question on the local measurement and definition - Comp-phys-alps-users

3 Jun 2010


      Dear all,
I would like to ask you a question about the local measurement and definition:
I want to calculate the density of fermions and the bond order
cdag(i)*c(j) on each site and each bond in a spinless Hubbard model.
How should I do it? Thank you very much!
Best
Jun
Here are my files:
=============================================================
lattice.xml
<LATTICES>
<LATTICE name="triangular lattice" dimension="2">
  <PARAMETER name="a" default="1"/>
  <BASIS><VECTOR>a 0</VECTOR><VECTOR>a/2 a*sqrt(3)/2</VECTOR></BASIS>
  <RECIPROCALBASIS><VECTOR>2*pi/a -2*pi/a/sqrt(3)</VECTOR><VECTOR>0
4*pi/a/sqrt(3)</VECTOR></RECIPROCALBASIS>
</LATTICE>
<UNITCELL name="Kagome" dimension="2">
  <VERTEX><COORDINATE>0 0</COORDINATE></VERTEX>
  <VERTEX><COORDINATE>0.5 0</COORDINATE></VERTEX>
  <VERTEX><COORDINATE>0 0.5</COORDINATE></VERTEX>
<EDGE><SOURCE vertex="1"/><TARGET vertex="2"/></EDGE>
  <EDGE><SOURCE vertex="1"/><TARGET vertex="3"/></EDGE>
  <EDGE><SOURCE vertex="2"/><TARGET vertex="3"/></EDGE>
  <EDGE><SOURCE vertex="1"/><TARGET vertex="2" offset="-1 0"/></EDGE>
  <EDGE><SOURCE vertex="2"/><TARGET vertex="3" offset="1 -1"/></EDGE>
  <EDGE><SOURCE vertex="1"/><TARGET vertex="3" offset="0 -1"/></EDGE>
</UNITCELL>
<LATTICEGRAPH name = "Kagome lattice">
  <FINITELATTICE>
    <LATTICE ref="triangular lattice"/>
    <PARAMETER name="W" default="L"/>
    <EXTENT dimension="1" size="L"/>
    <EXTENT dimension="2" size="W"/>
    <BOUNDARY type="periodic"/>
  </FINITELATTICE>
  <UNITCELL ref="Kagome"/>
</LATTICEGRAPH>
</LATTICES>
=========================================
models.xml
<MODELS>
<SITEBASIS name="spinless fermion">
  <QUANTUMNUMBER name="N" min="0" max="1" type="fermionic"/>
  <OPERATOR name="cdag" matrixelement="1">
    <CHANGE quantumnumber="N" change="1"/>
  </OPERATOR>
  <OPERATOR name="c" matrixelement="1">
    <CHANGE quantumnumber="N" change="-1"/>
  </OPERATOR>
  <OPERATOR name="n" matrixelement="N"/>
</SITEBASIS>
<SITEOPERATOR name="density" site="x">
   cdag(x)*c(x)
 </SITEOPERATOR>
<BASIS name="spinless fermion">
  <SITEBASIS ref="spinless fermion"/>
  <CONSTRAINT quantumnumber="N" value="N_total"/>
</BASIS>
<BONDOPERATOR name="fermion_hop" source="x" target="y">
  cdag(x)*c(y)+cdag(y)*c(x)
</BONDOPERATOR>
<HAMILTONIAN name="spinless fermions">
  <PARAMETER name="mu" default="0"/>
  <PARAMETER name="t" default="1"/>
  <PARAMETER name="V" default="0"/>
  <PARAMETER name="t'" default="0"/>
  <PARAMETER name="V'" default="0"/>
  <PARAMETER name="t0" default="t"/>
  <PARAMETER name="t1" default="t'"/>
  <PARAMETER name="V0" default="V"/>
  <PARAMETER name="V1" default="V'"/>
  <BASIS ref="spinless fermion"/>
  <SITETERM site="i">
    <PARAMETER name="mu#" default="mu"/>
    -mu#*n(i)
  </SITETERM>
  <BONDTERM source="i" target="j">
    <PARAMETER name="t#" default="0"/>
    <PARAMETER name="V#" default="0"/>
    -t#*(cdag(i)*c(j)+cdag(j)*c(i)) + V#*n(i)*n(j)
  </BONDTERM>
</HAMILTONIAN>
</MODELS>
=============================================
parameters.txt
MODEL="spinless fermions";
LATTICE="Kagome lattice";
LATTICE_LIBRARY="definitions/lattices.xml"
MODEL_LIBRARY="definitions/Copy of models.xml"
t=1;
N_total=4;
W=2;
L=2;
CONSERVED_QUANTUMNUMBERS="N";
NUMBER_EIGENVALUES=3;
MEASURE_AVERAGE[kinetic-energy]=fermion_kinetic_energy;
MEASURE_AVERAGE[density]=density;
{V=30;}