worms: a simple worm code

This is a sample code describing how the non-reversible worm algorithm (a.k.a directed-loop algorithm) can be implemented in the continuous imaginary time path integral representation. It calculates an S=1/2 antiferromagnetic Heisenberg chain in a longitudinal magnetic field.

Prerequisites

• CMake - http://www.cmake.org

Compilation

mkdir worms-build
cd worms-build
cmake [path-to-worms-source-directory]
make
make test

Command line options

Please see the output of

./worms -h

Release Note

• Release 1.0 (2013/09/12)

  • Initial version

• Release 1.1 (2014/02/24)

  • Fixed generation of transition matrix under the magnetic field
  • Updated logic to optimize number of worms per MCS
  • Added energy measurement
  • Added timer
  • Updated documents
  • Added check scripts and tests

References

• O.F. Syljuasen and A.W. Sandvik, "Quantum Monte Carlo with directed loops," Phys. Rev. E 66, 046701 (2002).
• N. Kawashima and K. Harada, "Recent Developments of World-Line Monte Carlo Methods," J. Phys. Soc. Jpn. 73, 1379 (2003).
• H. Suwa and S. Todo, "Markov Chain Monte Carlo Method without Detailed Balance," Physical Review Letters 105, 120603 (2010).
• S. Todo, "Loop Algorithm" in Strongly Correlated Systems: Numerical Methods (Springer Series in Solid-State Sciences), ed. A. Avella and F. Mancini (Springer-Verlag, Berlin, 2013), p. 153.

Developers

• Synge Todo (University of Tokyo)