Grids

AbstractGrid

An abstract type representing the imaginary axis. It is used to build the internal type system.

FermionicImaginaryTimeGrid

Mutable struct. It represents the fermionic imaginary time grid.

Members

• ntime -> Number of time slices.
• β -> Inverse temperature.
• τ -> Vector of grid points， τᵢ.

See also: FermionicFragmentTimeGrid.

FermionicFragmentTimeGrid

Mutable struct. It represents part of the fermionic imaginary time grid. In other words, the grid might be fragmentary。

Members

• ntime -> Number of time slices.
• β -> Inverse temperature.
• τ -> Vector of grid points, τᵢ.

See also: FermionicImaginaryTimeGrid.

FermionicMatsubaraGrid

Mutable struct. It represents the fermionic Matsubara frequency grid.

Members

• nfreq -> Number of Matsubara frequency points.
• β -> Inverse temperature.
• ω -> Vector of grid points, iωₙ.

See also: FermionicFragmentMatsubaraGrid.

FermionicFragmentMatsubaraGrid

Mutable struct. It represents part of the fermionic Matsubara frequency grid. In other words, the grid might be fragmentary。

Members

• nfreq -> Number of Matsubara frequency points.
• β -> Inverse temperature.
• ω -> Vector of grid points, iωₙ.

See also: FermionicMatsubaraGrid.

BosonicImaginaryTimeGrid

Mutable struct. It represents the bosonic imaginary time grid.

Members

• ntime -> Number of time slices.
• β -> Inverse temperature.
• τ -> Vector of grid points, τᵢ.

See also: BosonicFragmentTimeGrid.

BosonicFragmentTimeGrid

Mutable struct. It represents part of the bosonic imaginary time grid. In other words, the grid might be fragmentary。

Members

• ntime -> Number of time slices.
• β -> Inverse temperature.
• τ -> Vector of grid points, τᵢ.

See also: BosonicImaginaryTimeGrid.

BosonicMatsubaraGrid

Mutable struct. It represents the bosonic Matsubara frequency grid.

Members

• nfreq -> Number of Matsubara frequency points.
• β -> Inverse temperature.
• ω -> Vector of grid points, iωₙ.

See also: BosonicFragmentMatsubaraGrid.

BosonicFragmentMatsubaraGrid

Mutable struct. It represents part of the bosonic Matsubara frequency grid. In other words, the grid might be fragmentary。 However, the first frequency point should be present (ωₙ ≡ 0.0).

Members

• nfreq -> Number of Matsubara frequency points.
• β -> Inverse temperature.
• ω -> Vector of grid points, iωₙ.

See also: BosonicMatsubaraGrid.

FermionicImaginaryTimeGrid(ntime::I64, β::T) where {T}

A constructor for the FermionicImaginaryTimeGrid struct, which is defined in src/types.jl.

Arguments

• ntime -> Number of time slices in imaginary axis.
• β -> Inverse temperature.

Returns

• grid -> A FermionicImaginaryTimeGrid struct.

See also: FermionicImaginaryTimeGrid.

FermionicFragmentTimeGrid(β::T, τ::Vector{T}) where {T}

A constructor for the FermionicFragmentTimeGrid struct, which is defined in src/types.jl.

Arguments

• β -> Inverse temperature.
• τ -> Given imaginary time points.

Returns

• grid -> A FermionicFragmentTimeGrid struct.

See also: FermionicFragmentTimeGrid.

FermionicMatsubaraGrid(nfreq::I64, β::T) where {T}

A constructor for the FermionicMatsubaraGrid struct, which is defined in src/types.jl. The Matsubara grid is evaluated as ωₙ = (2n - 1) π / β.

Arguments

• nfreq -> Number of Matsubara frequencies.
• β -> Inverse temperature.

Returns

• grid -> A FermionicMatsubaraGrid struct.

See also: FermionicMatsubaraGrid.

FermionicFragmentMatsubaraGrid(β::T, ω::Vector{T}) where {T}

A constructor for the FermionicFragmentMatsubaraGrid struct, which is defined in src/types.jl. The Matsubara grid is from input.

Arguments

• β -> Inverse temperature.
• ω -> Given Matsubara frequency points.

Returns

• grid -> A FermionicFragmentMatsubaraGrid struct.

See also: FermionicFragmentMatsubaraGrid.

BosonicImaginaryTimeGrid(ntime::I64, β::T)

A constructor for the BosonicImaginaryTimeGrid struct, which is defined in src/types.jl.

Arguments

• ntime -> Number of time slices in imaginary axis.
• β -> Inverse temperature.

Returns

• grid -> A BosonicImaginaryTimeGrid struct.

See also: BosonicImaginaryTimeGrid.

BosonicFragmentTimeGrid(β::T, τ::Vector{T}) where {T}

A constructor for the BosonicFragmentTimeGrid struct, which is defined in src/types.jl.

Arguments

• β -> Inverse temperature.
• τ -> Given imaginary time points.

Returns

• grid -> A BosonicFragmentTimeGrid struct.

See also: BosonicFragmentTimeGrid.

BosonicMatsubaraGrid(nfreq::I64, β::T) where {T}

A constructor for the BosonicMatsubaraGrid struct, which is defined in src/types.jl. The Matsubara grid is evaluated as ωₙ = (2n - 2) π / β.

Arguments

• nfreq -> Number of Matsubara frequencies.
• β -> Inverse temperature.

Returns

• grid -> A BosonicMatsubaraGrid struct.

See also: BosonicMatsubaraGrid.

BosonicFragmentMatsubaraGrid(β::T, ω::Vector{T}) where {T}

A constructor for the BosonicFragmentMatsubaraGrid struct, which is defined in src/types.jl. The Matsubara grid is from input.

Arguments

• β -> Inverse temperature.
• ω -> Given Matsubara frequency points.

Returns

• grid -> A BosonicFragmentMatsubaraGrid struct.

See also: BosonicFragmentMatsubaraGrid.

Base.length(fg::FermionicImaginaryTimeGrid)

Return number of grid points in a FermionicImaginaryTimeGrid struct.

See also: FermionicImaginaryTimeGrid.

Base.length(fg::FermionicFragmentTimeGrid)

Return number of grid points in a FermionicFragmentTimeGrid struct.

See also: FermionicFragmentTimeGrid.

Base.length(fg::FermionicMatsubaraGrid)

Return number of grid points in a FermionicMatsubaraGrid struct.

See also: FermionicMatsubaraGrid.

Base.length(fg::FermionicFragmentMatsubaraGrid)

Return number of grid points in a FermionicFragmentMatsubaraGrid struct.

See also: FermionicFragmentMatsubaraGrid.

Base.length(bg::BosonicImaginaryTimeGrid)

Return number of grid points in a BosonicImaginaryTimeGrid struct.

See also: BosonicImaginaryTimeGrid.

Base.length(bg::BosonicFragmentTimeGrid)

Return number of grid points in a BosonicFragmentTimeGrid struct.

See also: BosonicFragmentTimeGrid.

Base.length(bg::BosonicMatsubaraGrid)

Return number of grid points in a BosonicMatsubaraGrid struct.

See also: BosonicMatsubaraGrid.

Base.length(bg::BosonicFragmentMatsubaraGrid)

Return number of grid points in a BosonicFragmentMatsubaraGrid struct.

See also: BosonicFragmentMatsubaraGrid.

Base.iterate(fg::FermionicImaginaryTimeGrid)

Advance the iterator of a FermionicImaginaryTimeGrid struct to obtain the next grid point.

See also: FermionicImaginaryTimeGrid.

Base.iterate(fg::FermionicFragmentTimeGrid)

Advance the iterator of a FermionicFragmentTimeGrid struct to obtain the next grid point.

See also: FermionicFragmentTimeGrid.

Base.iterate(fg::FermionicMatsubaraGrid)

Advance the iterator of a FermionicMatsubaraGrid struct to obtain the next grid point.

See also: FermionicMatsubaraGrid.

Base.iterate(fg::FermionicFragmentMatsubaraGrid)

Advance the iterator of a FermionicFragmentMatsubaraGrid struct to obtain the next grid point.

See also: FermionicFragmentMatsubaraGrid.

Base.iterate(bg::BosonicImaginaryTimeGrid)

Advance the iterator of a BosonicImaginaryTimeGrid struct to obtain the next grid point.

See also: BosonicImaginaryTimeGrid.

Base.iterate(bg::BosonicFragmentTimeGrid)

Advance the iterator of a BosonicFragmentTimeGrid struct to obtain the next grid point.

See also: BosonicFragmentTimeGrid.

Base.iterate(bg::BosonicMatsubaraGrid)

Advance the iterator of a BosonicMatsubaraGrid struct to obtain the next grid point.

See also: BosonicMatsubaraGrid.

Base.iterate(bg::BosonicFragmentMatsubaraGrid)

Advance the iterator of a BosonicFragmentMatsubaraGrid struct to obtain the next grid point.

See also: BosonicFragmentMatsubaraGrid.

Base.iterate(fg::FermionicImaginaryTimeGrid, i::I64)

This is the key method that allows a FermionicImaginaryTimeGrid struct to be iterated, yielding a sequences of grid points.

See also: FermionicImaginaryTimeGrid.

Base.iterate(fg::FermionicFragmentTimeGrid, i::I64)

This is the key method that allows a FermionicFragmentTimeGrid struct to be iterated, yielding a sequences of grid points.

See also: FermionicFragmentTimeGrid.

Base.iterate(fg::FermionicMatsubaraGrid, i::I64)

Create an iterable object for visiting each index of a FermionicMatsubaraGrid struct.

See also: FermionicMatsubaraGrid.

Base.iterate(fg::FermionicFragmentMatsubaraGrid, i::I64)

Create an iterable object for visiting each index of a FermionicFragmentMatsubaraGrid struct.

See also: FermionicFragmentMatsubaraGrid.

Base.iterate(bg::BosonicImaginaryTimeGrid, i::I64)

Create an iterable object for visiting each index of a BosonicImaginaryTimeGrid struct.

See also: BosonicImaginaryTimeGrid.

Base.iterate(bg::BosonicFragmentTimeGrid, i::I64)

Create an iterable object for visiting each index of a BosonicFragmentTimeGrid struct.

See also: BosonicFragmentTimeGrid.

Base.iterate(bg::BosonicMatsubaraGrid, i::I64)

Create an iterable object for visiting each index of a BosonicMatsubaraGrid struct.

See also: BosonicMatsubaraGrid.

Base.iterate(bg::BosonicFragmentMatsubaraGrid, i::I64)

Create an iterable object for visiting each index of a BosonicFragmentMatsubaraGrid struct.

See also: BosonicFragmentMatsubaraGrid.

Base.eachindex(fg::FermionicImaginaryTimeGrid)

Create an iterable object for visiting each index of a FermionicImaginaryTimeGrid struct.

See also: FermionicImaginaryTimeGrid.

Base.eachindex(fg::FermionicFragmentTimeGrid)

Create an iterable object for visiting each index of a FermionicFragmentTimeGrid struct.

See also: FermionicFragmentTimeGrid.

Base.eachindex(fg::FermionicMatsubaraGrid)

Create an iterable object for visiting each index of a FermionicMatsubaraGrid struct.

See also: FermionicMatsubaraGrid.

Base.eachindex(fg::FermionicFragmentMatsubaraGrid)

Create an iterable object for visiting each index of a FermionicFragmentMatsubaraGrid struct.

See also: FermionicFragmentMatsubaraGrid.

Base.eachindex(bg::BosonicImaginaryTimeGrid)

Create an iterable object for visiting each index of a BosonicImaginaryTimeGrid struct.

See also: BosonicImaginaryTimeGrid.

Base.eachindex(bg::BosonicFragmentTimeGrid)

Create an iterable object for visiting each index of a BosonicFragmentTimeGrid struct.

See also: BosonicFragmentTimeGrid.

Base.eachindex(bg::BosonicMatsubaraGrid)

Create an iterable object for visiting each index of a BosonicMatsubaraGrid struct.

See also: BosonicMatsubaraGrid.

Base.eachindex(bg::BosonicFragmentMatsubaraGrid)

Create an iterable object for visiting each index of a BosonicFragmentMatsubaraGrid struct.

See also: BosonicFragmentMatsubaraGrid.

Base.firstindex(fg::FermionicImaginaryTimeGrid)

Return the first index of a FermionicImaginaryTimeGrid struct.

See also: FermionicImaginaryTimeGrid.

Base.firstindex(fg::FermionicFragmentTimeGrid)

Return the first index of a FermionicFragmentTimeGrid struct.

See also: FermionicFragmentTimeGrid.

Base.firstindex(fg::FermionicMatsubaraGrid)

Return the first index of a FermionicMatsubaraGrid struct.

See also: FermionicMatsubaraGrid.

Base.firstindex(fg::FermionicFragmentMatsubaraGrid)

Return the first index of a FermionicFragmentMatsubaraGrid struct.

See also: FermionicFragmentMatsubaraGrid.

Base.firstindex(bg::BosonicImaginaryTimeGrid)

Return the first index of a BosonicImaginaryTimeGrid struct.

See also: BosonicImaginaryTimeGrid.

Base.firstindex(bg::BosonicFragmentTimeGrid)

Return the first index of a BosonicFragmentTimeGrid struct.

See also: BosonicFragmentTimeGrid.

Base.firstindex(bg::BosonicMatsubaraGrid)

Return the first index of a BosonicMatsubaraGrid struct.

See also: BosonicMatsubaraGrid.

Base.firstindex(bg::BosonicFragmentMatsubaraGrid)

Return the first index of a BosonicFragmentMatsubaraGrid struct.

See also: BosonicFragmentMatsubaraGrid.

Base.lastindex(fg::FermionicImaginaryTimeGrid)

Return the last index of a FermionicImaginaryTimeGrid struct.

See also: FermionicImaginaryTimeGrid.

Base.lastindex(fg::FermionicFragmentTimeGrid)

Return the last index of a FermionicFragmentTimeGrid struct.

See also: FermionicFragmentTimeGrid.

Base.lastindex(fg::FermionicMatsubaraGrid)

Return the last index of a FermionicMatsubaraGrid struct.

See also: FermionicMatsubaraGrid.

Base.lastindex(fg::FermionicFragmentMatsubaraGrid)

Return the last index of a FermionicFragmentMatsubaraGrid struct.

See also: FermionicFragmentMatsubaraGrid.

Base.lastindex(bg::BosonicImaginaryTimeGrid)

Return the last index of a BosonicImaginaryTimeGrid struct.

See also: BosonicImaginaryTimeGrid.

Base.lastindex(bg::BosonicFragmentTimeGrid)

Return the last index of a BosonicFragmentTimeGrid struct.

See also: BosonicFragmentTimeGrid.

Base.lastindex(bg::BosonicMatsubaraGrid)

Return the last index of a BosonicMatsubaraGrid struct.

See also: BosonicMatsubaraGrid.

Base.lastindex(bg::BosonicFragmentMatsubaraGrid)

Return the last index of a BosonicFragmentMatsubaraGrid struct.

See also: BosonicFragmentMatsubaraGrid.

Base.getindex(fg::FermionicImaginaryTimeGrid, ind::I64)

Retrieve the value(s) stored at the given key or index within a FermionicImaginaryTimeGrid struct.

See also: FermionicImaginaryTimeGrid.

Base.getindex(fg::FermionicFragmentTimeGrid, ind::I64)

Retrieve the value(s) stored at the given key or index within a FermionicFragmentTimeGrid struct.

See also: FermionicFragmentTimeGrid.

Base.getindex(fg::FermionicMatsubaraGrid, ind::I64)

Retrieve the value(s) stored at the given key or index within a FermionicMatsubaraGrid struct.

See also: FermionicMatsubaraGrid.

Base.getindex(fg::FermionicFragmentMatsubaraGrid, ind::I64)

Retrieve the value(s) stored at the given key or index within a FermionicFragmentMatsubaraGrid struct.

See also: FermionicFragmentMatsubaraGrid.

Base.getindex(bg::BosonicImaginaryTimeGrid, ind::I64)

Retrieve the value(s) stored at the given key or index within a BosonicImaginaryTimeGrid struct.

See also: BosonicImaginaryTimeGrid.

Base.getindex(bg::BosonicFragmentTimeGrid, ind::I64)

Retrieve the value(s) stored at the given key or index within a BosonicFragmentTimeGrid struct.

See also: BosonicFragmentTimeGrid.

Base.getindex(bg::BosonicMatsubaraGrid, ind::I64)

Retrieve the value(s) stored at the given key or index within a BosonicMatsubaraGrid struct.

See also: BosonicMatsubaraGrid.

Base.getindex(bg::BosonicFragmentMatsubaraGrid, ind::I64)

Retrieve the value(s) stored at the given key or index within a BosonicFragmentMatsubaraGrid struct.

See also: BosonicFragmentMatsubaraGrid.

Base.getindex(fg::FermionicImaginaryTimeGrid, I::UnitRange{I64})

Return a subset of a FermionicImaginaryTimeGrid struct as specified by I.

See also: FermionicImaginaryTimeGrid.

Base.getindex(fg::FermionicFragmentTimeGrid, I::UnitRange{I64})

Return a subset of a FermionicFragmentTimeGrid struct as specified by I.

See also: FermionicFragmentTimeGrid.

Base.getindex(fg::FermionicMatsubaraGrid, I::UnitRange{I64})

Return a subset of a FermionicMatsubaraGrid struct as specified by I.

See also: FermionicMatsubaraGrid.

Base.getindex(fg::FermionicFragmentMatsubaraGrid, I::UnitRange{I64})

Return a subset of a FermionicFragmentMatsubaraGrid struct as specified by I.

See also: FermionicFragmentMatsubaraGrid.

Base.getindex(bg::BosonicImaginaryTimeGrid, I::UnitRange{I64})

Return a subset of a BosonicImaginaryTimeGrid struct as specified by I.

See also: BosonicImaginaryTimeGrid.

Base.getindex(bg::BosonicFragmentTimeGrid, I::UnitRange{I64})

Return a subset of a BosonicFragmentTimeGrid struct as specified by I.

See also: BosonicFragmentTimeGrid.

Base.getindex(bg::BosonicMatsubaraGrid, I::UnitRange{I64})

Return a subset of a BosonicMatsubaraGrid struct as specified by I.

See also: BosonicMatsubaraGrid.

Base.getindex(bg::BosonicFragmentMatsubaraGrid, I::UnitRange{I64})

Return a subset of a BosonicFragmentMatsubaraGrid struct as specified by I.

See also: BosonicFragmentMatsubaraGrid.

rebuild!(fg::FermionicImaginaryTimeGrid, ntime::I64, β::T) where {T}

Rebuild the FermionicImaginaryTimeGrid struct via new ntime and β parameters.

Arguments

• fg -> A FermionicImaginaryTimeGrid struct.
• ntime -> Number of time slices.
• β -> Inverse temperature.

Returns

N/A

See also: FermionicImaginaryTimeGrid.

rebuild!(fg::FermionicFragmentTimeGrid, ntime::I64, β::T) where {T}

Rebuild the FermionicFragmentTimeGrid struct via new ntime and β parameters. Now its imaginary time points are continuous and complete.

Arguments

• fg -> A FermionicFragmentTimeGrid struct.
• ntime -> Number of time slices.
• β -> Inverse temperature.

Returns

N/A

See also: FermionicFragmentTimeGrid.

rebuild!(fg::FermionicMatsubaraGrid, nfreq::I64, β::T) where {T}

Rebuild the FermionicMatsubaraGrid struct via new nfreq and β parameters.

Arguments

• fg -> A FermionicMatsubaraGrid struct.
• nfreq -> Number of Matsubara frequencies.
• β -> Inverse temperature.

Returns

N/A

See also: FermionicMatsubaraGrid.

rebuild!(fg::FermionicFragmentMatsubaraGrid, nfreq::I64, β::T) where {T}

Rebuild the FermionicFragmentMatsubaraGrid struct via new nfreq and β parameters. Now its Matsubara frequency points are continuous and complete.

Arguments

• fg -> A FermionicFragmentMatsubaraGrid struct.
• nfreq -> Number of Matsubara frequencies.
• β -> Inverse temperature.

Returns

N/A

See also: FermionicFragmentMatsubaraGrid.

rebuild!(bg::BosonicImaginaryTimeGrid, ntime::I64, β::T) where {T}

Rebuild the BosonicImaginaryTimeGrid struct via new ntime and β parameters.

Arguments

• bg -> A BosonicImaginaryTimeGrid struct.
• ntime -> Number of time slices.
• β -> Inverse temperature.

Returns

N/A

See also: BosonicImaginaryTimeGrid.

rebuild!(bg::BosonicFragmentTimeGrid, ntime::I64, β::T) where {T}

Rebuild the BosonicFragmentTimeGrid struct via new ntime and β parameters. Now its imaginary time points are continuous and complete.

Arguments

• bg -> A BosonicFragmentTimeGrid struct.
• ntime -> Number of time slices.
• β -> Inverse temperature.

Returns

N/A

See also: BosonicFragmentTimeGrid.

rebuild!(bg::BosonicMatsubaraGrid, nfreq::I64, β::T) where {T}

Rebuild the BosonicMatsubaraGrid struct via new nfreq and β parameters.

Arguments

• bg -> A BosonicMatsubaraGrid struct.
• nfreq -> Number of Matsubara frequencies.
• β -> Inverse temperature.

Returns

N/A

See also: BosonicMatsubaraGrid.

rebuild!(bg::BosonicFragmentMatsubaraGrid, nfreq::I64, β::T) where {T}

Rebuild the BosonicFragmentMatsubaraGrid struct via new nfreq and β parameters. Now its Matsubara frequency points are continuous and complete.

Arguments

• bg -> A BosonicFragmentMatsubaraGrid struct.
• nfreq -> Number of Matsubara frequencies.
• β -> Inverse temperature.

Returns

N/A

See also: BosonicFragmentMatsubaraGrid.

Base.resize!(fg::FermionicMatsubaraGrid, nfreq::I64)

Reduce the size of the fermionic Matsubara grid. Note that nfreq should be smaller than or equal to fg.nfreq. This function is called by the NevanAC solver only.

Arguments

• fg -> A FermionicMatsubaraGrid struct.
• nfreq -> Number of Matsubara frequencies.

Returns

N/A

See also: FermionicMatsubaraGrid.

Base.resize!(fg::FermionicFragmentMatsubaraGrid, nfreq::I64)

Reduce the size of the fermionic fragment Matsubara grid. Note that nfreq should be smaller than or equal to fg.nfreq. This function is called by the NevanAC solver only.

Arguments

• fg -> A FermionicFragmentMatsubaraGrid struct.
• nfreq -> Number of Matsubara frequencies.

Returns

N/A

See also: FermionicFragmentMatsubaraGrid.

Base.resize!(bg::BosonicMatsubaraGrid, nfreq::I64)

Reduce the size of the bosonic Matsubara grid. Note that nfreq should be smaller than or equal to bg.nfreq. This function is called by the NevanAC solver only.

Arguments

• bg -> A BosonicMatsubaraGrid struct.
• nfreq -> Number of Matsubara frequencies.

Returns

N/A

See also: BosonicMatsubaraGrid.

Base.resize!(bg::BosonicFragmentMatsubaraGrid, nfreq::I64)

Reduce the size of the bosonic fragment Matsubara grid. Note that nfreq should be smaller than or equal to bg.nfreq. This function is called by the NevanAC solver only.

Arguments

• bg -> A BosonicFragmentMatsubaraGrid struct.
• nfreq -> Number of Matsubara frequencies.

Returns

N/A

See also: BosonicFragmentMatsubaraGrid.

Base.reverse!(fg::FermionicMatsubaraGrid)

Reverse the fermionic Matsubara grid. This function is called by the NevanAC solver only.

See also: FermionicMatsubaraGrid.

Base.reverse!(fg::FermionicFragmentMatsubaraGrid)

Reverse the fermionic fragment Matsubara grid. This function is called by the NevanAC solver only.

See also: FermionicFragmentMatsubaraGrid.

Base.reverse!(bg::BosonicMatsubaraGrid)

Reverse the bosonic Matsubara grid. This function is called by the NevanAC solver only.

See also: BosonicMatsubaraGrid.

Base.reverse!(bg::BosonicFragmentMatsubaraGrid)

Reverse the bosonic fragment Matsubara grid. This function is called by the NevanAC solver only.

See also: BosonicFragmentMatsubaraGrid.