[ALPS-users] Two-dimensional system with MPS

[Michele Dolfi]

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


> On 8 Jul 2017, at 00:11, H <w.boson at gmail.com> wrote:
> 
> Dear Michele,
> 
> I am in strong need of simulating the dynamics of higher dimensional but small systems.
> 
> I tried use mps_evolve on a trivial 2D system, but I cannot get it to work.
> 
> I put a particle on the corner of a LxW lattice, and measure <n> at its neighbor site as a function of time. 
> The matlab code and the python (alps) codes are attached.
> 
> When L=3, W=1, for 1D system, they agree quite well:
> 
> <1D.jpg><image.png>
> 
> When L=W=3, they are completely different (left is the correct result from matlab):
> 
> <2D.jpg><image.png>
> 
> Is there something I am missing? I think I have installed the newest version:
> ALPS/MPS Time Evolution version MAQUIS repo r4143 (2013-2014)
> 
> 
> 
> On Thu, Jul 6, 2017 at 2:37 PM, Michele Dolfi <dolfim at phys.ethz.ch <mailto:dolfim at phys.ethz.ch>> wrote:
> Hello,
> 
> Yes, the code can handle 2d systems.
> Yes, to use it you just have to specify the lattice.
> 
> Which sizes do you want to run?
> Unfortunately running higher dimensional DMRG simulations is a highly non trivial task.
> Special care has to be taken for understanding the convergence with respect to the number of sweeps and the MPS bond dimension.
> For an example on how to treat it for “just ladders”, you can have a look here: https://doi.org/10.1103/PhysRevB.92.195139 <https://doi.org/10.1103/PhysRevB.92.195139>
> 
> 
> Best regards,
> Michele
> 
> 
>> On 6 Jul 2017, at 06:32, H <w.boson at gmail.com <mailto:w.boson at gmail.com>> wrote:
>> 
>> Dear Michele or others,
>> 
>> In your paper (arXiv:1407.0872)'s abstract you mentioned the MPS code can handle 2D system. Is it as simple as setting the 'LATTICE' parameter to "open square lattice", or do I need to build a custom 1D lattice with long-range coupling?
>> 
>> I tried setting 'LATTICE' to "open square lattice" but the results seems different from my ED result. The system is spinful fermionic. Could it be due to fermion signs not properly taken care of internally?
>> 
>> Ultimately I need to simulate a small 3D system (3x3x3). Can I use the internal cubic lattice or do I need to build a custom 1D lattice with long-range coupling?
>> 
>> 
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