Tutorial IV: Quantum Monte Carlo Simulations (worm code)

Tutorial IV: Quantum Monte Carlo Simulations (worm code)

Part I: Quantum phase transitions in the Bose-Hubbard model

The Bose-Hubbard model

The parameter file quantum3/parm5a sets up Monte Carlo simulations of the quantum Bose Hubbard model on a square lattice with 4x4 sites for a couple of hopping parameters (t=0.01, 0.02, ..., 0.1) using the worm code. 

  LATTICE_LIBRARY="../lattices.xml";
  LATTICE="square lattice";
  L=4;

  MODEL_LIBRARY="../models.xml";
  MODEL="boson";
  U    = 1.0;
  mu   = 0.5;
  Nmax = 2;

  T = 0.1;

  SWEEPS=500000;
  THERMALIZATION=100000;

  { t=0.01; }
  { t=0.02; }
  { t=0.03; }
  { t=0.04; }
  { t=0.05; }
  { t=0.06; }
  { t=0.07; }
  { t=0.08; }
  { t=0.09; }
  { t=0.1; }

Using the following standard sequence of commands you can run the simulation using the quantum worm code and extract the calculated energy from the XML output files


parameter2xml parm5a

worm -Tmin 10 parm5a.in.xml

extractxmgr stiffnessplot.xml parm5a.task*.out.xml > plot5a.xmgr

xmgrace plot5a.xmgr

where the plot is specified in the file stiffnessplot.xml like

<?xml version="1.0" encoding="UTF-8"?>
<?xml-stylesheet type="text/xsl" href="http://xml.comp-phys.org/2003/4/plot2html.xsl"?>

<plot name="Stiffness versus temperature for the 2D BHM">
 
  <!-- general plot description -->
  <legend show="true"/>
  <xaxis label="Temperature"    type="PARAMETER" name="T"/>
  <yaxis label="Stiffness"      type="SCALAR_AVERAGE"/>

  <!-- set descriptions -->
  <set label="rho vs. T"/>

</plot>

Questions

The transition from the Mott insulator to suprafluidity

The parameter file quantum3/parm5b sets up Monte Carlo simulations of the quantum Bose Hubbard model on a two-dimensional square lattice for various system sizes. 

  LATTICE_LIBRARY="../lattices.xml";
  LATTICE="square lattice";

  MODEL_LIBRARY="../models.xml";
  MODEL="boson";
  U    = 1.0;
  mu   = 0.5;
  Nmax = 2;

  T = 0.05;

  SWEEPS=600000;
  THERMALIZATION=150000;

  { L=4; t=0.045; }
  { L=4; t=0.05; }
  { L=4; t=0.0525; }
  { L=4; t=0.055; }
  { L=4; t=0.0575; }
  { L=4; t=0.06; }
  { L=4; t=0.065; }

  { L=6; t=0.045; }
  { L=6; t=0.05; }
  { L=6; t=0.0525; }
  { L=6; t=0.055; }
  { L=6; t=0.0575; }
  { L=6; t=0.06; }
  { L=6; t=0.065; }

  { L=8; t=0.045; }
  { L=8; t=0.05; }
  { L=8; t=0.0525; }
  { L=8; t=0.055; }
  { L=8; t=0.0575; }
  { L=8; t=0.06; }
  { L=8; t=0.065; }

Using the following standard sequence of commands you can run the simulation using the quantum worm code and extract the calculated energy from the XML output files


parameter2xml parm5b

worm -Tmin 10 parm5b.in.xml

extractxmgr stiffnessplot2.xml parm5a.task*.out.xml > plot5b.xmgr

xmgrace plot5b.xmgr

Questions

(c) 2003-2004 by Simon Trebst and Synge Todo