## Learn to Use ITensor

main / classes / fermion

# Fermion and FermionSite

The Fermion class is a specialization of SiteSet which initializes its sites to be of type FermionSite, representing a spinless particle with maximum site occupancy of one (a fermion or "hard-core" boson).

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

A Fermion site set (and FermionSite) accepts the optional named argument "ConserveNf" which is true by default and will make the quantum numbers carried by a FermionSite include the particle number. If set to false, the quantum numbers will only reflect the particle number modulo 2 (the "parity").

Fermion and FermionSite are defined in the file "itensor/mps/sites/fermion.h"

## Synopsis

auto sites = Fermion(100);

auto N_3 = op(sites,"N",3);

auto A_4 = op(sites,"A",4);

//Make a Fermion site set which only conserves parity
auto psites = Fermion(100,{"ConserveNf",false});


## States of a FermionSite

• "Emp" or "0" — the vacuum (empty) state

• "Occ" or "1" — the occupied state (one particle)

## Operators Provided by FermionSite

• "N" — the density operator $\hat{n}$

• "A" — the annihilation operator $\hat{a}$

• "Adag" — the creation operator $\hat{a}^\dagger$

• "F" — the Jordan-Wigner fermion 'string' operator $\hat{F}=(1-2\hat{n})=(-1)^{\hat{n}}$

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.

• "C" — the annihilation operator $\hat{c}$ .

• "Cdag" — the creation operator $\hat{c}^\dagger$ .

Back to Classes
Back to Main