Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of Wannier functions from localized atomic-like orbitals   The problem of construction of the Wannier functions (WFs) in a restricted
Hilbert space of eigenstates of the one-electron Hamiltonian $\hat{H}$ (forming
the so-called low-energy part of the spectrum) can be formulated in several
different ways. One possibility is to use the projector-operator techniques,
which pick up a set of trial atomic orbitals and project them onto the given
Hilbert space. Another possibility is to employ the downfolding method, which
eliminates the high-energy part of the spectrum and incorporates all related to
it properties into the energy-dependence of an effective Hamiltonian. We show
that by modifying the high-energy part of the spectrum of the original
Hamiltonian $\hat{H}$, which is rather irrelevant to the construction of WFs in
the low-energy part of the spectrum, these two methods can be formulated in an
absolutely exact and identical form, so that the main difference between them
is reduced to the choice of the trial orbitals. Concerning the latter part of
the problem, we argue that an optimal choice for trial orbitals can be based on
the maximization of the site-diagonal part of the density matrix. The main idea
is illustrated for a simple toy model, consisting of only two bands, as well as
for a more realistic example of $t_{2g}$ bands in V$_2$O$_3$. An analogy with
the search of the ground state of a many-electron system is also discussed.

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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: cs
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin