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auto a = Index(2), 
auto b = Index(2), 
auto c = Index(2);

auto Z = ITensor(a,b), 
auto X = ITensor(c,b);

Z.set(a=1,b=1, +1.0);
Z.set(a=2,b=2, -1.0);

X.set(b=1,c=2, +1.0);
X.set(b=2,c=1, +1.0);

//the * operator finds and
//contracts common index 'b'
//regardless of index order:

ITensor R = Z * X;

Print( elt(R,a=2,c=1) ); 

//output:
// elt(R,a=2,c=1) = -1

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auto i = Index(3);
auto j = Index(5);
auto k = Index(2);
auto l = Index(7);

auto A = ITensor(i,j,k);
auto B = ITensor(l,j);

A.set(i=1,j=1,k=1, 11.1);
A.set(i=2,j=1,k=2, -21.2);
A.set(k=1,i=3,j=1, 31.1);
A.set(k=1,i=1,j=2, 11.2);

B.set(j=2,l=4, 2.+4._i);

auto C = A * B;
PrintData(C);

618ip伕理官网 D = randomITensor(k,j,i);

auto R = A + D;

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auto i = Index(3,"i");
auto j = Index(7,"j");
auto k = Index(2,"k");
auto l = Index(4,"l");

auto T = randomITensor(i,j,k,l);

auto [U,S,V] = svd(T,i,k);

Print(norm(T - U*S*V));

//output: 
// norm(T - U*S*V) = 4.7458E-14

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DMRG is a powerful algorithm for finding dominant eigenvectors of exponentially large matrices (such as quantum Hamiltonians) in matrix product state (MPS) form. It is adaptive and converges very quickly and to high precision.

In addition to state-of-the-art DMRG codes, ITensor features the AutoMPO system, which is a powerful domain-specific language for creating matrix product operator (MPO) tensor networks as a sum of local terms, which is especially useful for quantum mechanics applications.

//Define Hilbert space of N spin-one sites
int N = 100;
auto sites = SpinOne(N);

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auto ampo = AutoMPO(sites);
for(int j = 1; j < N; ++j)
    {
    ampo += 0.5,"S+",j,"S-",j+1;
    ampo += 0.5,"S-",j,"S+",j+1;
    ampo +=     "Sz",j,"Sz",j+1;
    }
auto H = toMPO(ampo);

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//to be a product state
auto psi0 = MPS(InitState(sites,"Z0"));

//Perform 5 sweeps of DMRG
auto sweeps = Sweeps(5);
//Specify max number of states kept each sweep
sweeps.maxdim() = 50, 50, 100, 100, 200;

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auto [energy,psi] = dmrg(H,psi0,sweeps,"Quiet");

//Continue to analyze wavefunction afterward 
Print(inner(psi,H,psi)); //<psi|H|psi>

for(int j = 1; j <= N; ++j)
    {
    //Make site j the MPS "orthogonality center"
    psi.position(j);
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    Real Szj = elt(psi(j)
               * op(sites,"Sz",j)
               * dag(prime(psi(j),"Site")));
    println("Sz_",j," = ",Szj);
    }