Tutorial III: Quantum Monte Carlo Simulations (SSE)

Tutorial III: Quantum Monte Carlo Simulations (SSE)

Part I: Susceptibility of one-dimensional Heisenberg models

The one-dimensional Heisenberg chain

The parameter file quantum1/parm3a sets up Monte Carlo simulations of the quantum mechanical Heisenberg model on a one-dimensional chain with 60 sites for a couple of temperatures (T=0.05, 0.1, ..., 2.0) using cluster updates. 

LATTICE="chain lattice"
MODEL="spin"
LATTICE_LIBRARY="../lattices.xml"
MODEL_LIBRARY="../models.xml"
local_S=1/2
L=60
J=1
THERMALIZATION=15000
SWEEPS=150000
REPRESENTATION="SSE"
{T=0.05;}
{T=0.1;}
{T=0.2;}
{T=0.3;}
{T=0.4;}
{T=0.5;}
{T=0.6;}
{T=0.7;}
{T=0.75;}
{T=0.8;}
{T=0.9;}
{T=1.0;}
{T=1.25;}
{T=1.5;}
{T=1.75;}
{T=2.0;}

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


parameter2xml parm3a

loop -Tmin 10 parm3a.in.xml

extracttext plot.xml parm3a.task*.out.xml

where the plot is specified in the file plot.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="Susceptibility versus temperature for one-dimesnional Heisenberg models">
 
  <!-- general plot description -->
  <legend show="true"/>
  <xaxis label="Temperature"    type="PARAMETER" name="T"/>
  <yaxis label="Susceptibility" type="SCALAR_AVERAGE"/>

  <!-- set descriptions -->
  <set label="One-dimensional chain"/>

</plot>

The one-dimensional Heisenberg ladder

The parameter file quantum1/parm3b sets up Monte Carlo simulations of the quantum mechanical Heisenberg model on a one-dimensional ladder with 60 sites for a couple of temperatures (T=0.1, 0.2, ..., 2.0) using cluster updates. 

LATTICE="ladder"
MODEL="spin"
LATTICE_LIBRARY="../lattices.xml"
MODEL_LIBRARY="../models.xml"
local_S=1/2
L=60
J=1
THERMALIZATION=15000
SWEEPS=150000
REPRESENTATION="SSE"
{T=0.1;}
{T=0.2;}
{T=0.3;}
{T=0.4;}
{T=0.5;}
{T=0.6;}
{T=0.7;}
{T=0.8;}
{T=1.0;}
{T=1.25;}
{T=1.5;}
{T=1.75;}
{T=2.0;}

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


parameter2xml parm3b

loop -Tmin 10 parm3b.in.xml

extracttext plot.xml parm3b.task*.out.xml

Questions

Part II: Magnetization versus magnetic field

One-dimensional Heisenberg chain in a magnetic field

The parameter file quantum2/parm4a sets up Monte Carlo simulations of the quantum mechanical S=1/2 Heisenberg model on a one-dimensional chain with 20 sites at fixed temperature T=0.08 for a couple of magnetic fields (h=0, 0.1, ..., 2.5). 

LATTICE="chain lattice"
MODEL   = "spin"
LATTICE_LIBRARY="../lattices.xml"
MODEL_LIBRARY="../models.xml"
local_S=1/2
L=20
J=1
T=0.08
THERMALIZATION=2000
SWEEPS=20000
{h=0;}
{h=0.1;}
{h=0.2;}
{h=0.3;}
{h=0.4;}
{h=0.5;}
{h=0.6;}
{h=0.7;}
{h=0.8;}
{h=0.9;}
{h=1.0;}
{h=1.2;}
{h=1.4;}
{h=1.6;}
{h=1.8;}
{h=2.0;}
{h=2.2;}
{h=2.4;}
{h=2.5;}

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


parameter2xml parm4a

sse -Tmin 10 parm4a.in.xml

extracttext plot2.xml parm4a.task*.out.xml

where plot2.xml specifies a plot of the magnetization versus magnetic field

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

<plot name="Magnetization versus magnetic field for one-dimesnional Heisenberg models">
 
  <!-- general plot description -->
  <legend show="true"/>
  <xaxis label="Magnetic field" type="PARAMETER" name="h"/>
  <yaxis label="Magnetization"  type="SCALAR_AVERAGE"/>

  <!-- set descriptions -->
  <set label="One-dimensional chain"/>

</plot>

Questions

One-dimensional Heisenberg ladder in a magnetic field

The parameter file quantum2/parm4b sets up Monte Carlo simulations of the quantum mechanical S=1/2 Heisenberg model on a one-dimensional ladder with 60 sites at fixed temperature T=0.08 for a couple of magnetic fields (h=0, 0.1, ..., 3.5). 

LATTICE="ladder"
MODEL   = "spin"
LATTICE_LIBRARY="../lattices.xml"
MODEL_LIBRARY="../models.xml"
local_S=1/2
L=20
J=1
T=0.08
THERMALIZATION=2000
SWEEPS=20000
{h=0;}
{h=0.1;}
{h=0.2;}
{h=0.3;}
{h=0.4;}
{h=0.5;}
{h=0.6;}
{h=0.8;}
{h=1.0;}
{h=1.25;}
{h=1.5;}
{h=1.75;}
{h=2.0;}
{h=2.25;}
{h=2.5;}
{h=2.75;}
{h=3.0;}
{h=3.25;}
{h=3.5;}

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


parameter2xml parm4b

sse -Tmin 10 parm4b.in.xml

extracttext plot2.xml parm4b.task*.out.xml

Questions

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