[ALPS-users] measuring truncation errors in mps_optim

[Robertson Esperanza]

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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