[1] I am trying to compute s-wave pair field correlation function, using full diagonalization routine for the fermionic Hubbard model.
This function is defined as:
P_s = \langle \Delta^{\dagger} \Delta + \Delta \Delta^{\dagger} \rangle, where
\Delta^{\dagger} = \frac {1} {\sqrt{N}} \sum_{k} c^{\dagger}_{n \uparrow} c^{\dagger}_{n \downarrow}
And I can not figure out how to measure this.
[2] How do I measure Kinetic energy? When I am trying use:
'MEASURE_AVERAGE[kinetic-energy]' : 'fermion_kinetic_energy'
I get error: Cannot evaluate expression 0.333333 * fermion_kinetic_energy(i)
Here is my model definition: ------------------------------ <MODELS> <SITEBASIS name="fermion"> <QUANTUMNUMBER name="Nup" min="0" max="1" type="fermionic"/> <QUANTUMNUMBER name="Ndown" min="0" max="1" type="fermionic"/> <OPERATOR name="Splus" matrixelement="1"> <CHANGE quantumnumber="Ndown" change="-1"/> <CHANGE quantumnumber="Nup" change="1"/> </OPERATOR> <OPERATOR name="Sminus" matrixelement="1"> <CHANGE quantumnumber="Nup" change="-1"/> <CHANGE quantumnumber="Ndown" change="+1"/> </OPERATOR> <OPERATOR name="Sz" matrixelement="(Nup-Ndown)/2"/> <OPERATOR name="Nup" matrixelement="Nup"/> <OPERATOR name="Ndown" matrixelement="Ndown"/> <OPERATOR name="N" matrixelement="Nup+Ndown"/> <OPERATOR name="c_down" matrixelement="1"> <CHANGE quantumnumber="Ndown" change="-1"/> </OPERATOR> <OPERATOR name="cdag_down" matrixelement="1"> <CHANGE quantumnumber="Ndown" change="1"/> </OPERATOR> <OPERATOR name="c_up" matrixelement="1"> <CHANGE quantumnumber="Nup" change="-1"/> </OPERATOR> <OPERATOR name="cdag_up" matrixelement="1"> <CHANGE quantumnumber="Nup" change="1"/> </OPERATOR> <OPERATOR name="n" matrixelement="Nup+Ndown"/> <OPERATOR name="n_up" matrixelement="Nup"/> <OPERATOR name="n_down" matrixelement="Ndown"/> <OPERATOR name="double_occupancy" matrixelement="Nup*Ndown"/> </SITEBASIS>
<BONDOPERATOR name="fermion_hop" source="x" target="y"> cdag_up(x)*c_up(y)+cdag_up(y)*c_up(x)+cdag_down(x)*c_down(y)+cdag_down(y)*c_down(x) </BONDOPERATOR>
<GLOBALOPERATOR name="fermion_kinetic_energy"> <BONDTERM type="0" source="i" target="j"> -t*fermion_hop(i,j) </BONDTERM> </GLOBALOPERATOR>
<BASIS name="fermion"> <SITEBASIS type="1" ref="fermion"/> <SITEBASIS type="2" ref="fermion"/> <SITEBASIS type="3" ref="fermion"/> <CONSTRAINT quantumnumber="Nup" value="Nup_total"/> <CONSTRAINT quantumnumber="Ndown" value="Ndown_total"/> <CONSTRAINT quantumnumber="N" value="N_total"/> <CONSTRAINT quantumnumber="Sz" value="Sz_total"/> </BASIS>
<HAMILTONIAN name="fermionic Hubbard"> <PARAMETER name="mu" default="0"/> <PARAMETER name="t" default="1"/> <PARAMETER name="U" default="0"/> <BASIS ref="fermion"/> <SITETERM site="i"> <PARAMETER name="mu#" default="mu"/> <PARAMETER name="U#" default="U"/> +U# * (n_up(i) - 0.5) * (n_down(i) - 0.5) - mu# * n(i) </SITETERM> <BONDTERM source="i" target="j"> -t*fermion_hop(i, j) </BONDTERM> </HAMILTONIAN> </MODELS>
----------------------- Lattice definition: ----------------------- <LATTICES> <LATTICE name="square" dimension="2"> <PARAMETER name="a" default="1"/> <BASIS> <VECTOR> a 0 </VECTOR> <VECTOR> 0 a </VECTOR> </BASIS> <RECIPROCALBASIS> <VECTOR>2*pi/a 0</VECTOR> <VECTOR>0 2*pi/a</VECTOR> </RECIPROCALBASIS> </LATTICE>
<UNITCELL name="Lieb" dimension="2"> <VERTEX id="1" type="1"> <COORDINATE>0 0</COORDINATE> </VERTEX> <VERTEX id="2" type="2"> <COORDINATE>0.5 0</COORDINATE> </VERTEX> <VERTEX id="3" type="3"> <COORDINATE>0 0.5</COORDINATE> </VERTEX> <EDGE> <SOURCE vertex="1" offset="0 0"/> <TARGET vertex="2" offset="0 0"/> </EDGE> <EDGE> <SOURCE vertex="1" offset="0 0"/> <TARGET vertex="3" offset="0 0"/> </EDGE> <EDGE> <SOURCE vertex="1" offset="1 0"/> <TARGET vertex="2" offset="0 0"/> </EDGE> <EDGE> <SOURCE vertex="1" offset="0 1"/> <TARGET vertex="3" offset="0 0"/> </EDGE> </UNITCELL>
<LATTICEGRAPH name="Lieb" vt_skip="true"> <FINITELATTICE> <LATTICE ref="square"/> <EXTENT dimension="1" size="nx"/> <EXTENT dimension="2" size="ny"/> <BOUNDARY type="periodic" /> </FINITELATTICE> <UNITCELL ref="Lieb"/> </LATTICEGRAPH> </LATTICES>