MC-04 Measurements

Correlation measurements in the directed loop and worm codes

In this tutorial, we will measure correlation functions with the directed loop and worm codes.

Two-dimensional Heisenberg square lattice

Preparing and running the simulation from the command line

The parameter file parm4 sets up Monte Carlo simulations of the quantum mechanical S=1/2 Heisenberg model on a square lattice, and enables various measurement options:

MODEL="spin";
LATTICE="square lattice";
REPRESENTATION="SSE";
MEASURE[Correlations]=true;
MEASURE[Structure Factor]=true;
MEASURE[Green Function]=true;
THERMALIZATION=10000;
SWEEPS=500000;
J= 1;
L=4;
W=4;
T=0.3;
{h=0.1;}

Using the standard sequence of commands you can run the simulation using the quantum SSE code.

parameter2xml parm4
dirloop_sse --Tmin 10 --write-xml parm4.in.xml

Preparing and running the simulation using Python

To set up and run the simulation in Python we use the script tutorial4.py:

import pyalps

parms = [{ 
        'LATTICE'                   : "square lattice", 
        'MODEL'                     : "spin",
        'MEASURE[Correlations]'     : True,
        'MEASURE[Structure Factor]' : True,
        'MEASURE[Green Function]'   : True,
        'local_S'                   : 0.5,
        'T'                         : 0.3,
        'J'                         : 1 ,
        'THERMALIZATION'            : 10000,
        'SWEEPS'                    : 500000,
        'L'                         : 4,
        'h'                         : 0.1
    }]

input_file = pyalps.writeInputFiles('parm4',parms)
res = pyalps.runApplication('dirloop_sse',input_file,Tmin=5)

Evaluating the simulation

To look at the results, we now load ALL measurements from output files starting with parm4. The code to do this is in tutorial4.py, but we may again copy it to a new script loader4.py if we ever want to view the results again without running the simulation.

data = pyalps.loadMeasurements(pyalps.getResultFiles())

We now loop through all measurements and print them:

for s in pyalps.flatten(data):
    if len(s.x)==1:
        print s.props['observable'], ' : ', s.y[0]
    else:
        for (x,y) in zip(s.x,s.y):
            print  s.props['observable'], x, ' : ', y

The if statement checks whether the measured quantity is a scalar or vector-valued quantity.

MC-03 Magnetization MC-05 Bosons