<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div class="">Well, there are multiple factors that makes it more computationally expensive, but not really thousand times…</div><div class=""><br class=""></div><div class="">The relevant factor are:</div><div class="">- 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</div><div class="">- because of the fermionic sign, each term in the trotter decomposition requires multiple operations</div><div class="">- 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</div><div class=""><br class=""></div><div class="">The algorithm used is described in section 2.3 of our paper <a href="https://doi.org/10.1016/j.cpc.2014.08.019" class="">https://doi.org/10.1016/j.cpc.2014.08.019</a>, or more a bit more extensively in section 2.5 of my thesis <a href="http://dx.doi.org/10.3929/ethz-a-010735455" class="">http://dx.doi.org/10.3929/ethz-a-010735455</a>.</div><div class=""><br class=""></div><div class=""><br class=""></div><div class="">Best,</div><div class="">Michele</div><div class=""><br class=""></div><div class=""><br class=""></div><br class=""><div><blockquote type="cite" class=""><div class="">On 8 Jul 2017, at 21:39, H <<a href="mailto:w.boson@gmail.com" class="">w.boson@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class="">Thank you. I have indeed overlooked this important parameter.<div class=""><br class=""></div><div class="">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?</div><div class=""><br class=""></div><div class=""><br class=""></div><div class="gmail_extra"><br class=""><div class="gmail_quote">On Sat, Jul 8, 2017 at 2:48 AM, Michele Dolfi <span dir="ltr" class=""><<a href="mailto:dolfim@phys.ethz.ch" target="_blank" class="">dolfim@phys.ethz.ch</a>></span> wrote:<br class=""><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word" class=""><div class="">Note that by default mps_evolve only works for nearest neighbors lattices.</div><div class="">In higher dimensions this is not the case, since the lattice is unrolled into a one dimensional chain with longer range interactions.</div><div class=""><br class=""></div><div class="">We have a second flavor of the time evolution algorithm for these cases, you can use it via the parameter:</div><div class="">te_type=mpo</div><div class="">Quite some improvements to this variant was introduced in ALPS 2.3, so I suggest you to use that version.</div><div class=""><br class=""></div><div class=""><br class=""></div><div class="">Best,</div><div class="">Michele</div><div class=""><br class=""></div></div></blockquote></div></div></div>
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