[ALPS-users] Two-dimensional system with MPS

[H]

Thank you.

For a mere 10 timesteps on a 3 by 3 system,
the time for 'spinless fermions' model is ~1s
while the time for 'fermion Hubbard' model is ~475s
Is this within your expectation? The source codes are attached

I tried changing 'mpo_compression' to 'singlesite' but the result becomes
incorrect.

Sorry for keep bothering you. I just want to get the most out of this
excellent library.

On Sun, Jul 9, 2017 at 4:26 AM, Michele Dolfi <dolfim at phys.ethz.ch> wrote:

> Well, there are multiple factors that makes it more computationally
> expensive, but not really thousand times…
>
> The relevant factor are:
> - hamiltonian terms are applied on two-sites, i.e. each will cost M^2*d^2.
> when you change from spinless d=2 to spinfull d=4, you are at least 4 times
> slower
> - because of the fermionic sign, each term in the trotter decomposition
> requires multiple operations
> - the compression to keep the MPS of a controllable dimension is done
> using an iterative scheme. depending on how strong you are compressing, it
> might take more iterations
>
> The algorithm used is described in section 2.3 of our paper
> https://doi.org/10.1016/j.cpc.2014.08.019, or more a bit more extensively
> in section 2.5 of my thesis http://dx.doi.org/10.3929/ethz-a-010735455.
>
>
> Best,
> Michele
>
>
>
> On 8 Jul 2017, at 21:39, H <w.boson at gmail.com> wrote:
>
> Thank you. I have indeed overlooked this important parameter.
>
> It now works smoothly with spinless fermions or bosons. However for
> spinful fermions the time it takes is more than a thousand times (or more)
> longer. Even for tiny 2D systems the time it takes is huge. Is it a known
> limitation and is there a physical reason?
>
>
>
> On Sat, Jul 8, 2017 at 2:48 AM, Michele Dolfi <dolfim at phys.ethz.ch> wrote:
>
>> Note that by default mps_evolve only works for nearest neighbors lattices.
>> In higher dimensions this is not the case, since the lattice is unrolled
>> into a one dimensional chain with longer range interactions.
>>
>> We have a second flavor of the time evolution algorithm for these cases,
>> you can use it via the parameter:
>> te_type=mpo
>> Quite some improvements to this variant was introduced in ALPS 2.3, so I
>> suggest you to use that version.
>>
>>
>> Best,
>> Michele
>>
>>
>
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