## Learn to Use ITensor

main / classes / siteset C++v3 | C++v2

# SiteSet

Class for specifying the local Hilbert space of each site of a lattice by storing the associated site index. A SiteSet does not store any information about the topology of the lattice, just the number of sites and information about each site.

ITensor comes with specialized subclasses of SiteSet, such as the SpinHalf and SpinOne classes, which provide facilities to create sites of a certain type (S=1/2 or S=1 spins, for example). However, these classes differ from SiteSet mainly in their constructors and read/write methods; after creating a specialized SiteSet type (such as SpinHalf) it can be safely converted to the base SiteSet type (for example, in the following code: SiteSet sites = SpinHalf(N);) without losing information about the underlying site type.

## Synopsis

auto sites = SpinHalf(100);

Print(length(sites)); //prints: length(sites) = 100

auto s3 = sites(3); //retrieve the Index defining site number 3

auto s3up = sites(3,"Up"); //obtain the IndexVal defining the "Up" state at site number 3

auto sz3 = op(sites,"Sz",3); //obtain the "Sz" operator at site number 3


## General SiteSet Interface

This part of the interface is common to all site set objects.

• length(SiteSet sites) -> int

Returns the number of sites of the SiteSet sites.

• operator()(int i) -> Index

Return the Index representing site i.

Show Example
auto sites = SpinHalf(100);

auto s4 = sites(4);

auto l = Index(5,"left"),
auto r = Index(4,"right");

auto T = ITensor(l,sites(3),r);

• operator()(int i, string state) -> IndexVal

Return the IndexVal representing a specific state of site i in the diagonal basis.

For example, the state string could be "Up" or "Dn" for the case of the SpinHalf SiteSet, or "Emp","Up","Dn", or "UpDn" in the case of the Electron SiteSet.

Show Example
  auto sites = SpinOne(100);

//Create an ITensor with all entries zero except
//the one corresponding to site 5 in the "Up" state
auto up5 = setElt(sites(5,"Up"));

• op(SiteSet sites,
string opname,
int i,
Args args = Args::global()) -> ITensor


Return a single-site operator acting on site i using the corresponding index and site type of the SiteSet sites.

For a list of operators available for a certain type of site, see the documentation on that particular type. For example, opname could be "Sz" for a S=1/2 site.

Some of the site types accept optional named arguments (Args).

Show Example
auto sites = Electron(40);

// Create a random MPS of all up spins
auto initstate = InitState(sites,"Up");
auto psi = randomMPS(initstate);

auto ndn5 = op(sites,"Ndn",5);

auto dens = elt(dag(prime(psi(8),"Site")) * op(sites,"Ntot",8) * psi(8));


A convenient feature of the op method is obtaining a product of two operators by joining their names with an asterisk *. For example, if opname is "Nup*Ndn", the operator return is the product (in the usual sense of a product of single-site operators written from left to right) of the operators "Nup" and "Ndn".

Show Example
// Continued from the example above
auto itcn = elt(dag(prime(psi(8),"Site")) * op(sites,"Nup*Ndn",8) * psi(8));

• inds(SiteSet sites) -> IndexSet

Return an IndexSet of the indices of the SiteSet (the SiteSet without the site type information).

Show Example
auto sites = SpinHalf(4);

auto is = inds(sites);

Print(is(3) == sites(3)); //prints: true

// Make an ITensor with the indices
auto T = ITensor(is);


## Operators Defined Automatically for all site types

Regardless of the specialized operators defined by each custom site type (such as the SpinHalfSite site type), the SiteSet class automatically provides the following operators which can be retrived as described from the .op method.

• "Id" — identity operator

Example:

 auto sites = SpinHalf(N);
auto id3 = op(sites,"Id",3);

• "Proj" — diagonal projection operator Requires additional named argument "State" specifying which state to project onto.

Example:

auto sites = SpinHalf(N);
//Projects site 3 onto state 2 (i.e. the down state)
auto P3_2 = op(sites,"Proj",3,{"State",2});


## Generic SiteSet class

You can also use the SiteSet class itself as a generic collection of site indices which defines only the minimal set of operators discussed above above (for example "Id" and "Proj"). A generic SiteSet can still be very useful for keeping track of Hilbert spaces not necessarily equipped with specific local site operators.

• SiteSet(int N, int d)

Construct a generic SiteSet object with N sites and local dimension size d.

The site indices created with this constructor have no QN information.

• SiteSet(IndexSet is)

Construct a SiteSet with the indices provided in the IndexSet (or any container of indices convertible to an IndexSet).

Show Example
auto sites = SpinHalf(10);

// Make an IndexSet of the indices
// of the SpinHalf siteset
auto is = inds(sites);

// Make a new SpinHalf site set from the indices
// grabbed from the original one
auto sites2 = SpinHalf(is);

Print(norm(op(sites,"Sz",1)-op(sites2,"Sz",1))); //prints: 0.0


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