Algebra with compatible Hamiltonians

[pablosanjose]

This PR allows one to do basic algebra with Hamiltonians (that share lattice and orbital structure). This includes ^, *, +, - and addition of the identity I.

An example

julia> h = LatticePresets.honeycomb() |> hamiltonian(hopping(I), orbitals = (Val(2), Val(1))) |> unitcell(2)
Hamiltonian{<:Lattice} : Hamiltonian on a 2D Lattice in 2D space
  Bloch harmonics  : 5 (SparseMatrixCSC, sparse)
  Harmonic size    : 8 × 8
  Orbitals         : ((:a, :a), (:a,))
  Element type     : 2 × 2 blocks (Complex{Float64})
  Onsites          : 0
  Hoppings         : 24
  Coordination     : 3.0

julia> 2h^2 + h
Hamiltonian{<:Lattice} : Hamiltonian on a 2D Lattice in 2D space
  Bloch harmonics  : 13 (SparseMatrixCSC, sparse)
  Harmonic size    : 8 × 8
  Orbitals         : ((:a, :a), (:a,))
  Element type     : 2 × 2 blocks (Complex{Float64})
  Onsites          : 8
  Hoppings         : 72
  Coordination     : 9.0

One possible usecase for this is the computation of the square of the shifted spectrum of h (doing e.g. spectrum((h-z*I)^2, method->ArpackPackage(which = :LM))) as a cheap way towards internal eigenvalues using Arnoldi.

(Note that the addition of UniformScaling respects the orbital structure of h)

[codecov-io]

Codecov Report

Merging #113 into master will increase coverage by 1.36%.
The diff coverage is 85.93%.

@@            Coverage Diff             @@
##           master     #113      +/-   ##
==========================================
+ Coverage   61.12%   62.48%   +1.36%     
==========================================
  Files          16       16              
  Lines        2765     2823      +58     
==========================================
+ Hits         1690     1764      +74     
+ Misses       1075     1059      -16     

Impacted Files	Coverage Δ
src/plot_vegalite.jl	0.00% <0.00%> (ø)
src/hamiltonian.jl	79.56% <91.37%> (+4.04%)	⬆️
src/tools.jl	57.67% <100.00%> (+1.19%)	⬆️

---

Continue to review full report at Codecov.

Legend - Click here to learn more
Δ = absolute <relative> (impact), ø = not affected, ? = missing data
Powered by Codecov. Last update 73c55f8...37ef4ac. Read the comment docs.