DWA-03 Time of Flight Images

As a third example of the directed worm algorithm QMC code, we shall study the time-of-flight images of an optical lattice in an harmonic trap.

Preparing and running the simulation from Python

import pyalps
import pyalps.dwa

parms = [
{
    'LATTICE' : 'inhomogeneous simple cubic lattice' ,
    'L'       : 120 ,

    'MODEL'   : 'boson Hubbard' ,
    'Nmax'    : 20 ,

    't'  : 1. ,
    'U'  : 8.11 ,
    'mu' : '4.05 - (0.0073752*(x-(L-1)/2.)*(x-(L-1)/2.) + 0.0036849*(y-(L-1)/2.)*(y-(L-1)/2.) + 0.0039068155*(z-(L-1)/2.)*(z-(L-1)/2.))' ,

    'T'  : 1. ,

    'THERMALIZATION' : 1500 ,
    'SWEEPS'         : 60000 ,
    'SKIP'           : 50 , 

    'tof_phase'    : pyalps.dwa.tofPhase(time_of_flight=15.5, wavelength=[765,843,843], mass=86.99) ,

    'MEASURE[Green Function]': 1
}
]

input_file = pyalps.writeInputFiles('parm3a', parms)
res = pyalps.runApplication('dwa', input_file)

Evaluating the simulation and preparing plots using Python

We load the results for the Green function from all output files starting with parm3a.

import pyalps
data = pyalps.loadMeasurements(pyalps.getResultFiles(prefix='parm3a'), 'Green Function');

To visualize the Green function:

import pyalps.plot as aplt;
aplt.plot3D(data, layer=0)
q_x = q_x[0:q_x.shape[0]:mag, 0:q_x.shape[1]:mag];
q_y = q_y[0:q_y.shape[0]:mag, 0:q_y.shape[1]:mag];
tof_image = tof_image[1:tof_image.shape[0]:mag, 0:tof_image.shape[1]:mag] * mag * mag
tof_image[tof_image < 0] = 0