## Learn to Use ITensor

main / formulas / itensor_single_site_op

# Making a single-site operator (no quantum numbers)

Measuring the properties of a wavefunction (for example, an MPS) usually involves expectation values of single-site operators or products and sums of such operators.

Say we have an Index s representing a particular site. We could have created s (thinking here of spin 1/2 or a hardcore boson):

auto s = Index("s",2,Site);


Or we could obtain s from a set of Site indices already created earlier (see the recipe for creating a set of Site indices).

Once we have this site index, we can make various operators as follows:

Index sP = prime(s); //convenient to save this as a different variable

auto sz = ITensor(s,sP);
sz.set(s(1),sP(1),+0.5);
sz.set(s(2),sP(2),-0.5);

auto sx = ITensor(s,sP);
sx.set(s(1),sP(2),0.5);
sx.set(s(2),sP(1),0.5);


We can even get fancy and create a 'factory' function which takes our site and an operator-name string and returns the operator we want:

ITensor
op(Index s, string name)
{
Index sP = prime(s);
auto res = ITensor(s,sP); //res is short for result

if(name == "Sz")
{
res.set(s(1),sP(1),+0.5);
res.set(s(2),sP(2),-0.5);
}
else
if(name == "Sx")
{
res.set(s(1),sP(2),0.5);
res.set(s(2),sP(1),0.5);
}
else
{
Print(name);
Error("Operator name not recognized.");
}

return res;
}


Finally, note that this 'operator factory' feature is actually built into the SiteSet classes which automate the creation of sites and operators for you. But of course there are always reasons you may want to get your hands dirty and create these operators yourself.

Complete sample code:

#include "itensor/all.h"

using namespace itensor;
using std::string;

ITensor
op(Index s, string name)
{
Index sP = prime(s);
ITensor res(s,sP); //res is short for result

if(name == "Sz")
{
res.set(s(1),sP(1),+0.5);
res.set(s(2),sP(2),-0.5);
}
else
if(name == "Sx")
{
res.set(s(1),sP(2),0.5);
res.set(s(2),sP(1),0.5);
}
else
{
Print(name);
Error("Operator name not recognized.");
}

return res;
}

int
main(int argc, char* argv[])
{
const int d = 2;

auto s1 = Index("s1",d,Site);
auto s2 = Index("s2",d,Site);

ITensor sz1 = op(s1,"Sz");
ITensor sz2 = op(s2,"Sz");
ITensor sx1 = op(s1,"Sx");

PrintData(sz1);
PrintData(sz2);
PrintData(sx1);

return 0;
}


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