## Learn to Use ITensor

main / classes / tj

# 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 = sites.op("Ntot",3);

auto Cup_4 = sites.op("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). 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 $\hat{c}^\dagger_\downarrow$ .

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