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

Michele Dolfi dolfim at phys.ethz.ch
Mon Jul 3 08:05:57 CEST 2017 

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.org/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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