[ALPS-users] measuring truncation errors in mps_optim

Matthias Troyer troyer at phys.ethz.ch
Thu Dec 7 05:30:36 CET 2017 

Hi,

No, that will not help. While you may be able to compensate too few SWEEPS with a larger number of STATES, once the simulation is converged with large enough SWEEPS the truncation error will depend on MAXSTATES

Matthias


> On 6 Dec 2017, at 19:46, Robertson Esperanza <robbie.esperanza at gmail.com> wrote:
> 
> Hello,
> 
> For a single DMRG simulation in mps_optim, how does the truncation error scale (roughly) with MAXSTATES and SWEEPS? For example, for the same set of Hamiltonian parameters, if I decrease the MAXSTATES but increase SWEEPS, would that increase in SWEEPS be able to "compensate" the decrease in MAXSTATES, such that i would get almost similar truncation errors for both simulations?
> 
> Regards,
> Robertson C. Esperanza
> 
> 
> On Thu, Jul 13, 2017 at 7:34 PM, Michele Dolfi <michele.dolfi at gmail.com <mailto:michele.dolfi at gmail.com>> wrote:
> All evaluation scripts of that paper are available in the supplemental material at http://dx.doi.org/10.5281/zenodo.31003 <http://dx.doi.org/10.5281/zenodo.31003>.
> Section III.C explains how the data is extrapolated for energy measurements or other observables. For the local density and correlations we used a second order polynomial, some of the extrapolations are shown in the panels in Fig. 6.
> 
> 
> Michele
> 
> 
> On Thu, Jul 13, 2017 at 11:37 AM, Robertson Esperanza <robbie.esperanza at gmail.com <mailto:robbie.esperanza at gmail.com>> wrote:
> I have seen that you have extrapolated to obtain quantities as M approaches infinity. I would like to know the extrapolation method used (especially in Figures 3 and 4).
> 
> Regards,
> Robertson Esperanza
> 
> On Sun, Mar 26, 2017 at 8:33 PM, Michele Dolfi <dolfim at phys.ethz.ch <mailto:dolfim at phys.ethz.ch>> wrote:
> We have some example in our paper at https://doi.org/10.1103/PhysRevB.92.195139 <https://doi.org/10.1103/PhysRevB.92.195139>.
> 
> Basically you should always extrapolate in the bond dimension.
> 
> 
> Best,
> Michele
> 
> 
>> On 26 Mar 2017, at 11:36, Robertson Esperanza <robbie.esperanza at gmail.com <mailto:robbie.esperanza at gmail.com>> wrote:
>> 
>> Now it makes sense, thank you for the clarification. You said earlier that I should address the convergence in the bond dimension separately, how is it done?
>> 
>> On Sun, Mar 26, 2017 at 3:50 PM, Michele Dolfi <dolfim at phys.ethz.ch <mailto:dolfim at phys.ethz.ch>> wrote:
>> I suppose you are just printing the values of the first sweep, then the math is as follow:
>> 
>> N=96*2-1 (number of bonds that gets optimized)
>> since one sweep is left-to-right and right-to-left: 2*N=382
>> 
>> 
>> 
>>> On 26 Mar 2017, at 01:45, Robertson Esperanza <robbie.esperanza at gmail.com <mailto:robbie.esperanza at gmail.com>> wrote:
>>> 
>>> To clarify, here is a text file showing an iteration ('iteration': 0) showing 'observable': 'TruncatedWeight':
>>> 
>>> from here, it shows 382 values for that observable. I'm wondering why there are 382 truncation error values.
>>> 
>>> On Sun, Mar 26, 2017 at 12:50 AM, Michele Dolfi <dolfim at phys.ethz.ch <mailto:dolfim at phys.ethz.ch>> wrote:
>>> First note that this refers only to convergence of a single simulation. One should then address the convergence in the bond dimension separately.
>>> 
>>> I would say that there is no exact rule for convergence, but I will give you some example of what we usually check.
>>> - Convergence of energy.
>>> - Truncation error. This is the sum of all discarded eigenvalues in the reduced density matrix.
>>> - Any other observable of interest, for example the local density is good indicator, because sometime you fall in a state which is not symmetric and you are pretty sure that something wrong happened.
>>> For this values the iteration values we store one number per optimization, i.e. one sweep are 2*N with N the system size.
>>> 
>>> It is a bit arbitrary how to aggregate the truncation errors. It should just be clear outlined in the publications, so that readers know what you are talking about. Usually you either sum them of take the maximum value.
>>> 
>>> 
>>> Regards,
>>> Michele
>>> 
>>> 
>>> > On 24 Mar 2017, at 22:24, Robertson Esperanza <robbie.esperanza at gmail.com <mailto:robbie.esperanza at gmail.com>> wrote:
>>> >
>>> > Thank you for all the help so far, now I'm trying to check for convergence of my results.
>>> >
>>> > First, is it enough to just check how the truncation error changes with sweeps (at a certain MAXSTATE value) or I need to both check the iteration history of the ground state energy and the truncation error?
>>> >
>>> > Second, checking the supplementary materials provided (Computer Physics Communications 185 (2014) 3430–3440) for the Hubbard ladder, why are there 381 values of energy and truncation weights for every iteration? Why is the total truncation error for that iteration is the sum of all the 381 truncation weight values (based on iteration.py)? How is truncation error defined (e.g. is it 1 - sum of all reduced density eigenvalues corresponding to all the picked states?) ?
>>> >
>>> >  As far as I understand the DMRG algorithm every iteration/sweep has a corresponding bond dimension in which as you progress through iterations (until you reach the "SWEEPS"th iteration), bond dimension increases until you reach "MAXSTATES" at the "SWEEPS"th iteration.
>>> >
>>> > Regards,
>>> > Robertson Esperanza
>>> >
>>> >
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