[Wannier] Is it possible to have extra states in frozen window?

[Chong Wang]

Dear Ivo,


You mentioned that hr eigenvalues always lie between the lowest and highest eigenvalues of the mixed ab initio states. But if the states above frozen window and states below frozen window are mixed in disentanglement, then I guess the eigenvalue could end up in frozen window.


Thanks!


Chong Wang

________________________________
From: Ivo Souza <ivo_souza at ehu.eus>
Sent: Friday, February 17, 2017 12:33:52 AM
To: Chong Wang
Cc: wannier at quantum-espresso.org
Subject: Re: [Wannier] Is it possible to have extra states in frozen window?

Dear Cheong,

On Thu, 16 Feb 2017, Chong Wang wrote:

> Hi Mostofi,
>
> Thanks for the reply.
>
> If I understand the original papers correctly, although all the states
> included in the frozen energy window are automatically included in the
> disentangled subspace, other states are chosen to minimize \Omega_i.
> These states are mixture of states out of frozen window and thus I
> think it is possible that somehow after diagonalization of hr these
> states enter frozen window unexpectedly.

I suspect that for the block of the hr matrix corresponding to states
that are linear combinations of eigenstates lying outside the frozen
window, the hr eigenvalues will always lie between the lowest and
highest eigenvalues of those ab initio states, and therefore also lie
outside the frozen window.

(Strictly speaking this is only guaranteed for points k belonging to the
ab initio mesh used in the wannierization. But for a sufficiently smooth
interpolation it should also be the case at generic interpolation
points.)

  Best,

  Ivo

>
>
> I guess you think these states should never appear in the frozen window. Do you have a good reason for that?
>
>
> Best!
>
>
> Chong Wang
>
> ________________________________
> From: Wannier <wannier-bounces at quantum-espresso.org> on behalf of Mostofi, Arash <a.mostofi at imperial.ac.uk>
> Sent: Thursday, February 16, 2017 8:30:00 PM
> To: wannier at quantum-espresso.org
> Subject: Re: [Wannier] Is it possible to have extra states in frozen window?
>
> Dear Chong Wang,
>
> I’m not sure that I’ve fully understood your question but your first statement is correct: all the states included in the frozen energy window are automatically included in the disentangled subspace. At each k-point there should always be n_k .le. num_wann such states. The remaining (num_wann - n_k) states needed to complete the subspace at each k-point are disentangled from the states outside the frozen window. The wannier functions are then constructed out of the num_wann-dimensional subspace at each k-point. You would expect the Wannier-interpolated bandstructure to give a very good representation of the states in the frozen window.
>
> If  other interpolated bands are present that do not seem to correspond to bands in the original bandstructure, then you have to ask yourself the question of whether you have obtained a good WF representation for your problem, eg, one that accurately reproduces the bandstructure in a particular range of energy.
>
> Hope this helps,
>
> Arash
>
> —
> Arash Mostofi — www.mostofigroup.org<http://www.mostofigroup.org<http://www.mostofigroup.org<http://www.mostofigroup.org>>
> Director, CDT in Theory and Simulation of Materials
> Imperial College London
>
>
>
> On 16 Feb 2017, at 03:00, Chong Wang <ch-wang at outlook.com<mailto:ch-wang at outlook.com>> wrote:
>
> Hi everyone,
>
> In my opinion, when a frozen window is set, every states in that window is taken into account in the calculation. However, this does not forbid that some extra states would enter frozen window in disentanglement. Thus, if band structures in frozen window is well reproduced except for some extra bands, it can still be considered a good Wannier interpolation. Is this correct?
>
> Best!
>
> Chong Wang
> Institute for Advanced Study, Tsinghua Univeristy
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