[ALPS-users] Conserve quantum number for composite unit cell

[Matthias Troyer]

I would suggest to use one quantum number for both Sz and N instead of two or three different quantum numbers. 

> On 18 Jan 2017, at 12:24, Axel Gagge <axel.gagge at fysik.su.se> wrote:
> 
> With extra quantum number, fixed n.o. excitations: runs in 124 s, E0, trunc_error = -1.0000000000001179, 0.00082901673330108058
> With no extra quantum number, no fixed n.o. excitations (grand canonical...): runs in 24 s, E0, trunc_error = -0.99999999999997691, -1.3941131613197575e-16
> 
> 
> I will proceed with the grand canonical and this is certainly enough, but is there some way around this slow-down? It would be nice to be able to conserve any charge which correspond to an abelian symmetry.
> 
> Thanks,
> /Axel
> 
> Från: Comp-phys-alps-users <comp-phys-alps-users-bounces at lists.phys.ethz.ch> för Matthias Troyer <troyer at phys.ethz.ch>
> Skickat: den 18 januari 2017 18:47
> Till: comp-phys-alps-users at lists.phys.ethz.ch
> Ämne: Re: [ALPS-users] Conserve quantum number for composite unit cell
>  
> Have you tried using a grandcanonical instead of fixing the quantum number?
> 
>> On 18 Jan 2017, at 09:15, Axel Gagge <axel.gagge at fysik.su.se> wrote:
>> 
>> ​It wasn't very hard to define such a quantum number, but it seems like it actually makes the simulation run much slower. I suppose this is because another quantum number needs to be stored which leads to a larger basis size again? On the other hand, I can think of no way to properly define the spin operators without using the quantum numbers S, Sz... ​
>> 
>> Many thanks,
>> Axel
>> 
>> Från: Comp-phys-alps-users <comp-phys-alps-users-bounces at lists.phys.ethz.ch> för Matthias Troyer <troyer at phys.ethz.ch>
>> Skickat: den 17 januari 2017 19:42
>> Till: comp-phys-alps-users at lists.phys.ethz.ch
>> Ämne: Re: [ALPS-users] Conserve quantum number for composite unit cell
>>  
>> You need to define a new combined quantum number, which is changed by the training and lowering operators for both types of particles.
>> 
>> 
>>> On 17 Jan 2017, at 08:54, Michele Dolfi <dolfim at phys.ethz.ch> wrote:
>>> 
>>> I hope somebody else could give you a better answer, but I don’t think this is possible out of the box, and I’m not 100% sure it is at all possible in the way you think about it.
>>> 
>>> What I would try is away to play around with a new model definition where you make a composite quantum number explicit.
>>> The "fermion Hubbard” and “alternative fermion Hubbard” could be of inspiration for how to conserve N and/or Sz instead of Nup and/or Ndown.
>>> 
>>> 
>>> Best,
>>> Michele
>>> 
>>> 
>>> --
>>> ETH Zurich
>>> Dr. Michele Dolfi
>>> Institute for Theoretical Physics
>>> HIT G 32.4
>>> Wolfgang-Pauli-Str. 27
>>> 8093 Zurich
>>> Switzerland
>>> 
>>> dolfim at phys.ethz.ch
>>> www.itp.phys.ethz.ch
>>> 
>>> +41 44 633 78 56 phone
>>> +41 44 633 11 15 fax 
>>> 
>>> 
>>> 
>>> 
>>> 
>>> 
>>>> On Jan 17, 2017, at 4:10 PM, Axel Gagge <axel.gagge at fysik.su.se> wrote:
>>>> 
>>>> ​Hello, I just wanted to ask if it is possible to preserve a combination of quantum numbers such as the total number of excitations:
>>>> 
>>>> N = \sum_{bosonic sites} n_j + 1/2 \sum_{spinful sites} s_z
>>>> 
>>>> and what the syntax for this would be? I guess that one option would be to define a new quantum number and let Splus raise it by 1/2 but I just thought that I would check this with you first!
>>>> 
>>>> Otherwise, thank you for an excellent library! I have had no problems so far with the new release.
>>>> 
>>>> Thanks,
>>>> /Axel Gagge
>>>> First year PhD Student, Stockholm University
>>>> 
>>>> 
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>> 
>> <my_models.xml><my_lattices.xml><Test of iDMRG.ipynb>
>> 
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