Observables

abstract type AbstractDensityMatrix

Abstract super-type of all density matrices.

See also: DensityMatrix, and PurifiedDensityMatrix.

struct DensityMatrix{P<:TensorRenormalizationGroups.AbstractUnitCell, T<:TensorRenormalizationGroups.Renormalization} <: AbstractDensityMatrix

Concrete type representing a normalized density matrix with associated trace environment of type T.

See also: PurifiedDensityMatrix, trace, and partialtrace.

struct PurifiedDensityMatrix{P<:TimeEvolutionPEPO.HilbertSchmidt, T<:TensorRenormalizationGroups.Renormalization} <: AbstractDensityMatrix

Concrete type representing a normalized purified density matrix with associated trace environment of type T, i.e. a density matrix of the form $\rho = X^{\dagger}X$ where $X$ is represented by tensor network.

Note, this should be used for thermal state evolution only.

See also: DensityMatrix, trace, and partialtrace.

trace(rho::DensityMatrix) -> Any

Calculate the full trace density of the density matrix rho for each site in the unit cell. Note, if rho is constructed properly, then trace(rho) .≈ one(scalartype(rho)).

partialtrace(
    rho::DensityMatrix,
    inds::T<:Union{Tuple{Int64, Int64}, CartesianIndex{2}}...
) -> TensorKit.TensorMap

Calculate the partial trace of rho returning a TensorMap. Indices in inds define those sites that remain untraced. Site indices in inds are mapped to tensor indices in the same order as in inds.

expval(rho::TensorMap, ops::Vararg{T, N}; inds=NTuple{N}(1:N))

Calculate the expectation value of product of local operators ops applied to the indices inds respectively. The keyword inds defaults to applying all ops to the first indices of rho consecutively.

negativity(rho) -> Number

Calculate the entanglement negativity of bipartite rho represented as a TensorMap with codomain(rho) == domain(rho).

correlator(rho::DensityMatrix, A1, i1, A2, i2)

Calculate the two-point correlator of rho between observables A1 and A2 on sites i1 end i2 respectively.

correlationlength(state::DensityMatrix) -> Float64
correlationlength(state::PEPO, env::AbstractBoundary) -> Float64
correlationlength(state::PEPO, alg::AbstractBoundaryAlgorithm) -> Float64

Calculate the correlation length zeta of the quantum state state by constructing the transfer matrix and computing the the inverse of the sub-leading eigenvalue.

The correlation length characterizes how quickly correlations decay with distance in a quantum system. For a state with exponentially decaying correlations of the form C(r) ∝ exp(-r/ξ), the correlation length ξ quantifies the characteristic distance over which quantum correlations persist.