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

John Ian Kenneth E. Felismino jfelismino at nip.upd.edu.ph
Wed Jul 5 03:37:15 CEST 2017 

Hi.

Thank you very much. It works now.

Sincerely,
Ian Felismino

On Mon, Jul 3, 2017 at 2:05 PM, Michele Dolfi <dolfim at phys.ethz.ch> wrote:

> Hi Ian,
>
> 1. The id of the edge has to be an index, as for the vertex.
>
> 2. In your Hamiltonian definition you need to add a bond term like
> coeff#*cdag(i)*c(j). The value of coeff# will then be determined by the
> edge type between site i and j.
>
> Since you want something like all-to-all interaction, you cannot use the
> inhomogeneous lattice definition, therefore you cannot use the coordinates
> inside functions (as you are doing with "abs()").
>
>
> Michele
>
>
>
> On 3 Jul 2017, at 07:02, John Ian Kenneth E. Felismino <
> jfelismino at nip.upd.edu.ph> wrote:
>
> 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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