# tJ and tJSite

The tJ class is a specialization of [[SiteSet|classes/siteset]] which initializes
its sites to be of type tJSite, representing a particle with spin 1/2
single local orbital, but constrained never to doubly-occupy this orbital as in the
t-J model.

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

tJ and tJSite are defined in the file "itensor/mps/sites/tj.h"

## Synopsis

    auto sites = tJ(100);

    auto Ntot_3 = op(sites,"Ntot",3);

    auto Cup_4 = op(sites,"Cup",4);

## States of a tJSite

* `"Emp"` — the vacuum (empty) state (alternate name `"0"`)

* `"Up"` — site occupied by one spin up particle (alternate name `"+"`)

* `"Dn"` — site occupied by one spin down particle (alternate name `"-"`)

## Operators Provided by tJSite

* `"Nup"` — density of up-spin particles @@\hat{n}\_\uparrow@@

* `"Ndn"` — density of down-spin particles @@\hat{n}\_\downarrow@@

* `"Ntot"` — the total density operator @@\hat{n}\_\text{tot} = \hat{n}\_\uparrow + \hat{n}\_\downarrow@@

* `"Aup"` — the up-spin annihilation operator @@\hat{a}\_\uparrow@@

* `"Adagup"` — the up-spin creation operator @@\hat{a}^\dagger\_\uparrow@@

* `"Adn"` — the down-spin annihilation operator @@\hat{a}\_\downarrow@@

* `"Adagdn"` — the down-spin creation operator @@\hat{a}^\dagger\_\downarrow@@

* `"F"` — the Jordan-Wigner fermion 'string' operator @@\hat{F}=(-1)^{\hat{n}\_\text{tot}}@@

* `"S+"` — the spin raising operator

* `"S-"` — the spin lowering operator

For the following fermionic operators, it is crucial to note that when obtaining them as individual
tensors from a site set, they do not anti-commute with each other on different sites, only on 
the same site (for more details on how these operators act on a single site read more at
[[this tutorial|tutorials/fermions]]). In contrast, when used as operator names in the
construction of an AutoMPO, they do anti-commute but only in that context.

* `"Cup"` — the up-spin annihilation operator @@\hat{c}\_\uparrow@@. 

* `"Cdagup"` — the up-spin creation operator @@\hat{c}^\dagger\_\uparrow@@.

* `"Cdn"` — the down-spin annihilation operator @@\hat{c}\_\downarrow@@. 

* `"Cdagdn"` — the down-spin creation operator @@\hat{c}^\dagger\_\downarrow@@.