## Learn to Use ITensor

main / classes / tj C++v3 | C++v2

# tJ and tJSite

The tJ class is a specialization of 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}_\[email protected]@ • "Ndn" — density of down-spin particles$\hat{n}_\[email protected]@

• "Ntot" — the total density operator $\hat{n}_\text{tot} = \hat{n}_\uparrow + \hat{n}_\[email protected]@ • "Aup" — the up-spin annihilation operator$\hat{a}_\[email protected]@

• "Adagup" — the up-spin creation operator $\hat{a}^\dagger_\[email protected]@ • "Adn" — the down-spin annihilation operator$\hat{a}_\[email protected]@

• "Adagdn" — the down-spin creation operator $\hat{a}^\dagger_\[email protected]@ • "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). 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}_\[email protected]@ .

• "Cdagup" — the up-spin creation operator $\hat{c}^\dagger_\[email protected]@ . • "Cdn" — the down-spin annihilation operator$\hat{c}_\[email protected]@ .

• "Cdagdn" — the down-spin creation operator @@\hat{c}^\dagger_\[email protected]@ .

Back to Classes
Back to Main