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;}