triqs.operators

Second-quantization operators and many-body operator algebra.

Provides the Operator class together with the canonical factories c() (annihilation), c_dag() (creation) and n() (number operator), as well as the Hermitian-conjugate function dagger(). Higher- level helpers — model Hamiltonians, observables, interaction tensors and coefficient extractors — live in triqs.operators.util.

Examples

Build many-body operators from the canonical factories and combine them with the usual algebra (sums, products, multiplication by a scalar). The factory arguments are arbitrary indices, e.g. a spin name and an orbital index:

>>> from triqs.operators import c, c_dag, n, dagger

A single-orbital Hubbard interaction (two spins):

>>> U = 4.0
>>> H = U * n('up', 0) * n('dn', 0)

Nearest-neighbour hopping on a two-site spinless chain:

>>> t = 1.0
>>> H = -t * (c_dag('s', 0) * c('s', 1) + c_dag('s', 1) * c('s', 0))

The number operator is n(*idx) == c_dag(*idx) * c(*idx), so the following operator is identically zero:

>>> (n('up', 0) - c_dag('up', 0) * c('up', 0)).is_zero()
True

Operators can be Hermitian-conjugated with dagger():

>>> op = c_dag('up', 0) * c('dn', 1)
>>> H = op + dagger(op)              # a Hermitian hopping term

Modules

`operators`	Second-quantization operators and many-body operator algebra.
`util`	Utilities built on top of `Operator`.