[ALPS-users] measuring truncation errors in mps_optim

Thu Dec 7 04:46:30 CET 2017

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>
wrote:

> 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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