Part specification error

Question

I am doing a solved exercise shared here.

However, while running the code, I encountered an error on page-8, under the Dynamics section.

with error :

I think this error is due to the absence of range for i or initialstate . However, I cannot find a solution to provide a proper range.

Here is the code:

(*Parameters of the Hamiltonian*)

Clear[chainsize, upspins, downspins, dim, Jxy, Jz, open];
chainsize = 10;(*number of sites*)
upspins = chainsize/2;(*number of spins pointing up in the z direction*)
downspins = chainsize - upspins;
dim = chainsize! /(upspins! downspins!);(*dimension of the subspace  being studied=upspins = (chainsize
upspins
)*)
Jxy = 
  1.0;(*strength of the flip-flop term between nearest neighbors*)

Jz = 0.5;(*strength of the Ising interaction between nearest neighbors*)

open = 1;(*determines whether the chain is open or closed. For closed chain,open=0. For open chain, open=1*)

(*Creating the basis*)
Clear[onebasisvector, basis];
onebasisvector = 
  Flatten[{Table[1, {k, 1, upspins}], Table[0, {k, 1, downspins}]}];
basis = Permutations[onebasisvector];

(*ELEMENTS OF THE HAMILTONIAN*)
(*Initialization*)
Clear[HH];
Do[Do[HH[i, j] = 0., {j, 1, dim}], {i, 1, dim}];

(*Diagonal elements-Ising interaction*)

Do[Do[HH[i, i] = 
      HH[i, i] + (Jz/4)*(-1.)^(basis[[i, k]] + basis[[i, k + 1]]);
    , {k, 1, chainsize - 1}];
  , {i, 1, dim}];

(*Term included in the Ising interaction if the chain is closed*)

If[open == 0, 
  Do[HH[i, i] = 
    HH[i, i] + (Jz/
       4.0)*(-1.0)^(basis[[i, chainsize]] + basis[[i, 1]]), {i, 1, 
    dim}]];

(*Off-diagonal elements-flip-flop term*)
Clear[howmany, site];
Do[Do[(*Initialization*)
    howmany = 0;
    Do[site[z] = 0, {z, 1, chainsize}];
    (*Sites where states i and j differ*)
    
    Do[If[basis[[i, k]] != basis[[j, k]], {howmany = howmany + 1, 
        site[howmany] = k}];, {k, 1, chainsize}];
    (*Coupling matrix element-when only two neighbor sites differ*)
  
      If[howmany == 2, 
     If[site[2] - site[1] == 1, {HH[i, j] = HH[i, j] + Jxy/2.0, 
       HH[j, i] = HH[j, i] + Jxy/2.0}]];
    (*Additional term for closed system*)
    
    If[open == 0, 
     Ifpsite[2] - site[1] == 
      chainsize - 1, {HH[i, j] = HH[i, j] + Jxy/2.0, 
      HH[j, i] = HH[j, i] + Jxy/2.0}];
    , {j, i + 1, dim}];
  , {i, 1, dim - 1}];

(*Hamiltonian*)
Clear[Hamiltonian];
Hamiltonian = Table[Table[HH[i, j], {i, 1, dim}], {j, 1, dim}];
MatrixForm[Hamiltonian];

(*Diagonalization*)
Clear[Energy, Vector];
Energy = Chop[Eigenvalues[Hamiltonian]];
Vector = Chop[Eigenvectors[Hamiltonian]];

(*Parameters of the Hamiltonian*)

Clear[chainsize, upspins, downspins, dim, Jxy, Jz, open];
chainsize = 6;
upspins = 1;
downspins = chainsize - upspins;
dim = chainsize! /(upspins! downspins!) ;
Jxy = 1.0;
Jz = 0.5;
open = 1;

Do[If[basis[[i, 1]] == 1 && basis[[i, 2]] == 0, initialstate = i];
  , {i, 1, dim}];

(*DYNAMICS*)
Clear[endtime, PSI, increment, Magsite];
endtime = 81;
increment = 0.1;
Do[PSI[t] = Sum[Vector[[j, initialstate]]*
     Vector[[j]]*Exp[-I*Energy[[j]]*(t - 1)*increment], {j, 1, dim}];
  
  (*Magnetization*)
  
  Do[Magsite[j, t] = 
     0.5*Sum[Abs[PSI[t][[i]]]^2*(-1.0)^(1 + basis[[i, j]]), {i, 
        dim}];
   , {j, 1, chainsize}];
  (*Print[{(t-1)increment,Magsite[1,t]}];*)
  , {t, 1, endtime}];


<< PlotLegends`;

Clear[magT, ProbT];
Do[magT[j] = 
   Table[{(t - 1) increment, Magsite[j, t]}, {t, 1, endtime}], {j, 1, 
   chainsize}];
Do[ProbT[k] = 
   Table[{(t - 1) increment, Abs[PSI[t][[k]]]^2}, {t, 1, 
     endtime}], {k, 1, dim}];
Print[];
Print["Magnetization of each site"];

ListPlot[Table[magT[j], {j, 1, chainsize}], PlotRange -> All, 
 Joined -> True, 
 PlotStyle -> {{Thick, Black}, {Thick, Blue}, {Thick, Red}, {Thick, 
    Darker[Green]}, {Thick, Magenta}, {Thick, Brown}}, 
 LabelStyle -> Directive[Black, Bold, Medium], 
 PlotLegend -> Table["mag"[x], {x, 1, dim}], LegendPosition -> {1, 0},
  AxesLabel -> {"time", "Magnetization"}]

Print[];
Print["Probability of each site-basis"];

ListPlot[Table[ProbT[k], {k, 1, dim}], PlotRange -> All, 
 Joined -> True, 
 PlotStyle -> {{Thick, Black}, {Thick, Blue}, {Thick, Red}, {Thick, 
    Darker[Green]}, {Thick, Magenta}, {Thick, Brown}}, 
 LabelStyle -> Directive[Black, Bold, Medium], 
 PlotLegend -> Table[basis[[k]], {k, 1, dim}], 
 LegendPosition -> {1, 0}, LegendSize -> {1, 1}, 
 AxesLabel -> {"time", "Probability"}]

Please help me out solving this problem.