Density profile

As a second example of the dwa QMC code, we will study the density profile of an optical lattice in an harmonic trap which resembles the experiment

Mimicking the experiment

Preparing and running the simulation from the command line

The parameter file parm2a sets up Monte Carlo simulation of a 1003 optical lattice trap that mimicks the Bloch experiment:

LATTICE="inhomogeneous simple cubic lattice"
L=100

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.))"

THERMALIZATION=50000
SWEEPS=200000
SKIP=100

MEASURE[Local Density]=1

{ T=1. }

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

parameter2xml parm2a
dwa parm2a.in.xml

Preparing and running the simulation from Python

import pyalps

parms = [
{
'LATTICE' : 'inhomogeneous simple cubic lattice' ,
'L'       : 100 ,

'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' : 50000 ,
'SWEEPS'         : 2000000 ,
'SKIP'           : 100 ,

'MEASURE[Local Density]': 1
}
)

input_file = pyalps.writeInputFiles('parm2a', parms)
res = pyalps.runApplication('dwa', input_file)