Utilities

convert_ITensor_to_matrix(tens, sinit, sterm)

Converts an ITensor with two indices to a matrix. The index sinit is mapped to the column and sterm is mapped to the row.

identity_MPO(sites)

Returns the identity MPO based on the given sites.

MPO_to_MPS(ρ::MPO, fbcombiner)

Convert a given MPO to an MPS by combining the two site indices on every tensor into a single one using the vector of combiner tensors.

MPS_to_MPO(ρ::MPS, fbcombiner)

Split a given MPS to an MPO by using the vector of combiner tensors.

ITensors.expect(ρ::MPO, ops; kwargs...)

Extends ITensors' expect function to handle density matrices in the form of MPOs.

create_and_select_group(base, new_group)

Checks if new_group exists in base. Selects it if it does, else creates it.

check_or_insert_value(base, variable, value)

Inserts value into base[variable]. If it already exists, checks if the value is correct, and throws if not.

merge_into(source::String, destination::String)

Merge data from the HDF5 file at source to the one at destination.

get_BLAS_implementation()

Reports the BLAS implementation under use. The default implementation used by Julia is OpenBlas. MKL is supported through the external package MKL.jl, which needs to be installed and loaded before the loading of QuantumDynamics.jl

trapezoid(x, y; discrete::Bool=false, exec=ThreadedEx())

Returns the trapezoidal integration of y with respect to x. If discrete is set to true, then returns sum of y. exec encodes the execution paradigm and is one of seq or par.

fourier_transform(time::AbstractArray{<:Real}, corr::AbstractArray{<:Complex}; full=true, unitary=false)

Returns the Fourier transform of corr:

$C(\omega) = \mathcal{N}\,\int_a^\infty C(t)\,e^{i\omega t}\,dt$

If unitary is true, then $\mathcal{N}=\frac{1}{2\pi}$, else $\mathcal{N}=1$.

If full is true, then $a=-\infty$, else $a=0$.

commutator(A, B)

Returns the commutator A and B: AB - BA.

nh_commutator(A, B)

Returns the commutator A and B: AB - BA'.

calculate_Liouvillian(H::OpSum, sites)

Returns the forward-backward space combiner and the Liouvillian MPO corresponding to the Hamiltonian provided as an ITensor OpSum, to be built on the sites.

calculate_Liouvillian(Hamiltonian::AbstractMatrix{Complex})

Returns the Liouvillian corresponding to the given Hamiltonian.

ExternalField provides an abstract interface for encoding an external field, V(t), interacting with the system through the operator, coupling_op.

density_matrix_to_vector(ρ::AbstractMatrix{<:Complex})

Returns the vector representation of the density matrix ρ compatible with the forward-backward propagators.

density_matrix_vector_to_matrix(ρvec::AbstractVector{<:Complex})

Returns the matrix form of the vector ρvec.

hash_path(states, sdim)

Returns the hashed location of a path for a system with sdim dimensions.

unhash_path(path_num::Int, ntimes::Int, sdim::Int)

Construct a path for a system with sdim dimensions, corresponding to the number path_num, with ntimes time steps.

unhash_path_blips(ntimes::Int, sdim::Int, nblips::Int)

Construct all the paths for a system with sdim dimensions with ntimes time steps and nblips blips.

apply_propagator(; propagators, ρ0, ntimes, dt)

Apply a series of ntimes propagators to an initial reduced density matrix ρ0 and return the result as a tuple of (time, ρs).

create_tls_hamiltonian(; ϵ::AbstractFloat, Δ::AbstractFloat)

Creates a two-level system Hamiltonian:

$H = \frac{ϵ}{2}σ_z - \frac{Δ}{2}σ_x$

create_nn_hamiltonian(; site_energies::AbstractVector{AbstractFloat}, couplings::AbstractVector{AbstractFloat}, periodic::Bool)

Creates a nearest neighbour Hamiltonian with the given site_energies and couplings. Periodic boundary conditions can also be used by passing true into the periodic argument.

Abstract type for encoding all the method specific numerical parameters.

Extra parameters for solving differential equations. Currently has a threshold for magnitude-based filtering. The default values are:

• reltol = 1e-10
• abstol = 1e-10
• solver = Tsit5()

Extra parameters for tensor network algorithms. Currently has an SVD cutoff, a maximum bond dimension maxdim, and the contraction algorithm. The default values are as follows:

• cutoff = 1e-8
• maxdim = 500
• algorithm = "naive"

Other options for algorithm are "densitymatrix" and "fit".