SparseIR.jl

Documentation for SparseIR.jl.

There is a guide available which explains the intermediate representation and how SparseIR.jl computes it by means of a worked example.

The notation and conventions are those of the notation page, shared by the Julia, Python and Rust libraries. In brief:

• The statistics have the parity $ζ$ (SparseIR.zeta): 1 for fermions, 0 for bosons; a function of imaginary time obeys $G(τ + β) = (-1)^ζ G(τ)$.
• Matsubara frequencies are $ν = nπ/β$ with the reduced frequency $n$, odd for fermions and even for bosons; the functions of Matsubara frequency take $n$ or a MatsubaraFreq.
• $G(\mathrm{i}ν) = ∫_0^β dτ\, e^{\mathrm{i}ντ} G(τ)$, and $G_l = -S_l ∫ dω\, ρ(ω) V_l(ω)$ with $ρ = A$ for fermions and $ρ = A/\tanh(βω/2)$ for bosons.
• The basis functions accept $τ ∈ [-β, β]$; 0.0 is read as $0^+$, β as $β^-$, -0.0 as $0^-$ and -β as $(-β)^+$.
• The index $l$ of $U_l$, $S_l$ and $V_l$ counts from 0; Julia's basis.u[l+1] is $U_l$.

For listings of all documented names, see Public names index and the Private names index.