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}_\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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