## Workshop 4

**Density Matrix Renormalization Group 101: Introduction to Theory and Practice**

August 12, 2016

**Organizer(s): ** Gonzalo Alvarez and Alberto Nocera

**AGENDA**: The latest version of this document is 1.02, was posted on 08/03/2016, and it might be updated before the tutorial. Please make sure you have the latest version.

This workshop will present the basics of the Density Matrix Renormalization Group algorithm.

The Density Matrix Renormalization Group (DMRG) is one of the most powerful numerical techniques

for studying many-body systems. It was developed in 1992 by Steven R. White at the University of California

in Irvine to overcome the problems arising in the application of the Numerical Renormalization Group

to quantum lattice many-body systems such as the Hubbard model of strongly correlated electrons.

Since then the approach has been extended to a great variety of problems in all fields of physics and to

quantum chemistry.

We will start with an introduction of the algorithm, and a brief explanation of the foundations.

There will be an overview of the literature for those interested in a more rigorous theoretical treatment.

Most of focus will then turn to the practice of the algorithm using the DMRG++ application, which is

a free and open source implementation of the DMRG algorithm.

The workshop will explain how to simulate the Heisenberg model, the Hubbard model and the t-J model, starting

from the calculation of energies, followed by static observables, such as densities, and charge

and spin correlations. We will end with a brief overview of applications for time evolution,

temperature, and spectral functions.

**Needed Material**: Participants need to bring a computer that can compile C++ programs, with the gcc compiler

or the clang compiler. The LAPACK and BLAS libraries, and the computer programs perl, make and git are needed as well.