## Learn to Use ITensor

main / formulas / index_sites

# Creating a set of Site indices to use as a lattice

To begin most calculations you need a set of lattice sites to define your Hilbert space. Although the ITensor library defines a set of SiteSet classes which automate this for you, there could be a lot of reasons why you would want to do it yourself. Below is a simple pattern you can use to create a set of site Indices and save them in a vector.

int N = 100; //number of sites
int d = 2; //dimension of local Hilbert space of each site
auto site = vector<Index>(N+1); //convenient for these to be 1-indexed
for(int j = 1; j <= N; ++j)
{
site.at(j) = Index(nameint("s",j),d,Site);
}

//Now we can use these sites, for example, to make tensors
//such as operators

auto sz3 = ITensor(site[3],prime(site[3]));
sz.set(site[3](1),prime(site[3])(1), 0.5);
sz.set(site[3](2),prime(site[3])(2),-0.5);


A few comments on the above code are in order. The function nameint is convenience function we provide which simply takes a string and an integer and makes a string with the integer appended. So for example:

auto myname = nameint("mysite_",7);
Print(myname); //prints "mysite_7"


Also, in the Index constructor, after the name and dimension of each Index we passed the Site flag. This flags all of our site indices as having an IndexType of Site (accessible through the .type() accessor on a given Index e.g. site[4].type() == Site). Later this allows useful idioms such as priming only the Site indices of a certain tensor but not of the Link indices, etc. (For more info see the docs on class Index.)

Complete sample code:

#include "itensor/all.h"

using namespace itensor;
using std::vector;

int main()
{
int N = 100; //number of sites
int d = 2; //dimension of local Hilbert space of each site
auto site = vector<Index>(N+1); //convenient for these to be 1-indexed
for(int j = 1; j <= N; ++j)
{
site.at(j) = Index(nameint("s",j),d,Site);
}

auto sz3 = ITensor(site[3],prime(site[3]));
sz3.set(site[3](1),prime(site[3])(1), 0.5);
sz3.set(site[3](2),prime(site[3])(2),-0.5);
PrintData(sz3);

auto myname = nameint("mysite_",7);
Print(myname); //prints "mysite_7"

return 0;
}


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