Quick reference

Terms

Add terms together to define the structure of your Hamiltonian and multiply with constants and coupling matrices (only once!) to set up a concrete realization.

• X(h), Y(h) and Z(h) stand for $\sum_i h_i \sigma_\alpha^{(i)},$ where $\alpha$ is $x$, $y$ or $z$.
• XX(J), YY(J) and ZZ(J) stand for $\sum_{i,j} J_{i,j} \sigma_\alpha^{(i)}\sigma_\alpha^{(j)},$ where $\alpha$ is $x$, $y$ or $z$.
• FlipFlop(J) (or equivalently Hopp(J)) is the same as 0.5*J*(XX()+YY())
• XXZ(Δ, J) is the same as 2*Hopp(J)+Δ*ZZ(J) which is the same as XX(J)+YY(J)+Δ*ZZ(J)

Geometries

Current implemented are (N always denotes the total number of spins):

• Chain(N)
• Box(N, dims)
• NoisyChain(N, σ; spacing=1)
• PartiallyFilledChain(numspins, numsites; spacing=1)
• Blockaded(geometry; retries=1000, blockade=1.0)
• PBC(geometry)
• NN(geometry, k=1)

Interactions

Currently implemented are

• ConstantInteraction(value)
• PowerLaw(α)
• NN(interaction, k=1)

Note about nearest neighbor (NN)

For isotropic interactions (i.e. all currently implemented ones) it does not matter whether you apply NN to the interaction or the geometry. In principle for anisotropic interaction there will be a subtle difference:

• NN on geometry is based on distances and will remove all but the ksmallest distances
• NN on interactions is based on coupling strength and will remove all but the kstrongest couplings