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<p class="western" style="margin-bottom: 0in; line-height: 100%">Dear All,</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><br>

</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">I'm trying to get some results for the Periodic Anderson model (PAM) using DMRG.</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">Precisely, I'm trying to analyze the PAM with crossed hybridizations. However,</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">I'm getting different results for symmetric situations, where they must be equal.</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">I will try to explain it below.</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><br>

</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">In order to have the crossed PAM, I first created the lattice below.</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><br>

</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><LATTICES></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><LATTICEGRAPH name="PAM_cross"></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><FINITELATTICE></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><LATTICE dimension="1"></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><BASIS></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><VECTOR>1</VECTOR></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"></BASIS></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"></LATTICE></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><PARAMETER name="L"/></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><EXTENT size="L"/></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><BOUNDARY type="open"/></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"></FINITELATTICE></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><UNITCELL dimension="1" vertices="2"></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><VERTEX id="1" type="0"></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"></VERTEX></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><VERTEX id="2" type="1"></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"></VERTEX></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><EDGE type="2"></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><SOURCE vertex="1"/><TARGET vertex="2"/></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"></EDGE></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><EDGE type="1"></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><SOURCE vertex="1"/><TARGET vertex="1" offset="1"/></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"></EDGE></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><EDGE type="3"></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><SOURCE vertex="1"/><TARGET vertex="2" offset="1"/></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"></EDGE></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><EDGE type="4"></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><SOURCE vertex="2"/><TARGET vertex="1" offset="1"/></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"></EDGE></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"></UNITCELL></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"></LATTICEGRAPH></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"></LATTICES></p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><br>

</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">where vertex ‘0’ and ‘1’ will describe d- and f-electrons, respectively. Furthermore,</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">the edge ‘1’ will correspond to the hopping of d-electrons, edge ‘2’ the local</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">hybridization, and edges ‘3’ and "4" the crossed hybridizations.</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><br>

</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">I chose the "alternative fermion Hubbard" Hamiltonian, since I'm interested to</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">conserve the total number of particles operator. In this notation, I have t1=t,</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">t2=V_local, t3=Vcross1 and t4=V_cross2.</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><br>

</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">My first test was for t1=1, t2=t4=0.75 and t3=0, which corresponds to a sawtooth chain.</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">Notice that in this case exchanging the index 3 and 4 (i.e. making t3=0.75 and t4=0) just</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">reflects the lattice, and should not have any physical effect. Thus, the results *must* be</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">the same. However, I getting different results for these two cases in a vast variety of</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">parameters. For instance, fixing</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><br>

</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">SWEEPS=5</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">MAXSTATES=100</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">CONSERVED_QUANTUMNUMBERS= "N"</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">N_total = 24;</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">L=12;</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">t1=1.0;</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">t2=0.75;</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">t4=0.0;</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">U0=0.0;</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">U1=1.0;</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">mu1=0.5;</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">{t3=0.75;}</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><br>

</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">I get E=-31.251093744938501. But for t3=0 and t4=0.75, it is -31.785332039272376.</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><br>

</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">I checked it with an old code I have, and the latter is the right one. So, do you know</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">what is happening? Did I do something wrong?</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><br>

</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">I appreciate if you can help me with it.</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><br>

</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">Thanks in advance.</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><br>

</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">I look forward to hearing from you in due course.</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><br>

</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">Yours Sincerely,</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%"><br>

</p>

<p class="western" style="margin-bottom: 0in; line-height: 100%">Natanael C. Costa</p>

<p><br>

</p>

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