"NRG Ljubljana" is a flexible framework for performing large scale numerical
renormalization group (NRG) calculations for quantum impurity problems. It
is highly extensible without sacrificing numerical efficiency.

Copyright (C) 2006-2014 Rok Zitko


Framework "NRG Ljubljana" is a set of interrelated computer codes for
performing numerical renormalization group (NRG) calculations for quantum
impurity problems, described by models such as the Kondo exchange (s-d)
model or the Anderson single impurity model, and their multi-impurity and
multi-channel generalizations. It also contains a number of tools for
analyzing results (thermodynamic properties, such as magnetic and charge
susceptibility, entropy and heat capacity; expectation values of arbitrary
operators; spectral functions). It is user friendly, in the sense that it is
easy to set up new types of problems (Hamiltonians, perturbation terms,
etc.) and the output is formatted and annotated for easy interpretation,
parsing and plotting. It efficiently handles problems with different
symmetries, such as spin SU(2) symmetry, charge SU(2) symmetry, Z_2
reflection symmetry (parity), etc.

To achieve a high degree of flexibility without sacrificing numerical
efficiency, "NRG Ljubljana" is composed of a hierarchy of modules:
high level modules are written in a mixture of functional and
procedural Mathematica code, while the low level numerically intensive
parts are programmed in the object oriented approach in the C++
language. The foundation of the framework is a Mathematica package for
performing calculations with non-commutative second quantisation
operators, SNEG. Next layer is a Mathematica program which defines the
Hamiltonian, the basis of states, and the physical operators of
interest: with the help of SNEG, Hamiltonian and operators can be
defined using the familiar second-quantization expressions. This
program performs the diagonalization of the initial Hamiltonian and
prepares the input for the NRG iteration proper.

For efficiency, NRG iteration is performed by a separate C++ program:
for a typical problem, most of the time (90%) is spent in the LAPACK
dsyev routine which solves the eigenvalue problem. There is very
little housekeeping overhead due to the tasks required by the NRG
iteration; "NRG Ljubljana" is thus suitable for performing large scale
NRG calculations on computer clusters.



1. Features

- all parameters and model definitions (!) configurable at run-time, no need
  to recompile for different runs
- support for a large number of different symmetry types
- flexible truncation schemes (energy cut-off truncation, avoidance
  of trunction within gaps, etc.)
- density-matrix NRG (DM-NRG) for all symmetry types
- full-density matrix (FD-NRG) for all symmetry types
- FDM calculation of expectation values at finite temperatures
- sum-rule conserving spectral function calculations (CFS approach)
- various spectral-function broadening schemes & stand-alone tools
- self-energy trick calculations 
- arbitrary number of channels (in practice 1,2,3)
- calculations with real and complex numbers
- support for superconducting bands, spin-polarized bands, etc.
- support for global operators (i.e., operators defined on the
  Wilson chain sites)
- calculation of temperature-dependent conductance, G(T)
- flexibility in definition of the Hamiltonian, which is simply
  written using a second-quantization operator expression
- automatic exact diagonalisation of the initial Hamiltonian with
  automagic generation of the (Q,S) (or some other) basis
- flexibility in the choice of operators whose thermodynamical averages
  are computed, they can be expressed using operators of second
  quantization
- dynamic spin susceptibility, dynamic charge susceptibility, etc.
  It is possible to compute arbitrary spectral functions for any
  pair of local operators.
- multiple logarithmic discretization schemes (Wilson/Krishnamurthy,
  Yoshida/Whitaker/Oliveira, Campo/Oliveira, ODE scheme)
- support for non-flat bands (i.e. cosine band that arrises from
  tight-binding description of leads in quantum transport problems,
  or arbitrary hybridization as needed in DMFT), see dmft.m
- heavily commented code with reference to original publications of
  formulas and approaches used
- object-oriented code for easy maintenance and expandability
- FAST!: very high numeric efficiency with optimized-for loops in the most
  numerically demanding parts of the code (chiefly the recalculation
  of irreducible matrix elements of operators)
- N/N+2 trick (patching) in calculation of spectral densities
- amount of verbosity in log files is configurable
- automatic recording of time elapsed in various parts of the program
- monitoring of memory use
- formated output files for easy interpretation of the results
  (for example, headers with parameters and heading lines in tables
  with operator names)
- internal consistency checks, assertions, parameter compatibility
  and reasonableness checks that reduce the possibility of undetected
  bugs
  

2. Documentation

Presently, there is no up-to-date documentation. Sorry.


3. License

   This program is free software; you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published by
   the Free Software Foundation; either version 2 of the License, or
   (at your option) any later version.

   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.

   You should have received a copy of the GNU General Public License
   along with this program; if not, write to the Free Software
   Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA

The full text of the GPL General Public License can be found
in file LICENSE.


4. Compiling and dependencies

NRG Ljubljana is very portable and it should work without any modification
on any modern Linux distribution and, with some tweaking, on any Unix or
Unix-like operating system with a good standards-compliant C++ compiler. It
has been reported to me that it can also be compiled under Windows.

The following libraries are required to compile the C++ part of the
NRG code:

    * LAPACK and BLAS linear algebra libraries
    * boost C++ libraries

Due to the heavy use of template metaprogramming in boost libraries, a
high-quality standards-compliant C++ compiler must be used. 

Wolfram Reasearch Mathematica must be installed for running the
Mathematica part of the NRG code. Versions 5.0, 5.1, 5.2, 6.0, 7.0 and
8.0 have been tested. Mathematica is only required for the
initialization of the problem (basis construction, diagonalisation of
the initial Hamiltonian, transformations of the operator matrices,
etc.) which is relatively fast. When "NRG Ljubljana" is used on a
cluster, it is therefore sufficient to have Mathematica installed on a
single computer (for example on the cluster host computer), while the
numerically demanding (C++) part of the program can be ran on the
cluster nodes.

Usually, the compilation consists of configuring and compiling NRG:

./configure --prefix=$HOME --with-tools
make

(The tools are optional: you might not need them. In this case
do not use the "--with-tools" option.)

5. "Installation"

To install "NRG Ljubljana", copy the executables to an appropriate location.
Furthermore, the Mathematica scripts *.m must be accessible; you may simply
copy them to the directory from which the NRG code will be started.

You can also do a "make install". Note, however, that the scripts from
scripts/ and tools from tools/ will end up in the installation bin/
directory.


6. Contributing to "NRG Ljubljana"

If you make improvements to "NRG Ljubljana", you are encouraged to
share them with other users. Bug reports (and fixes) are very welcome
as well.  The contact information is in the next section.


7. Contact information:

"NRG Ljubljana" home-page: http://nrgljubljana.ijs.si/

Rok Zitko
"Jozef Stefan" Institute
F1 - Theoretical physics
Jamova 39
SI-1000 Ljubljana
Slovenia

rok.zitko@ijs.si


8. Acknowledgements 

The development of the "NRG Ljubljana" framework started during author's PhD
studies at the Faculty for mathematics and physics of the University of
Ljubljana, and the "Jozef Stefan" Institute, Ljubljana, Slovenia.
Discussions and collaboration with prof. Janez Bonca, prof. Anton Ramsak,
dr. Jernej Mravlje and dr. Tomaz Rejec from the F1, Theoretical Physics
department are acknowledged. I'm also grateful to prof. Thomas Pruschke,
Robert Peters and Oliver Bodensiek from the University in Goettingen for many
very fruitful discussions. I thank Marcus Greger from the University
in Augsburg for contributing optimized routines for the spectral
function calculation.