Hi again,
 
I wonder, whether the effect might be due to the boundary conditions: As the usual chain lattice has a single-site basis and the dimerized model exhibits a a doubled unit-cell. Therefore the details on how the ends of a finite chain are treated should have different effects for each. This then should be true both for open and for periodic boundary conditions, as in both cases the simpler unit cell has one site at each length to be continued whereas the doubled cell does have to site being continued one way or the other and thee effect should be the stronger, the shorter the system under consideration. I have done some simulations with the same models within exact diagonalization with periodic boundary conditions and found the same effect. As this method is exact (nomen est omen), numerical effects are excluded. Therefore the only remaining candidates are a wrong dimerized J1J2-model (I was unable to find a mistake in the lattices and the model) or boundary conditions being different as the unit-cells do contain different numbers of sites.
 
Could the mentoined effect be attributed to this?
 
Best regards,
 
Alex
 
Gesendet: Freitag, 15. Mai 2015 um 00:24 Uhr
Von: "Alexander Herzog" <Metalhead@web.de>
An: comp-phys-alps-users@lists.phys.ethz.ch
Betreff: Re: [ALPS-users] Equivalence of models
Hi Matthias,
 
thank you for the quick response. I had hoped that the answer to the question was of general nature, therfor I did not include any files.
 
Please find attached the parameter file for the spin-model AFMSp5L50ref, the parameter file for the dimerized J1-J2 chain AFMSp5L50, as well as the respective excerpts from my lattice and model library.
 
<UNITCELL name="complex1d_alt" dimension="1">
  <VERTEX id="1" type="0"><COORDINATE> 0 </COORDINATE></VERTEX>
  <VERTEX id="2" type="1"><COORDINATE> 0.5 </COORDINATE></VERTEX>
  <EDGE type="0"><SOURCE vertex="1" offset="0"/><TARGET vertex="1" offset="1"/></EDGE>
  <EDGE type="2"><SOURCE vertex="1" offset="0"/><TARGET vertex="2" offset="0"/></EDGE>
  <EDGE type="1"><SOURCE vertex="2" offset="0"/><TARGET vertex="1" offset="1"/></EDGE>
  <EDGE type="3"><SOURCE vertex="2" offset="0"/><TARGET vertex="2" offset="1"/></EDGE>
</UNITCELL>
 
<LATTICEGRAPH name = "nnn chain lattice with dimerization">
  <FINITELATTICE>
  <LATTICE name="chain lattice" dimension="1">
    <PARAMETER name="a" default="1"/>
    <BASIS><VECTOR>a</VECTOR></BASIS>
    <RECIPROCALBASIS><VECTOR>2*pi/a</VECTOR></RECIPROCALBASIS>
  </LATTICE>
    <EXTENT dimension="1" size ="L"/>
    <BOUNDARY type="open"/>
  </FINITELATTICE>
  <UNITCELL ref="complex1d_alt"/>
</LATTICEGRAPH>
 

<HAMILTONIAN name="dimfrust">
  <PARAMETER name="J1" default="0"/>
  <PARAMETER name="J2" default="0"/>
  <PARAMETER name="delta" default="0"/>
  <PARAMETER name="Jxy'" default="J'"/>
  <PARAMETER name="Jz1" default="Jz'"/>
  <PARAMETER name="Jxy1" default="Jxy'"/>
  <PARAMETER name="h" default="0"/>
  <PARAMETER name="Gamma" default="0"/>
  <PARAMETER name="D" default="0"/>
  <PARAMETER name="K" default="0"/>
  <BASIS ref="spin"/>
  <SITETERM site="i">
  <PARAMETER name="h#" default="h"/>
  <PARAMETER name="Gamma#" default="Gamma"/>
  <PARAMETER name="D#" default="D"/>
    -h#*Sz(i)-Gamma#*Sx(i)+D#*Sz(i)*Sz(i)
  </SITETERM>
  <BONDTERM type="0" source="i" target="j">
    <PARAMETER name="J1"/>
    <PARAMETER name="J2"/>
    <PARAMETER name="delta"/>
    J1*(1+delta)*exchange(i,j)
  </BONDTERM>
  <BONDTERM type="2" source="i" target="j">
    <PARAMETER name="J1"/>
    <PARAMETER name="J2"/>
    <PARAMETER name="delta"/>
    J2*exchange(i,j)
  </BONDTERM>
  <BONDTERM type="1" source="i" target="j">
    <PARAMETER name="J1"/>
    <PARAMETER name="J2"/>
    <PARAMETER name="delta"/>
    J1*(1-delta)*exchange(i,j)
  </BONDTERM>
  <BONDTERM type="3" source="i" target="j">
    <PARAMETER name="J1"/>
    <PARAMETER name="J2"/>
    <PARAMETER name="delta"/>
    J2*exchange(i,j)
  </BONDTERM>
</HAMILTONIAN>
 
 
Thank you for your interest.
 
Best regards,
 
 
Alex
Gesendet: Donnerstag, 14. Mai 2015 um 23:09 Uhr
Von: "Matthias Troyer" <troyer@phys.ethz.ch>
An: "comp-phys-alps-users@lists.phys.ethz.ch" <comp-phys-alps-users@lists.phys.ethz.ch>
Betreff: Re: [ALPS-users] Equivalence of models
Hi Alex,
 
As usual, we can only help if you send both your input files and the results. 
 
Best regards
 
Matthias
 
 
 

On May 14, 2015, at 22:01, Alexander Herzog <Metalhead@web.de> wrote:
 
Hello everybody,
 
the following might be stupid question or a question, which has already been adressed somewhere:
 
Does DMRG (or also ED for that matter) conserve equivalence between lattices and models?
 
Let me explain this question on the occasion of an example: I have created a lattice and a model for the 1D dimerized J1-J2-model, that is:
 
H=\sum_j^{L/2} (J_1(1-(-1)^j\delta)S_j*S_{j+1}+J_2\S_j*S_{j+2}).
 
In order to validate the lattice and the model, i ran the program for \delta=J_2=0 and J_1=1 for various lengths. In doing so, the ground state energy did not converge to e0=-0.443... but to a value close to it (something between -0.41 and -0.43 depending on the number of sweeps, warm-up states, states to be kept and on L). First I attributed this fact to finite size effects for one and  numerical effects on the other hand. However to be sure I compared the model with the standard alps model for spin (with L sites, as in the case of the dimerized J1-J2 chain the unit-cell is doubled), which is the Heisenberg AFM chain and the outcome is different from the other result.
 
So now, I am asking myself, and I would like to raise the question within the ALPS community, whether this is plausible, as the numerics behind the scenes does not treat the two cases on equal footing, or whether I should critically reconsider the implementation of the dimierized J1-J2 model.
 
Thank you in advance,
 
Alex