01478nas a2200169   4500008004100000022001400041245008500055210006900140260000800209300001200217490000700229520096100236100002301197700002101220700002101241856004601262       2016                        eng d  a1424-066100aConstruction of Real-Valued Localized Composite Wannier Functions for Insulators0 aConstruction of RealValued Localized Composite Wannier Functions  cJan  a63–970 v173 a<p>We consider a real periodic Schrödinger operator and a physically relevant family of $m \geq 1$ Bloch bands, separated by a gap from the rest of the spectrum, and we investigate the localization properties of the corresponding composite Wannier functions. To this aim, we show that in dimension $d\leq 3$, there exists a global frame consisting of smooth quasi-Bloch functions which are both periodic and time-reversal symmetric. Aiming to applications in computational physics, we provide a constructive algorithm to obtain such a Bloch frame. The construction yields the existence of a basis of composite Wannier functions which are real-valued and almost-exponentially localized. The proof of the main result exploits only the fundamental symmetries of the projector on the relevant bands, allowing applications, beyond the model specified above, to a broad range of gapped periodic quantum systems with a time-reversal symmetry of bosonic type.</p>1 aFiorenza, Domenico1 aMonaco, Domenico1 aPanati, Gianluca  uhttps://doi.org/10.1007/s00023-015-0400-6