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<p>Dear Ivo,</p>
<p><br>
</p>
<p><span style="font-size:12pt">You mentioned that hr eigenvalues always lie between the lowest and </span><span style="font-size:12pt">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.</span></p>
<p><span style="font-size:12pt"><br>
</span></p>
<p>Thanks!</p>
<p><br>
</p>
<p>Chong Wang</p>
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<div id="x_divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>From:</b> Ivo Souza <ivo_souza@ehu.eus><br>
<b>Sent:</b> Friday, February 17, 2017 12:33:52 AM<br>
<b>To:</b> Chong Wang<br>
<b>Cc:</b> wannier@quantum-espresso.org<br>
<b>Subject:</b> Re: [Wannier] Is it possible to have extra states in frozen window?</font>
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<div class="PlainText">Dear Cheong,<br>
<br>
On Thu, 16 Feb 2017, Chong Wang wrote:<br>
<br>
> Hi Mostofi,<br>
><br>
> Thanks for the reply.<br>
><br>
> If I understand the original papers correctly, although all the states<br>
> included in the frozen energy window are automatically included in the<br>
> disentangled subspace, other states are chosen to minimize \Omega_i.<br>
> These states are mixture of states out of frozen window and thus I<br>
> think it is possible that somehow after diagonalization of hr these<br>
> states enter frozen window unexpectedly.<br>
<br>
I suspect that for the block of the hr matrix corresponding to states<br>
that are linear combinations of eigenstates lying outside the frozen<br>
window, the hr eigenvalues will always lie between the lowest and<br>
highest eigenvalues of those ab initio states, and therefore also lie<br>
outside the frozen window.<br>
<br>
(Strictly speaking this is only guaranteed for points k belonging to the<br>
ab initio mesh used in the wannierization. But for a sufficiently smooth<br>
interpolation it should also be the case at generic interpolation<br>
points.)<br>
<br>
Best,<br>
<br>
Ivo<br>
<br>
><br>
><br>
> I guess you think these states should never appear in the frozen window. Do you have a good reason for that?<br>
><br>
><br>
> Best!<br>
><br>
><br>
> Chong Wang<br>
><br>
> ________________________________<br>
> From: Wannier <wannier-bounces@quantum-espresso.org> on behalf of Mostofi, Arash <a.mostofi@imperial.ac.uk><br>
> Sent: Thursday, February 16, 2017 8:30:00 PM<br>
> To: wannier@quantum-espresso.org<br>
> Subject: Re: [Wannier] Is it possible to have extra states in frozen window?<br>
><br>
> Dear Chong Wang,<br>
><br>
> 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.<br>
><br>
> 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.<br>
><br>
> Hope this helps,<br>
><br>
> Arash<br>
><br>
> —<br>
> Arash Mostofi — <a href="http://www.mostofigroup.org<http://www.mostofigroup.org">
www.mostofigroup.org<http://www.mostofigroup.org</a>><br>
> Director, CDT in Theory and Simulation of Materials<br>
> Imperial College London<br>
><br>
><br>
><br>
> On 16 Feb 2017, at 03:00, Chong Wang <ch-wang@outlook.com<mailto:ch-wang@outlook.com>> wrote:<br>
><br>
> Hi everyone,<br>
><br>
> 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?<br>
><br>
> Best!<br>
><br>
> Chong Wang<br>
> Institute for Advanced Study, Tsinghua Univeristy<br>
> _______________________________________________<br>
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