FRTRG

Floquet real-time renormalization group (RTRG) for the isotropic single-channel Kondo model. The method implemented here can be used to describe strongly correlated open quantum systems at zero temperature with time-dependent driving.

Publications:

• my thesis contains the latest and most complete documentation of the method implemented here
• Phys. Rev. B 106, 115440 (arXiv:2206.06263) contains a more compact explanation of the method based on an earlier version of the code. Also have a look at the interactive plots.

The modules in this package are mainly intended as a reference for these publications, and as a possible source of inspiration for other applications of Floquet or RTRG methods.

Building and installing

To install the full package, run (the file name in the last line may vary):

git clone https://github.com/stiglers-eponym/frtrg
cd frtrg
python -m build
pip install --user dist/frtrg-0.14.16-cp311-cp311-linux_x86_64.whl

Documentation

An automatically generated documentation of the python package can be found here: https://stiglers-eponym.github.io/frtrg/. If you wish to use this module, do not hesitate to ask for better documentation! The python modules contain docstrings of varying quality. Only the documentation of the kondo module is formatted according to some standards.

Usage

This code can be used as a python library, or to generate and save data. The individual modules contain a brief documentation in the beginning.

Library

The FRTRG package provides the following modules:

• kondo: FRTRG solution of the isotropic spin-1/2 Kondo model with two reservoirs. Create a Kondo object and use Kondo.run() to run the RG flow.
• data_management: save and load Kondo RG flow results in a database and in HDF5 files. Use DataManager.list() to obtain main results (such as the conductance) in a pandas table.
• gen_data: interface for generating data for AC driving from the command line and for saving the results.
• gen_pulse_data: interface for generating data for pulsed driving from the command line and for saving the results.
• visualize: basic 3d visualization command line interface using PyQtGraph
• rtrg: helper module for Floquet matrix RG objects
• compact_rtrg: variant of rtrg that uses (and requires) a symmetry in the bias voltage of the form V(-t)=-V(t).
• reservoirmatrix: helper module for matrices in reservoir space, which are also Floquet matrices and RG objects
• rtrg_c: helper module for modified matrix product of Floquet matrices
• frequency_integral: helper module for exact and approximate solutions of an integral required in the RG equations.
• settings: global settings

Generating data

Results for the isotropic spin-1/2 Kondo model with two reservoirs and a bias voltage of the form V(t) = Vdc + Vac cos(Ωt) can be calculated from the command line as in the following example:

OMP_NUM_THREADS=1 python -m frtrg.gen_data \
    --filename=data.h5 \
    --db_filename=database.sqlite \
    --threads=1 \
    --method=mu \
    --omega=3.4425 \
    --vdc=0 \
    --vac=3.4425 \
    --voltage_branches=0 \
    --nmax=12 \
    --log_time=10

In this example, the results will be saved in a file data.h5. Metadata and main results (DC and AC current, conductance) are also saved in database.sqlite. It is possible to create arrays data points with a single command line. See python -m frtrg.gen_data --help for more information.

Visualization

A basic visualization using PyQtGraph is available in the visualize submodule (requires matplotlib and PyQtGraph):

python -m frtrg.visualize --omega=3.4425

Exporting data

To select, export or visualize data, you can access a pandas table. Example:

from frtrg.data_management import DataManager
dm = DataManager()
table = dm.list(omega=3.4425)

This assumes that the correct database is set in settings. To change this database, use

from frtrg import settings
settings.defaults.DB_CONNECTION_STRING='sqlite:////path/to/database.sqlite'
settings.defaults.update_globals()