https://github.com/kleinhenz/keldysh.jl

julia package for working with Keldysh Green's functions
https://github.com/kleinhenz/keldysh.jl

condensed-matter julia physics

Last synced: 3 months ago
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julia package for working with Keldysh Green's functions

• Host: GitHub
• URL: https://github.com/kleinhenz/keldysh.jl
• Owner: kleinhenz
• License: mit
• Created: 2019-04-26T20:42:25.000Z (almost 6 years ago)
• Default Branch: master
• Last Pushed: 2023-05-28T12:15:30.000Z (over 1 year ago)
• Last Synced: 2024-11-02T07:23:51.871Z (3 months ago)
• Topics: condensed-matter, julia, physics
• Language: Julia
• Homepage:
• Size: 276 KB
• Stars: 31
• Watchers: 6
• Forks: 4
• Open Issues: 2
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Keldysh.jl

[![Build Status](https://github.com/kleinhenz/Keldysh.jl/workflows/CI/badge.svg?branch=master)](https://github.com/kleinhenz/Keldysh.jl/actions)

`Keldysh.jl` provides a set of tools for working with non-equilibrium Keldysh Green's functions.

It contains types to represent contours, grids defined on these contours, and two-time Green's functions defined on these grids.

Additionally, it provides functions for generating Green's functions, performing integration on a contour and hdf5 serialization.

Credit to Andrey Antipov and Igor Krivenko for designing a first version of the abstractions implemented here.

## Usage

The following code constructs a Green's function object from a spectral density and plots the Matsubara, retarded, and lesser Keldysh components.

```Julia

using Keldysh, PyPlot

# first define a contour

tmax = 5.0

β = 10.0

c = FullContour(; tmax, β)

# now define a grid which represents a discretization of the contour

nt = 51

ntau = 101

grid = FullTimeGrid(c, nt, ntau)

# construct a spectral density

dos = flat_dos(; D=5.0, ν=10.0)

# construct a Green's function from a spectral density

G = FullTimeGF(dos, grid)

fig, axes = plt.subplots(nrows=2, ncols=2)

make_plot = (ax, xlabel, ylabel, t, f...) -> begin

  map(fi -> ax.plot(t, fi), f)

  ax.set_xlabel(xlabel); ax.set_ylabel(ylabel)

end

ω = range(-10.0, 10.0, length=1001)

t = realtimes(grid)

τ = imagtimes(grid)

make_plot(axes[1], L"ω", L"Γ(ω)/π", ω, dos.(ω))

make_plot(axes[2], L"τ", L"G^M(τ)", τ, G[:matsubara])

make_plot(axes[3], L"t", L"G^<(t, 0)", t, real(G[:lesser][:,1]), imag(G[:lesser][:,1]))

make_plot(axes[4], L"t", L"G^R(t, 0)", t, real(G[:retarded][:,1]), imag(G[:retarded][:,1]))

fig.tight_layout()

fig.savefig("keldysh_components.jpg", dpi=200)

```

This produces the following output:

![keldysh_components](doc/images/keldysh_components.jpg)

See also [anderson_nca.jl](doc/examples/anderson_nca.jl) which implements a NCA solver for the anderson impurity model using `Keldysh.jl`.