Dear All,
I'm trying to get some results for the Periodic Anderson model (PAM) using DMRG.
Precisely, I'm trying to analyze the PAM with crossed hybridizations. However,
I'm getting different results for symmetric situations, where they must be equal.
I will try to explain it below.
In order to have the crossed PAM, I first created the lattice below.
<LATTICES>
<LATTICEGRAPH name="PAM_cross">
<FINITELATTICE>
<LATTICE dimension="1">
<BASIS>
<VECTOR>1</VECTOR>
</BASIS>
</LATTICE>
<PARAMETER name="L"/>
<EXTENT size="L"/>
<BOUNDARY type="open"/>
</FINITELATTICE>
<UNITCELL dimension="1" vertices="2">
<VERTEX id="1" type="0">
</VERTEX>
<VERTEX id="2" type="1">
</VERTEX>
<EDGE type="2">
<SOURCE vertex="1"/><TARGET vertex="2"/>
</EDGE>
<EDGE type="1">
<SOURCE vertex="1"/><TARGET vertex="1" offset="1"/>
</EDGE>
<EDGE type="3">
<SOURCE vertex="1"/><TARGET vertex="2" offset="1"/>
</EDGE>
<EDGE type="4">
<SOURCE vertex="2"/><TARGET vertex="1" offset="1"/>
</EDGE>
</UNITCELL>
</LATTICEGRAPH>
</LATTICES>
where vertex '0' and '1' will describe d- and f-electrons, respectively. Furthermore,
the edge '1' will correspond to the hopping of d-electrons, edge '2' the local
hybridization, and edges '3' and "4" the crossed hybridizations.
I chose the "alternative fermion Hubbard" Hamiltonian, since I'm interested to
conserve the total number of particles operator. In this notation, I have t1=t,
t2=V_local, t3=Vcross1 and t4=V_cross2.
My first test was for t1=1, t2=t4=0.75 and t3=0, which corresponds to a sawtooth chain.
Notice that in this case exchanging the index 3 and 4 (i.e. making t3=0.75 and t4=0) just
reflects the lattice, and should not have any physical effect. Thus, the results *must* be
the same. However, I getting different results for these two cases in a vast variety of
parameters. For instance, fixing
SWEEPS=5
MAXSTATES=100
CONSERVED_QUANTUMNUMBERS= "N"
N_total = 24;
L=12;
t1=1.0;
t2=0.75;
t4=0.0;
U0=0.0;
U1=1.0;
mu1=0.5;
{t3=0.75;}
I get E=-31.251093744938501. But for t3=0 and t4=0.75, it is -31.785332039272376.
I checked it with an old code I have, and the latter is the right one. So, do you know
what is happening? Did I do something wrong?
I appreciate if you can help me with it.
Thanks in advance.
I look forward to hearing from you in due course.
Yours Sincerely,
Natanael C. Costa