[ALPS-users] Long Range Kitaev Model site dependent Hamiltonian

Mon Jul 3 07:02:29 CEST 2017

Hello again.

The first method unfortunately didn't work.

And the second method, I tried using this lattice:

<LATTICES>
 <GRAPH name = "long range kitaev chain" dimension="1" vertices="5"
edges="10">
  <VERTEX id="1" type="0"><COORDINATE>1</COORDINATE></VERTEX>
  <VERTEX id="2" type="1"><COORDINATE>2</COORDINATE></VERTEX>
  <VERTEX id="3" type="1"><COORDINATE>3</COORDINATE></VERTEX>
  <VERTEX id="4" type="1"><COORDINATE>4</COORDINATE></VERTEX>
 <VERTEX id="5" type="0"><COORDINATE>5</COORDINATE></VERTEX>
  <EDGE source="1" target="2" id="1-2" type="1"vector="1"/>
  <EDGE source="1" target="3" id="1-3" type="2"vector="1"/>
  <EDGE source="1" target="4" id="1-4" type="3"vector="1"/>
  <EDGE source="1" target="5" id="1-5" type="4"vector="1"/>
  <EDGE source="2" target="3" id="2-3" type="1"vector="1"/>
  <EDGE source="2" target="4" id="2-4" type="2"vector="1"/>
  <EDGE source="2" target="5" id="2-5" type="3"vector="1"/>
  <EDGE source="3" target="4" id="3-4" type="1"vector="1"/>
  <EDGE source="3" target="5" id="3-5" type="2"vector="1"/>
  <EDGE source="4" target="5" id="4-5" type="1"vector="1"/>
 </GRAPH>
</LATTICES>

With extra parameters like this:

        'coeff1'         :1,
        'coeff2'         :2,
        'coeff3'         :3,
        'coeff4'         :4

but maintained the abs(i-j) as I'm not quite sure what to substitute with
and it still didn't work (as can probably expected). My question has to do
in what to substitute this term with.

Thanks in advance.
Ian Felismino

On Thu, Jun 29, 2017 at 1:01 PM, Michele Dolfi <dolfim at phys.ethz.ch> wrote:

> I think you need:
> <INHOMOGENEOUS><EDGE/></INHOMOGENEOUS>
>
> For the second case, you need to define a graph with different edge types,
> then you can assign the values in the parameters with:
> coeff0=…
> coeff1=…
> …
>
>
> Note that there is no automatic lattice graph for an all-to-all graph.
> This you need to define yourself in a graph file.
>
>
> Michele
>
>
> On 28 Jun 2017, at 09:38, John Ian Kenneth E. Felismino <
> jfelismino at nip.upd.edu.ph> wrote:
>
> Hello again.
>
> I tried using an inhomogenous periodic 1D chain lattice defined as
>
> <LATTICEGRAPH name = "inhomogeneous periodic chain lattice" vt_skip="true">
>   <FINITELATTICE>
>     <LATTICE ref="chain lattice"/>
>     <EXTENT dimension="1" size="L"/>
>     <BOUNDARY type="periodic"/>
>   </FINITELATTICE>
>   <UNITCELL ref="simple1d"/>
>   <INHOMOGENEOUS><VERTEX/></INHOMOGENEOUS>
> </LATTICEGRAPH>
>
> and it still didn't work.
>
> For the second solution, how do you assign coefficients for every source
> and target? I need to find the difference for varying (long) ranges.
>
> Thanks.
> Ian Felismino
>
>
> On Wed, Jun 28, 2017 at 12:53 PM, Michele Dolfi <dolfim at phys.ethz.ch>
> wrote:
>
>> Actually both the “abs” and “^” operators seem to be allowed, but the
>> problem might come from the (i-j) term.
>> Using the coordinates in the coefficients is instead a non-trivial
>> feature. It only works if you define the lattice as inhomogeneous. You
>> should see some examples non the lattices.xml file.
>>
>> As an alternative solution, you could define the lattice as a graph and
>> set independent coefficients on the bonds and edges. You should find other
>> examples in the mailing list, or on this page https://alps.comp-phys.or
>> g/mediawiki/index.php/Tutorials:LatticeHOWTO:SimpleGraphs
>>
>>
>> Best,
>> Michele
>>
>>
>> On 27 Jun 2017, at 08:14, John Ian Kenneth E. Felismino <
>> jfelismino at nip.upd.edu.ph> wrote:
>>
>> Hi!
>>
>> The hamiltonian I'm using is attached as a picture file. As you can see,
>> the bond terms are proportional to abs(i - j)^\alpha. i was wondering if
>> this is possible in Alps because I have tried doing it (crudely) with DMRG
>> and found that it did not produce an output xml. I had simply added the
>> term "/abs(i-j)^alpha#" in my hamiltonian.  When I remove this term, the
>> Hamiltonian works, so clearly the problem is with this proportionality term.
>>
>> Thanks.
>> Ian Felismino
>> <Kitaev Hamiltonian.png>
>>
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