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

[Axel Gagge]

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<mailto: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<mailto:comp-phys-alps-users-bounces at lists.phys.ethz.ch>> för Matthias Troyer <troyer at phys.ethz.ch<mailto:troyer at phys.ethz.ch>>
Skickat: den 17 januari 2017 19:42
Till: comp-phys-alps-users at lists.phys.ethz.ch<mailto: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<mailto: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
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8093 Zurich
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dolfim at phys.ethz.ch<mailto:dolfim at phys.ethz.ch>
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On Jan 17, 2017, at 4:10 PM, Axel Gagge <axel.gagge at fysik.su.se<mailto: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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