[ALPS-users] measuring truncation errors in mps_optim

[Robertson Esperanza]

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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