Glossary
This is a summary of the type of objects you will be studying.
Sublat
: a sublattice, representing a number of identical sites within the unit cell of a bounded or unbounded lattice. Each site has a position in anE
-dimensional space (E
is called the embedding dimension). All sites in a givenSublat
will be able to hold the same number of orbitals, and they can be thought of as identical atoms. EachSublat
in aLattice
can be given a unique name, by default:A
,:B
, etc.Lattice
: a collection ofSublat
s plus a collection ofL
Bravais vectors that define the periodicity of the lattice. A bounded lattice hasL=0
, and no Bravais vectors. ALattice
withL > 0
can be understood as a periodic (unbounded) collection of unit cells, each containing a set of sites, each of which belongs to a different sublattice.SiteSelector
: a rule that defines a subset of sites in aLattice
(not necessarily restricted to a single unit cell)HopSelector
: a rule that defines a subset of site pairs in aLattice
(not necessarily restricted to the same unit cell)LatticeSlice
: a finite subset of sites in aLattice
, defined by their cell index (anL
-dimensional integer vector, usually denoted byn
orcell
) and their site index within the unit cell (an integer). ALatticeSlice
an be constructed by combining aLattice
and a (bounded)SiteSelector
.AbstractModel
: either aTightBindingModel
or aParametricModel
TightBindingModel
: a set ofHoppingTerm
s andOnsiteTerm
sOnsiteTerm
: a rule that, applied to a single site, produces a scalar or a (square) matrix that represents the intra-site Hamiltonian elements (single or multi-orbital)HoppingTerm
: a rule that, applied to a pair of sites, produces a scalar or a matrix that represents the inter-site Hamiltonian elements (single or multi-orbital)
ParametricModel
: a set ofParametricOnsiteTerm
s andParametricHoppingTerm
sParametricOnsiteTerm
: anOnsiteTerm
that depends on a set of free parameters that can be adjusted, and that may or may not have a default valueParametricHoppingTerm
: aHoppingTerm
that depends on parameters, likeParametricOnsiteTerm
above
AbstractHamiltonian
: either aHamiltonian
or aParametricHamiltonian
Hamiltonian
: aLattice
combined with aTightBindingModel
.It also includes a specification of the number of orbitals in each
Sublat
in theLattice
. AHamiltonian
represents a tight-binding Hamiltonian sharing the same periodicity as theLattice
(it is translationally invariant under Bravais vector shifts).ParametricHamiltonian
: like the above, but using aParametricModel
, which makes it dependent on a set of free parameters that can be efficiently adjusted.
An
h::AbstractHamiltonian
can be used to produce a Bloch matrixh(ϕ; params...)
of the same size as the number of orbitals per unit cell, whereϕ = [ϕᵢ...]
are Bloch phases andparams
are values for the free parameters, if any.Spectrum
: the set of eigenpairs (eigenvalues and corresponding eigenvectors) of a Bloch matrix. It can be computed with a number ofEigenSolvers
.Bandstructure
: a collection of spectra, evaluated over a discrete mesh (typically a discretization of the Brillouin zone), that is connected to its mesh neighbors into a linearly-interpolated approximation of theAbstractHamiltonian
's bandstructure.SelfEnergy
: an operatorΣ(ω)
defined to act on aLatticeSlice
of anAbstractHamiltonian
that depends on energyω
.OpenHamiltonian
: anAbstractHamiltonian
combined with a set ofSelfEnergies
GreenFunction
: anOpenHamiltonian
combined with anAbstractGreenSolver
, which is an algorithm that can in general compute the retarded or advanced Green function at any energy between any subset of sites of the underlying lattice.GreenSlice
: aGreenFunction
evaluated on a specific set of sites, but at an unspecified energyGreenSolution
: aGreenFunction
evaluated at a specific energy, but on an unspecified set of sites
OrbitalSliceArray
: anAbstractArray
that can be indexed with aSiteSelector
, in addition to the usual scalar indexing. Particular cases areOrbitalSliceMatrix
andOrbitalSliceVector
. This is the most common type obtained fromGreenFunction
s and observables obtained from them.Observables: Supported observables, obtained from Green functions using various algorithms, include local density of states, density matrices, current densities, transmission probabilities, conductance and Josephson currents