On the web: https://github.com/simple-dmrg/simple-dmrg/
The goal of this tutorial (given at the 2013 summer school on quantum spin liquids, in Trieste, Italy) is to present the density-matrix renormalization group (DMRG) in its traditional formulation (i.e. without using matrix product states). DMRG is a numerical method that allows for the efficient simulation of quantum model Hamiltonians. Since it is a low-entanglement approximation, it often works quite well for one-dimensional systems, giving results that are nearly exact.
Typical implementations of DMRG in C++ or Fortran can be tens of thousands of lines long. Here, we have attempted to strike a balance between clear, simple code, and including many features and optimizations that would exist in a production code. One thing that helps with this is the use of Python. We have tried to write the code in a very explicit style, hoping that it will be (mostly) understandable to somebody new to Python. (See also the included Python cheatsheet, which lists many of the Python features used by simple-dmrg, and which should be helpful when trying the included exercises.)
The four modules build up DMRG from its simplest implementation to more complex implementations and optimizations. Each file adds lines of code and complexity compared with the previous version.
- Infinite system algorithm (~180 lines, including comments)
- Finite system algorithm (~240 lines)
- Conserved quantum numbers (~310 lines)
- Eigenstate prediction (~370 lines)
Throughout the tutorial, we focus on the spin-1/2 Heisenberg XXZ model, but the code could easily be modified (or expanded) to work with other models.
The requirements are:
Download the code using the Download ZIP button on github, or run the following command from a terminal:
$ wget -O simple-dmrg-master.zip https://github.com/simple-dmrg/simple-dmrg/archive/master.zipWithin a terminal, execute the following to unpack the code:
$ unzip simple-dmrg-master.zip
$ cd simple-dmrg-master/Note
If you are using the computers in the lab at SISSA, you will need to activate three modules for the correct version of Python to run. These commands are given in activate_sissa_modules, or you can run the following command to activate them:
$ source activate_sissa_modulesOnce the relevant software is installed, each program is contained entirely in a single file. The first program, for instance, can be run by issuing:
$ python simple_dmrg_01_infinite_system.pyNote
If you see an error that looks like this:
SyntaxError: future feature print_function is not definedthen you are using a version of Python below 2.6. If you are in the SISSA computer lab, follow the instructions above to activate the correct modules. If you are using your own machine, we may be able to make the code work on versions of Python prior to 2.6 without much trouble.
Note
The version of Python in the SISSA computer lab is compiled with many debugging checks enabled. For instance, after running the code, you may see something that looks like:
[32067 refs]As a result of these checks, the code runs approximately 15 times slower on these machines than it does on our laptops.
- James R. Garrison (UCSB)
- Ryan V. Mishmash (UCSB)
Licensed under the MIT license. If you plan to publish work based on this code, please contact us to find out how to cite us.