# SpinHalf and SpinHalfSite

The SpinHalf class is a specialization of [[SiteSet|classes/siteset]] which initializes
its sites to be of type SpinHalfSite, representing a S=1/2 spin.

The SpinHalfSite class can also be used to create custom SiteSets which mix SpinHalfSites 
with other types of sites.

SpinHalf and SpinHalfSite are defined in the file "itensor/mps/sites/spinhalf.h"

## Synopsis

    //Make a spinhalf site with no QNs
    auto s = SpinHalfSite({"ConserveQNs=",false});

    //Make an Sz operator
    auto Sz = op(s,"Sz");

    //Get the Index of the site
    auto i = index(s);

    Print(hasInds(Sz,{i,prime(i)}));

    //Make a set of SpinHalfSites
    auto sites = SpinHalf(100);

    auto Sz3 = op(sites,"Sz",3);

    auto Sp4 = op(sites,"S+",4);

    //Use IndexVals to get the +,+ element of the Sz operator
    auto Szpp = elt(Sz3,sites(3,"Up"),prime(sites(3,"Up")));


## Args of a SpinHalfSite

* `"ConserveQNs"` — sets if the site has QN information or not. Defaults to true.

* `"ConserveSz"` — sets if the site has QN information or not. Defaults to true.

* `"SiteNumber"` — integer n. If specified, add a tag `"n="+str(n)` to the Index of the SpinHalfSite.

## States of a SpinHalfSite

* `"Up"` — the @@m\_z=+1/2@@ spin state

* `"Dn"` — the @@m\_z=-1/2@@ spin state

## Operators Provided by SpinHalfSite

* `"Sz"` — the @@S^z = \frac{1}{2}\sigma^z@@ spin operator 

* `"S+"` — the @@S^+ = \sigma^+@@ operator (alternate name is `"Sp"`)

* `"S-"` — the @@S^- = \sigma^-@@ operator (alternate name is `"Sm"`)

* `"Sx"` — the @@S^x = \frac{1}{2}\sigma^x@@ operator (must be converted to an ITensor prior to usage)

* `"Sy"` — the @@S^y = \frac{1}{2}\sigma^y@@ operator (must be converted to an ITensor prior to usage)

* `"ISy"` — defined as @@i\,S^y = \frac{i}{2}\sigma^y@@ (must be converted to an ITensor prior to usage)