[ALPS-users] Two-dimensional system with MPS

[Michele Dolfi]

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 <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 <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 <mailto: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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