Quantum Basis

Basis of condensed matter quantum lattice problems, for usage in exact diagonalization (ED). The code is designed for any general bosonic or fermionic problem (or a mix of both), as long as the user can provide the matrix form of the elementary operators of the Hamiltonian.

Human-friendly usage (Heisenberg model as example)

Note: the grammars below may differ slightly from the acutal code, please refer to the folder "examples" for exact usage.

• Writing a two-site spin-1/2 Heisenberg model can be as easy as:

auto Heisenberg = Sx1 * Sx2 + Sy1 * Sy2 + Sz1 * Sz2;

• Add a site "3"?

Heisenberg += Sx2 * Sx3 + Sy2 * Sy3 + Sz2 * Sz3;

• Add more exotic interactions?

Heisenberg += (Sx1 * Sx2 + Sy1 * Sy2 + Sz1 * Sz2) * (Sx1 * Sx2 + Sy1 * Sy2 + Sz1 * Sz2);

• Eigen problem?

Heisenberg.locate_E0_lanczos();

• Measurement?

Heisenberg.measure(Sx1*Sx2);

• More featuers (good quantum numbers, translation symmetry, dynamical response, etc.)? Explore the folder "examples"!
• Need design very different Hamiltonians? Explore the folder "examples" for ideas!

Examples

To learn how to use this library to design ED code for your own models, please refer to the folder "examples":

• Chain
  • Heisenberg spin-1/2
  • Heisenberg spin-1
  • Kondo Lattice model
  • t-J model
• Honeycomb lattice
  • Spinless fermion
• Kagome lattice
  • Heisenberg spin-1/2
  • t-J model
• Square lattice
  • Bose-Hubbard model
  • Fermi-Hubbard model
  • Kondo Lattice model
• Triangular lattice
  • Heisenberg spin-1/2

Install from source (Linux):

0. (Optional but recommended) Create a local folder to keep the manually installed libraries:

   mkdir ~/installs; mkdir ~/installs/lib; mkdir ~/installs/include

   Then add the following to the end of your ~/.bashrc file and restart the terminal:

   export LD_LIBRARY_PATH=${HOME}/installs/lib:$LD_LIBRARY_PATH
   if [ -d ${HOME}/installs/lib/pkgconfig ]; then
       export PKG_CONFIG_PATH=${HOME}/installs/lib/pkgconfig:$PKG_CONFIG_PATH
   fi
   

1. Install MKL. There are two options:

   • For regular users, you can install from your linux distro. e.g., in Ubuntu, you can simply type

     sudo apt install libmkl-dev

   • For developers, it is recommended to download directly from Intel.

   Either way, after installaltion, you should add the following to the end of your ~/.bashrc file and restart the terminal:

   if [ -f /opt/intel/oneapi/setvars.sh ]; then
       source /opt/intel/oneapi/setvars.sh intel64 
       export MKL_INC_DIR=${MKLROOT}/include
       export MKL_LIB_DIR=${MKLROOT}/lib/intel64
   elif [ -d /usr/include/mkl ] && [ -d /usr/lib/x86_64-linux-gnu ]; then
       export MKL_INC_DIR=/usr/include/mkl
       export MKL_LIB_DIR=/usr/lib/x86_64-linux-gnu
   fi
   

   Note: The variable {intel64} and the destination folders may vary depending on the system, should change the above lines accordingly.

2. Install the following dependencies:

   libboost-dev

   (for example, if on Ubuntu, simply type sudo apt install libboost-dev)

3. Install ARPACK-NG:

   cd /tmp
   wget https://github.com/opencollab/arpack-ng/archive/refs/tags/3.9.0.tar.gz
   tar xf 3.9.0.tar.gz
   cd arpack-ng-3.9.0
   sh bootstrap
   FFLAGS="-m64 -I${MKL_INC_DIR}" FCFLAGS="-m64 -I$MKL_INC_DIR" CFLAGS="-DMKL_ILP64 -m64 -I${MKL_INC_DIR}" CXXFLAGS="-DMKL_ILP64 -m64 -I${MKL_INC_DIR}" LIBS="-L${MKL_LIB_DIR} -Wl,--no-as-needed -lmkl_gf_ilp64 -lmkl_tbb_thread -lmkl_core -lpthread -ltbb -lstdc++ -lm -ldl" LIBSUFFIX="ILP64" INTERFACE64="1" ./configure --with-blas=mkl_gf_ilp64 --with-lapack=mkl_gf_ilp64 --enable-icb --prefix=$HOME/installs
   make check
   make install
   

4. Test Quantum Basis:

   Create a directory "bin" that sits at the same level of "src": mkdir bin, then go inside "src": cd src, then type

   make clean; make test

   Then execute the file ./test.x in folder bin. :beer: if you see "All tests passed!" :beer:

5. Install Quantum Basis as a library:

   make clean; make install

Restrictions on lattice:

When using translational symmetry, at least one of the dimensions (Lx, Ly, Lz, or number of sublattices) has to be an even number (current implementation of the generalized Lin Table).