ALPS 2 Tutorials:MC-01 Equilibration

Equilibration

Rule of thumb: All Monte Carlo simulations have to be equilibrated before taking measurements.

Example: Quantum Monte Carlo (directed worm algorithm) simulations

As an example, we consider a Quantum Monte Carlo simulation implemented in the directed worm algorithm for boson Hubbard model in square lattice geometry of size 20².

Using command line

The parameter file parm1a:

LATTICE="square lattice"
MODEL="boson Hubbard"

L=20  
Nmax=20

t=1.
U=16.
mu=32.

THERMALIZATION=10000
SWEEPS=100000 
SKIP=400

{T=1.0}

We first convert the input parameters to XML and then run the application dwa:

parameter2xml parm1a
dwa parm1a.in.xml

To check for equilibration, we need to look at

h5dump -g /simulation/results/Density parm1a.task1.out.h5

Using Python

The following describes what is going on within the script file tutorial1a.py.

The headers:

import pyalps

Set up a python list of parameters (python) dictionaries:

parms = [{
  'LATTICE'         : "square lattice",          
  'MODEL'           : "boson Hubbard",
  'L'               : 20,
  'Nmax'            : 20,
  't'               : 1.,
  'U'               : 16.,
  'mu'              : 32.,
  'T'               : 1.,
  'THERMALIZATION'  : 10000,
  'SWEEPS'          : 100000,
  'SKIP'            : 400
}]

Write into XML input file:

input_file = pyalps.writeInputFiles('parm1a',parms)

and run the application dwa:

pyalps.runApplication('dwa', input_file, Tmin=10, writexml=True)