DWA-02 Density Profile

Density profile

As a second example of the directed worm algorithm QMC code, we will study the density profile of an optical lattice in an harmonic trap.

Column integrated density

In this subsection, we want to mimick the experimental setup.

Preparing and running the simulation from the command line

We create the parameter file parm2a to set up a Monte Carlo simulation of a $120^3$ optical lattice trap that mimicks the experiment:

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.))"

THERMALIZATION=1500
SWEEPS=7000
SKIP=50

MEASURE[Local Density]=1

{ T=1. }

(This simulation roughly takes roughly 3 hours.)

We load the local density measurements from all output files starting with parm2a.

import pyalps
data = pyalps.loadMeasurements(pyalps.getResultFiles(prefix='parm2a'), 'Local Density');

and visualize the column integrated density:

import pyalps.plot as aplt;
aplt.plot3D(data, centeredAtOrigin=True)

Cross section density

We want to observe a Mott plateau.

We create the parameter file parm2a to set up a Monte Carlo simulation of a $80^3$ optical lattice trap that mimicks the Bloch experiment:

LATTICE="inhomogeneous simple cubic lattice"
L=60

MODEL="boson Hubbard"
Nmax=20

t=1.
U=60.
mu="40. - (0.09416*(x-(L-1)/2.)*(x-(L-1)/2.) + 0.12955*(y-(L-1)/2.)*(y-(L-1)/2.) + 0.11496*(z-(L-1)/2.)*(z-(L-1)/2.))"

THERMALIZATION=1000000
SWEEPS=3000000
SKIP=1000

MEASURE[Local Density]=1

{ T=1. }

We run the same code as last time on parm1b to prepare the plots, except this time, we want to visualize the cross-section density at the center. Therefore, we pass layer="center" to aplt.plot3D.

aplt.plot3D(data, centeredAtOrigin=True, layer="center")

Contributors

• Matthias Troyer
• Ping Nang Ma