GitHub

Getting Started

This page introduces the core EDKit workflow:

  1. define local terms,
  2. specify where they act,
  3. choose a basis,
  4. build an operator,
  5. apply it or convert it to an explicit matrix.

The Main Abstraction

The central user-facing object in EDKit is Operator.

An Operator stores a many-body operator as a sum of local terms on a chosen basis. That means you can describe your Hamiltonian once and then decide how you want to use it:

  • apply it directly to a state vector,
  • convert it to Array(H) for dense exact diagonalization,
  • convert it to sparse(H) for sparse workflows.

A First Example

Here is a compact open-chain XXZ Hamiltonian on L = 8 sites:

using EDKit, LinearAlgebra, SparseArrays

L = 8
Delta = 1.5

mats = [
    fill(spin("XX"), L - 1);
    fill(spin("YY"), L - 1);
    fill(Delta * spin("ZZ"), L - 1);
]

inds = vcat(
    [[i, i + 1] for i in 1:L-1],
    [[i, i + 1] for i in 1:L-1],
    [[i, i + 1] for i in 1:L-1],
)

H = operator(mats, inds, L)

H is now an Operator acting on the full TensorBasis of a spin-1/2 chain.

Using The Operator

Apply it to a state:

psi = normalize(randn(ComplexF64, 2^L))
Hpsi = H * psi

Convert it to explicit matrix representations:

Hdense = Array(H)
Hsparse = sparse(H)

Diagonalize the dense version:

vals = eigvals(Hermitian(Hdense))

Working In A Symmetry Sector

EDKit becomes especially useful when you do not want the full Hilbert space.

For example, the half-filling momentum-zero sector can be built with the high-level basis(...) helper:

using EDKit, LinearAlgebra

L = 12
B = basis(L = L, N = L ÷ 2, k = 0)

h2 = spin((1.0, "xx"), (1.0, "yy"), (1.0, "zz"))
H = trans_inv_operator(h2, 1:2, B)

vals, vecs = eigen(Hermitian(Array(H)))

The construction logic is the same as before, but the basis is now symmetry reduced.