Tutorial:loop

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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"
   local_S=1/2
   L=60
   J=1
   THERMALIZATION=15000
   SWEEPS=150000
   REPRESENTATION="path integral"
   {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;}

In ALPS version 1.3.5 or later, parameter ALGORITHM is required instead of REPRESENTATION in the parameter file

   ALGORITHM="path integral" // for ALPS 1.3.5
   ALGORITHM="loop; path integral" // for ALPS 1.4 or later

Using the following standard sequence of commands you can run the simulation using the loop algorithm QMC 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">
  
   <legend show="true"/>
   <xaxis label="Temperature"    type="PARAMETER" name="T"/>
   <yaxis label="Susceptibility" type="SCALAR_AVERAGE"/>
   
   <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"
 local_S=1/2
 L=60
 J=1
 J1=1
 THERMALIZATION=15000
 SWEEPS=150000
 REPRESENTATION="path integral"
 {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;}

In ALPS version 1.3.5 or later, parameter ALGORITHM is required instead of REPRESENTATION in the parameter file

   ALGORITHM="path integral" // for ALPS 1.3.5
   ALGORITHM="loop; path integral" // for ALPS 1.4 or later

Using the following standard sequence of commands you can run the simulation using the loop algorithm QMC 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

  • Is there a difference between the classical and quantum calculation?
  • How does the susceptibility depend on the lattice?
  • Why does the susceptibility change?