Different DMRG results between Version 3 and Version 2?

Question

Hello Matt,

I found that the DMRG results in ITensor v3 and v2 are different. Maybe this is not an issue because the difference is decreasing during the sweeps. But if the initial state and the iterative process are the same, the numbers should be the same for all sweeps. What changes in Version 3 compared to Version 2? Or what do I missed? Thanks.

Jin

Answer 1

Hi Jin, it could be a number of things but most likely it’s some recent changes to the truncation logic used in the SVD (or density matrix diagonalization) part of DMRG.

Is the energy decreasing slower than before, and if so by a significant amount? If it’s decreasing faster than this is actually a good thing and would be evidence that the changes we made were a success.

Best regards,
Miles

Comments

Hi Miles, thanks for the reply. I did some tests using the sample code for 2D Hamiltonian with Lx = 8, Ly = 3, nsweeps = 50. It is found that

1. With large bond dimension or small cutoff, the energy decreasing rate is almost the same for both versions.

2. When the maximal bond dimension is arbitrarily large and the cutoff is the main accuracy parameter, version2 always converges to a smaller value than version3 does. The final energy difference is more than 100 times bigger than the cutoff. Version2 is better in this case.

3. When the cutoff is arbitrarily small and the maximal bond dimension is the main accuracy parameter,  the final energy difference is the order of or smaller than the smallest cutoff in the final sweep. Two versions have the same accuracy in this case.

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From the sound of it only case 2 sounds like it’s not ideal. Could you please post some sample sweep parameters so we can try to reproduce? Thanks!

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Hi Miles,

I used the following sweep parameters.

    auto sweeps = Sweeps(50);
    sweeps.maxdim() = 10,20,100,100,200,200,300,300,400,400,500,500,600;
    sweeps.cutoff() = 1E-4;
    sweeps.niter() = 2;
    sweeps.noise() = 1E-7,1E-8,0.0;
For cutoff = [1e-4, 1e-5, 1e-6, 1e-7, 1e-8, 1e-9, 1e-10], Ev3 = [-11.592512491595, -11.644549496655, -11.648325909394, -11.648603685809, -11.648630715598, -11.648633432203, -11.648633725977], Ev2 = [-11.637580459566, -11.647706401323, -11.648540555337, -11.648624067026, -11.648632913158, -11.648633665882, -11.648633742644].

The log-log-plot of Ev3-Ev2 v.s. cutoff is a straight line, linear fit gives log10(Ev3-Ev2) = 1.06 log10(cutoff) + 2.78.

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Aha, I see the most recent version give the same results as version2. Thanks.

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Glad to hear it! Thanks for following up -