An algorithm to simulate an isotropic S=1/2 antiferromagnetic quantum Heisenberg model in 1D, 2D or 3D lattice, all of them with periodic bondary condition.
The original program was made by Anders W. Sandvik [1] for a lecture about Quantum Monte Carlo Methods at Work for Novel Phases of Matter, presented in Trieste, Italy, Jan 23 - Feb 3, 2012. A more complete introduction about quantum spin systems and computational methods can be found here.
Prerequisites:
- Any Fortran compiler
For Ubuntu users with gfortran installed run in the terminal:
gfortran heisenberg_sse.f90 -o heisenberg && ./heisenbergParameters:
- All the program parameters are in Module Variables.
In this lecture you will find simple tests to check the program correctness.
Ground state energy of Heisenberg chain:
The exact ground state energy is Eg=-0.44395398. So, the mean energy per spin should converge to Eg as the inverse temperature beta goes to infinity, like in the figure below.
Simulation made with a lattice size Lx=32, 10.000 thermalization steps, 10.000 Monte Carlo steps and 20 bins.
Square lattice expansion cut-off:
Evolution of the expansion cut-off:
Distribution of the number of H-operators (n):
Phase transition in a cubic lattice:
In a cubic lattice this model has a phase transition at Tc = 0.945J [2].
Comparing results from ALPS and this algorithm:
The ALPS project (Algorithms and Libraries for Physics Simulations) can be found here.
Energy:
Number of H-operators (n):
Specific Heat:
Uniform Susceptibility:
