Getting Started

Welcome to Getting Started. This page is intended for users who want to jackknife DGA self-energies and DMFT susceptibilities with the jackknife_adga script. It gives a brief introduction of jackknife resampling and tells you how to install, configure and run the code. If you are interested in the implementation details of the modules and scripts please check out the source code documentation.

Introduction

The jackknife is a resampling method that allows to estimate the bias, variance and other statistics of a parameter. It is a very general method applicable to a wide range of problems, hence the name.

In short, if you want to know \(y=f(x)\), where \(f\) is a in general non-linear but known function and you only have access to random samples of \(x\), you can estimate \(y\) with \(f(\bar{x})\). Here \(\bar{x}\) denotes the sample mean of the input samples \(x\). However, since \(f\) can be non-linear this estimator can carry a bias. With the help of jackknife resampling this bias can be reduced resulting in a bias-corrected estimate for the observable \(y\). In addition it also allows to estimate its variance, covariance and other common statistics.

In case of the jackknife_adga script the observables of interest \(y\) are DGA self-energies and DMFT susceptibilities. It is possible to jackknife multiple of them at once. The non-linear function \(f\) is the ADGA program and the random input samples \(x\) are DMFT Green’s functions obtained with w2dynamics. Since multiple input samples are needed, you have to use worm sampling to generate the desired number of 2-particle Green’s functions. The more worm samples you use, the better your statistics will get.

Installation

jackknife is written in Python 3, but should also work with Python 2.7 and requires the following packages.

NumPy (1.16.2)

h5py (1.10.2)

configparser (3.7.4)

The numbers in parenthesis are not the minimum required version, but just one set of versions that are tested and work. In addition

w2dynamics and

ADGA

must also be installed (instructions on how to do that are provided in their respective documentation). ADGA is the program that actually calculates the self-energies and susceptibilities. w2dynamics is a DMFT code used to calculate 1- and 2-particle Green’s functions, which are the input quantities of ADGA.

Usage

The jackknife_adga script is relatively easy to use, but one needs to generate quite a few input and config files with/for w2dynamics and ADGA beforehand.

Input

The following input and config files are necessary:

an ADGA config file

a file containing the momentum resolved values of the tight-binding hamiltonian \(H(k)\) (needed for w2dynamics and ADGA)

a file containing the 1-particle Green’s function from w2dynamics

a file containing multiple 2-particle Green’s functions from w2dynamics using worm sampling

a jackknife config file

In the ADGA config file the correct HkFile and 1PFile must be specified, but the 2PFile and Outfile key will be set automatically by the script according to the values given in the jackknife config file. For further details on the files regarding ADGA and w2dynamics, see their respective documentation.

jackknife config file

An example of a jackknife config file is provided in the code repository (jackknife_adga.ini). In the [General] section there are three obligatory keys that every file must contain:

adga_root_directory: the ADGA directory which contains the scripts and bin folder

adga_config_file: ususally called dga.conf

two_particle_file: the file containing the 2-particle Green’s functions from w2dynamics

More control is possible with the following optional keys:

output_file_prefix: default value = jackknife; the current date and time will be appended to this prefix of the output file

store_output_samples: default value = no; if set to yes, the transformed bias-corrected ouput samples will also be stored in the output file (see Jackknife for a definition of these)

In the [Observables] section the group name of at least one HDF5 dataset of the ADGA output file must be given. The keys of this section will be used as the names of the observables in the jackknife output file.

Note

See the documentation of configparser.ConfigParser.getboolean() for the possible values of boolean keys in the jackknife config file.

Run

If all input and config files are available execute the following command to start the actual calculation:

python jackknife_adga.py [jackknife_config_file] [number_of_processes]

If the name of the jackknife config file is not given, the default value jackknife_adga.ini will be used. If the number of processes is not specified, it is set to 1.

Note

The jackknife_adga script itself is not parallelized but ADGA is called and executed with the given number of processes.

Output

The output is written to an HDF5 file named according to the output_file_prefix set in the jackknife config file with the date and time of the calculation appended to it. The exact structure is as follows:

`output_file_prefix`_<YYYY-mm-dd_HH-MM-SS>.hdf5
      ├── .config
      │       ├── jk.n_samples
      │       ├── jk.store_output_samples
      │       ├── qmc.nmeas
      │       ├── adga.executable
      │       ├── adga.symmetrize_script
      │       ├── adga.two_particle_file
      │       ├── adga.n_processes
      │       ├── adga.<section>.<key>
      │       :
      ├── <name_of_observable_1>
      │       ├── mean
      │       ├── variance
      │       ├── standard_deviation
      │       ├── standard_error_of_mean
      │       ├── transformed_input_mean
      │       ├── covariance
      │       └── correlation
      ├── <name_of_observable_2>
      │       ├── mean
      :       :

For each observable given in the jackknife config file there is a group of datasets containing the jackknife estimator (mean) as well as some other common statistics. The attributes of the group .config contain useful metadata including all entries of the adga config file (adga.<section>.<key>).