[ALPS-users] measuring truncation errors in mps_optim

[Michele Dolfi]

All evaluation scripts of that paper are available in the supplemental
material at 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> 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>
> wrote:
>
>> We have some example in our paper at https://doi.org/10.1103/Phy
>> sRevB.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>
>> 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>
>> 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> 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>
>>> 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> 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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>>>
>>>
>>> <sample_result.rtf>
>>>
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