Single-particle Green's functions

`computegf()`

KeldyshED.computegf — Method

computegf(
    ed::EDCore,
    t1::Keldysh.BranchPoint,
    t2::Keldysh.BranchPoint,
    c_index::Vector{Union{Int64, String}},
    cdag_index::Vector{Union{Int64, String}},
    β::Float64
) -> ComplexF64

Compute single-particle Keldysh Green's function

\[G_{ij}(t_1, t_2) = -i \mathrm{Tr}[\hat\rho \mathbb{T}_\mathcal{C} c_i(t_1) c^\dagger_j(t_2)], \quad \hat\rho = \frac{e^{-\beta\hat H}}{\mathrm{Tr}[e^{-\beta\hat H}]}\]

at given contour times $t_1$, $t_2$ for given compound indices of creation/annihilation operators $i$ and $j$.

Arguments

ed: Exact Diagonalization object.
t1: Contour time $t_1$.
t2: Contour time $t_2$.
c_index: Compound index $i$.
cdag_index: Compound index $j$.
β: Inverse temperature $\beta$.

source

KeldyshED.computegf — Method

computegf(
    ed::EDCore,
    t1::Keldysh.BranchPoint,
    t2::Keldysh.BranchPoint,
    c_index::Vector{Union{Int64, String}},
    cdag_index::Vector{Union{Int64, String}};
    en,
    ρ
)

Compute single-particle Keldysh Green's function

\[G_{ij}(t_1, t_2) = -i \mathrm{Tr}[\hat\rho \mathbb{T}_\mathcal{C} c_i(t_1) c^\dagger_j(t_2)]\]

at given contour times $t_1$, $t_2$ for given compound indices of creation/annihilation operators $i$ and $j$. This method is useful if the density matrix $\hat\rho$ has already been computed.

Arguments

ed: Exact Diagonalization object.
t1: Contour time $t_1$.
t2: Contour time $t_2$.
c_index: Compound index $i$.
cdag_index: Compound index $j$.
en: Energy levels of the system as returned by energies().
ρ Density matrix $\hat\rho$ as returned by density_matrix().

source

KeldyshED.computegf — Method

computegf(
    ed::EDCore,
    grid::Keldysh.FullTimeGrid,
    c_index::Vector{Union{Int64, String}},
    cdag_index::Vector{Union{Int64, String}};
    gf_filler
) -> Keldysh.TimeInvariantFullTimeGF{ComplexF64, true}

Compute single-particle Keldysh Green's function

\[G_{ij}(t_1, t_2) = -i \mathrm{Tr}[\hat\rho \mathbb{T}_\mathcal{C} c_i(t_1) c^\dagger_j(t_2)]\]

on a 3-branch Konstantinov-Perel' contour for given compound indices of creation/annihilation operators $i$ and $j$.

Arguments

ed: Exact Diagonalization object.
grid: Time grid on the 3-branch contour.
c_index: Compound index $i$.
cdag_index: Compound index $j$.
gf_filler: Algorithm selector for GF computation.

source

KeldyshED.computegf — Method

computegf(
    ed::EDCore,
    grid::Keldysh.KeldyshTimeGrid,
    c_index::Vector{Union{Int64, String}},
    cdag_index::Vector{Union{Int64, String}},
    β::Float64;
    gf_filler
) -> Keldysh.TimeInvariantKeldyshTimeGF{ComplexF64, true}

Compute single-particle Keldysh Green's function

\[G_{ij}(t_1, t_2) = -i \mathrm{Tr}[\hat\rho \mathbb{T}_\mathcal{C} c_i(t_1) c^\dagger_j(t_2)], \quad \hat\rho = \frac{e^{-\beta\hat H}}{\mathrm{Tr}[e^{-\beta\hat H}]}\]

on a 2-branch Keldysh contour for given compound indices of creation/annihilation operators $i$ and $j$ with a decoupled initial thermal state at inverse temperature $\beta$.

Arguments

ed: Exact Diagonalization object.
grid: Time grid on the 2-branch contour.
c_index: Compound index $i$.
cdag_index: Compound index $j$.
β: Inverse temperature $\beta$.
gf_filler: Algorithm selector for GF computation.

source

KeldyshED.computegf — Method

computegf(
    ed::EDCore,
    grid::Keldysh.ImaginaryTimeGrid,
    c_index::Vector{Union{Int64, String}},
    cdag_index::Vector{Union{Int64, String}};
    gf_filler
) -> Keldysh.ImaginaryTimeGF{ComplexF64, true}

Compute single-particle Keldysh Green's function

\[G_{ij}(t_1, t_2) = -i \mathrm{Tr}[\hat\rho \mathbb{T}_\mathcal{C} c_i(t_1) c^\dagger_j(t_2)]\]

on the imaginary time segment $[0;-i\beta]$ for given compound indices of creation/annihilation operators $i$ and $j$.

Arguments

ed: Exact Diagonalization object.
grid: Time grid on the imaginary time segment.
c_index: Compound index $i$.
cdag_index: Compound index $j$.
gf_filler: Algorithm selector for GF computation.

source

KeldyshED.computegf — Method

computegf(
    ed::EDCore,
    grid::Keldysh.FullTimeGrid,
    c_cdag_index_pairs::Vector{Tuple{Vector{Union{Int64, String}}, Vector{Union{Int64, String}}}};
    gf_filler
) -> Vector{Keldysh.TimeInvariantFullTimeGF{ComplexF64, true}}

Compute multiple single-particle Keldysh Green's functions

\[G_{ij}(t_1, t_2) = -i \mathrm{Tr}[\hat\rho \mathbb{T}_\mathcal{C} c_i(t_1) c^\dagger_j(t_2)]\]

on a 3-branch Konstantinov-Perel' contour for given compound indices of creation/annihilation operators $i$ and $j$.

Arguments

ed: Exact Diagonalization object.
grid: Time grid on the 3-branch contour.
c_cdag_index_pairs: List of compound index pairs $(i, j)$.
gf_filler: Algorithm selector for GF computation.

source

KeldyshED.computegf — Method

computegf(
    ed::EDCore,
    grid::Keldysh.KeldyshTimeGrid,
    c_cdag_index_pairs::Vector{Tuple{Vector{Union{Int64, String}}, Vector{Union{Int64, String}}}},
    β::Float64;
    gf_filler
) -> Vector{Keldysh.TimeInvariantKeldyshTimeGF{ComplexF64, true}}

Compute multiple single-particle Keldysh Green's functions

\[G_{ij}(t_1, t_2) = -i \mathrm{Tr}[\hat\rho \mathbb{T}_\mathcal{C} c_i(t_1) c^\dagger_j(t_2)], \quad \hat\rho = \frac{e^{-\beta\hat H}}{\mathrm{Tr}[e^{-\beta\hat H}]}\]

on a 2-branch Keldysh contour for given compound indices of creation/annihilation operators $i$ and $j$ with a decoupled initial thermal state at inverse temperature $\beta$.

Arguments

ed: Exact Diagonalization object.
grid: Time grid on the 2-branch contour.
c_cdag_index_pairs: List of compound index pairs $(i, j)$.
β: Inverse temperature $\beta$.
gf_filler: Algorithm selector for GF computation.

source

KeldyshED.computegf — Method

computegf(
    ed::EDCore,
    grid::Keldysh.ImaginaryTimeGrid,
    c_cdag_index_pairs::Vector{Tuple{Vector{Union{Int64, String}}, Vector{Union{Int64, String}}}};
    gf_filler
) -> Vector{Keldysh.ImaginaryTimeGF{ComplexF64, true}}

Compute multiple single-particle Keldysh Green's functions

\[G_{ij}(t_1, t_2) = -i \mathrm{Tr}[\hat\rho \mathbb{T}_\mathcal{C} c_i(t_1) c^\dagger_j(t_2)]\]

on the imaginary time segment $[0;-i\beta]$ for given compound indices of creation/annihilation operators $i$ and $j$.

Arguments

ed: Exact Diagonalization object.
grid: Time grid on the imaginary time segment.
c_cdag_index_pairs: List of compound index pairs $(i, j)$.
gf_filler: Algorithm selector for GF computation.

source

KeldyshED.computegf — Method

computegf(
    ed::EDCore,
    grid::Keldysh.FullTimeGrid,
    c_indices::Vector{Vector{Union{Int64, String}}},
    cdag_indices::Vector{Vector{Union{Int64, String}}};
    gf_filler
) -> Keldysh.TimeInvariantFullTimeGF{ComplexF64, false}

Compute a matrix-valued single-particle Keldysh Green's function

\[G_{ij}(t_1, t_2) = -i \mathrm{Tr}[\hat\rho \mathbb{T}_\mathcal{C} c_i(t_1) c^\dagger_j(t_2)]\]

on a 3-branch Konstantinov-Perel' contour for all possible pairs of compound indices $(i, j)$ given a list of $i$ and a list of $j$ (the lists must have equal length).

Arguments

ed: Exact Diagonalization object.
grid: Time grid on the 3-branch contour.
c_indices: List of compound indices $i$.
cdag_indices: List of compound indices $j$.
gf_filler: Algorithm selector for GF computation.

source

KeldyshED.computegf — Method

computegf(
    ed::EDCore,
    grid::Keldysh.KeldyshTimeGrid,
    c_indices::Vector{Vector{Union{Int64, String}}},
    cdag_indices::Vector{Vector{Union{Int64, String}}},
    β::Float64;
    gf_filler
) -> Keldysh.TimeInvariantKeldyshTimeGF{ComplexF64, false}

Compute a matrix-valued single-particle Keldysh Green's function

\[G_{ij}(t_1, t_2) = -i \mathrm{Tr}[\hat\rho \mathbb{T}_\mathcal{C} c_i(t_1) c^\dagger_j(t_2)], \quad \hat\rho = \frac{e^{-\beta\hat H}}{\mathrm{Tr}[e^{-\beta\hat H}]}\]

on a 2-branch Keldysh contour for all possible pairs of compound indices $(i, j)$ given a list of $i$ and a list of $j$ (the lists must have equal length).

Arguments

ed: Exact Diagonalization object.
grid: Time grid on the 2-branch contour.
c_indices: List of compound indices $i$.
cdag_indices: List of compound indices $j$.
β: Inverse temperature $\beta$.
gf_filler: Algorithm selector for GF computation.

source

KeldyshED.computegf — Method

computegf(
    ed::EDCore,
    grid::Keldysh.ImaginaryTimeGrid,
    c_indices::Vector{Vector{Union{Int64, String}}},
    cdag_indices::Vector{Vector{Union{Int64, String}}};
    gf_filler
) -> Keldysh.ImaginaryTimeGF{ComplexF64, false}

Compute a matrix-valued single-particle Keldysh Green's function

\[G_{ij}(t_1, t_2) = -i \mathrm{Tr}[\hat\rho \mathbb{T}_\mathcal{C} c_i(t_1) c^\dagger_j(t_2)]\]

on the imaginary time segment $[0;-i\beta]$ for all possible pairs of compound indices $(i, j)$ given a list of $i$ and a list of $j$ (the lists must have equal length).

Arguments

ed: Exact Diagonalization object.
grid: Time grid on the imaginary time segment.
c_indices: List of compound indices $i$.
cdag_indices: List of compound indices $j$.
gf_filler: Algorithm selector for GF computation.

source

Auxiliary types

KeldyshED.AbstractGFFiller — Type

Abstract supertype for GF filler types.

source

KeldyshED.SerialGFFiller — Type

An argument of this type instructs Green's function computation routines to use a serial (non-parallelized) algorithm.

source

KeldyshED.DistributedGFFiller — Type

An argument of this type instructs Green's function computation routines to use Distributed.@distributed to speed up calculation.

source