print some useful information about the calculated states.
file = io.open("Expect2.txt", "w");
OppSpar= Jvec[3]*OppSz_3d+Jvec[2]*OppSy_3d+Jvec[1]*OppSx_3d
OppLpar= Jvec[3]*OppLz_3d+Jvec[2]*OppLy_3d+Jvec[1]*OppLx_3d
OppList = {H_sc, OppSsqr, OppLsqr, OppJsqr, OppSpar, OppLpar, OppN_2p, OppN_3d, OppN_Ld}
ConfNds={OppConfNd[6], OppConfNd[7], OppConfNd[8], OppConfNd[9], OppConfNd[10]}
Psitemp={}
print(' # <E> <S^2> <L^2> <J^2> <S||> <L||> <Np> <Nd> <NL>');
file:write(' # <E> <S^2> <L^2> <J^2> <Sz> <Lz> <Np> <Nd> <NL>');
file:write('\n')
for key, Psi in pairs(Psis) do
expectationValues = Psi * OppList * Psi
file:write(string.format('%3d', key))
for key, expectationValue in pairs(expectationValues) do
io.write(string.format('%9.4f', Complex.Re(expectationValue)))
file:write(string.format('%9.4f', Complex.Re(expectationValue)))
--io.write(string.format('%9.4f', Complex.Re(expectationValue)))
end
-- for k=6,10 do
-- Psitemp = OppConfNd[k] * Psi
-- ConfNdValue = Psitemp * OppConfNd[k] * Psitemp
-- file:write(string.format('%9.4f', ConfNdValue))
-- end
io.write('\n')
file:write('\n')
end
file:close()
OppList = {H_sc, OppNa1, OppNb1, OppNe, OppNb2}
print(' # <E> <Na1> <Nb1> <Ne> <Nb2> ');
for key, Psi in pairs(Psis) do
expectationValues = Psi * OppList * Psi
for key, expectationValue in pairs(expectationValues) do
io.write(string.format('%9.4f', Complex.Re(expectationValue)))
end
io.write('\n')
end
os.exit()