[ALPS-users] Two-dimensional system with MPS

[Michele Dolfi]

Something you should still consider is to avoid recomputing the Hamiltonian
at all time steps.
At the moment you are forcing this with the option "update_each=1". Just
set it to "steps".
For a test, you could do the same also with "measure_each".

On Sun, Jul 9, 2017 at 8:25 PM, H <w.boson at gmail.com> wrote:

> 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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