API Reference

SpinModel(N; Jxy=1.0, Jz=1.0, hx=zeros(N), hz=zeros(N), Jmn=zeros(N, N))

Construct a quantum spin model.

Arguments

• N: Number of spins.

Keywords

• Jxy: XY coupling strength.
• Jz: Ising coupling strength.
• hx: Local x-fields.
• hz: Local z-fields.
• Jmn: Coupling matrix.

Returns

A SpinModel containing the Hamiltonian and model parameters.

update_model!(model::SpinModel, Jxy::Float64, Jz::Float64; kwargs...)

Updates the Hamiltonian of an existing SpinModel object with new parameters.

Arguments:

• model: The SpinModel instance to update.
• Jxy: XY coupling constant.
• Jz: Z coupling constant.

Keyword arguments:

• hx: New magnetic field in the x-direction.
• hz: New magnetic field in the z-direction.
• Jmn: New coupling matrix.

Returns: Nothing. Modifies the SpinModel in place.

neel_state(N; direction=:z)

Construct a normalized Néel product state for N spins.

The first spin points along the positive direction, followed by alternating spins. direction may be :z or :x.

polarized_state(N; direction=:z)

Construct a normalized fully polarized product state for N spins.

direction may be :z or :x.

evolve(model, ψ0, time_points, observables; kwargs...)

Evolve a pure state under a SpinModel.

Supported methods:

• :krylov
• :arnoldi
• :trajectories

evolve(model, ρ0, time_points, observables; lindblad_ops, method=:expm)

Evolve a density matrix under Lindblad dynamics.

Supported methods:

• :expm
• :ode

SpinOperators

Collection of single-site spin operators for an N-spin Hilbert space.

The fields contain sparse operators acting on the full Hilbert space:

• x[i]: Pauli $σ_x$ operator acting on site i.
• z[i]: Pauli $σ_z$ operator acting on site i.
• plus[i]: raising operator $σ_+$ acting on site i.
• minus[i]: lowering operator $σ_-$ acting on site i.

spin_operators(N::Int)

Construct single-site spin operators for an N-spin system.

Returns a SpinOperators object containing the $σ_x$, $σ_z$, $σ_+$, and $σ_-$ operators for every site, represented as sparse matrices on the full $2^N$-dimensional Hilbert space.

Arguments

• N: Number of spins. Must be positive.

Example

ops = spin_operators(4)

ops.z[1]
ops.plus[2]

LongRangeCouplingClean

Clean long-range power-law coupling between N spins.

The interaction between sites i and j is

\[J_{ij} = \frac{1}{|i-j|^\alpha},\]

with zero diagonal.

LongRangeCouplingDisorder

Random long-range power-law coupling between N spins distributed over a lattice of size L.

Couplings decay with distance as

\[J_{ij} = \frac{1}{|r_i-r_j|^\alpha}.\]

The generated coupling matrix is symmetric with zero diagonal.

Fields

• matrix: Coupling matrix.
• α: Power-law exponent.
• L: Lattice size.
• N: Number of spins.
• reordered: Whether sampled sites are reordered.

NearestNeighborCoupling

Nearest-neighbor coupling with alternating bond strengths.

For neighboring sites, the coupling is

\[J_{n,n+1} = 1 + (-1)^n \delta,\]

while all non-nearest-neighbor couplings vanish.