[ALPS-users] measuring truncation errors in mps_optim

[Robertson Esperanza]

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/
> 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>
> 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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