[ALPS-users] Free fermion models and diagonalisation

[Michele Dolfi]

Dear Anya,

1. If you need custom lattices, the easiest option is to write a “graph file”.
https://alps.comp-phys.org/mediawiki/index.php/Tutorials:LatticeHOWTO:SimpleGraphs <https://alps.comp-phys.org/mediawiki/index.php/Tutorials:LatticeHOWTO:SimpleGraphs>
You can then specify different edge types and refer to them in the parameters, e.g. J0 for the value of J on the bond of type 0, J1 for the bond of type 1, etc.

2. I think everything you need is the application example/model/print_symbolic3.cpp

3. The diagonalization applications do not perform any fourier transform of the model automatically. Actually the ALPS model library supports only up to two-body interaction.
The sparsediag and fulldiag codes perform a basis decomposition in symmetry sectors of the translation operator. https://alps.comp-phys.org/mediawiki/index.php/Tutorials:Parameters#Additional_parameters_for_exact_diagonalization <https://alps.comp-phys.org/mediawiki/index.php/Tutorials:Parameters#Additional_parameters_for_exact_diagonalization>
You can disable this feature with the parameter TRANSLATION_SYMMETRY=false


Best,
Michele


> On 20 Mar 2017, at 06:19, Anya Weng <anya.weng.physics at gmail.com> wrote:
> 
>  Dear All,
> I am new to ALPS and would really appreciate any help on the following -
> 
> 1. I am trying to numerically reproduce the results in this paper by Chen and Nussinov (https://arxiv.org/abs/cond-mat/0703633 <https://arxiv.org/abs/cond-mat/0703633>) - the part where they describe free fermion on the kitaev model.
> 
> One can see that the lattice of the fermions is a square one with 2 bond types(anisotropy). How do I mention that in ALPS?
> 
> 2. Can I see the matrix elements of the matrix that ALPS diagonalises?
> 3. Also, does ALPS dmrg, sparsediag, full diag etc use fourier transform for free fermion models? Where can I see the source codes?
>  What if I don't want to FT to momentum space because k will not be a good quantum number if I introduce some translation symmetry destroying disorder?
> 
> 
> 
> Thank you very much,
> Anya Weng 
>  
> 
> 
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