publication . Article . Preprint . Other literature type . 2018

Variational formulation for Wannier functions with entangled band structure

Damle, Anil; Levitt, Antoine; Lin, Lin;
Open Access
  • Published: 30 Jan 2018 Journal: Multiscale Modeling & Simulation, volume 17, pages 167-191 (issn: 1540-3459, eissn: 1540-3467, Copyright policy)
  • Publisher: Society for Industrial & Applied Mathematics (SIAM)
  • Country: France
Abstract
Comment: 26 pages, 10 figures
Subjects
free text keywords: Ecological Modelling, Modelling and Simulation, General Physics and Astronomy, General Chemistry, Computer Science Applications, Physics - Computational Physics, Mathematics - Numerical Analysis, Physics - Chemical Physics, 65Z05, 82D25, 65F30, 65K10, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA], [PHYS.PHYS.PHYS-CHEM-PH]Physics [physics]/Physics [physics]/Chemical Physics [physics.chem-ph]
40 references, page 1 of 3

[1] P-A. Absil, R. Mahony, and R. Sepulchre, Optimization algorithms on matrix manifolds, Princeton University Press, 2009.

[2] J. Bezanson, A. Edelman, S. Karpinski, and V.B. S., Julia: A fresh approach to numerical computing, SIAM Review, 59 (2017), pp. 65{98.

[3] E. I. Blount, Formalisms of band theory, Solid State Phys., 13 (1962), pp. 305{373.

[4] D. R. Bowler and T. Miyazaki, O(N) methods in electronic structure calculations, Rep. Prog. Phys., 75 (2012), p. 036503.

[5] C. Brouder, G. Panati, M. Calandra, C. Mourougane, and N. Marzari, Exponential localization of Wannier functions in insulators, Phys. Rev. Lett., 98 (2007), p. 046402. [OpenAIRE]

[6] E. Cances, A. Levitt, G. Panati, and G. Stoltz, Robust determination of maximallylocalized Wannier functions, Phys. Rev. B, 95 (2017), p. 075114. [OpenAIRE]

[7] H. Cornean, D. Gontier, A. Levitt, and D. Monaco, Localised wannier functions in metallic systems. in preparation, 2017.

[8] A. Damle and L. Lin, Disentanglement via entanglement: A uni ed method for wannier localization, arXiv:1703.06958, (2017). [OpenAIRE]

[9] A. Damle, L. Lin, and L. Ying, Compressed representation of Kohn{Sham orbitals via selected columns of the density matrix, J. Chem. Theory Comput., 11 (2015), pp. 1463{1469.

[10] Anil Damle, Lin Lin, and Lexing Ying, Scdm-k: Localized orbitals for solids via selected columns of the density matrix, J. Comput. Phys., 334 (2017), pp. 1 { 15.

[11] M. Dauge, Elliptic boundary value problems on corner domains: smoothness and asymptotics of solutions, vol. 1341, Springer, 2006. [OpenAIRE]

[12] W. E, T. Li, and J. Lu, Localized bases of eigensubspaces and operator compression, Proc. Natl. Acad. Sci., 107 (2010), pp. 1273{1278.

[13] A. Edelman, T.A. Arias, and S.T. Smith, The geometry of algorithms with orthogonality constraints, SIAM journal on Matrix Analysis and Applications, 20 (1998), pp. 303{353.

[14] J. M. Foster and S. F. Boys, Canonical con gurational interaction procedure, Rev. Mod. Phys., 32 (1960), p. 300.

[15] Paolo Giannozzi, Stefano Baroni, Nicola Bonini, Matteo Calandra, Roberto Car, Carlo Cavazzoni, Davide Ceresoli, Guido L Chiarotti, Matteo Cococcioni, Ismaila Dabo, Andrea Dal Corso, Stefano de Gironcoli, Stefano Fabris, Guido Fratesi, Ralph Gebauer, Uwe Gerstmann, Christos Gougoussis, Anton Kokalj, Michele Lazzeri, Layla Martin-Samos, Nicola Marzari, Francesco Mauri, Riccardo Mazzarello, Stefano Paolini, Alfredo Pasquarello, Lorenzo Paulatto, Carlo Sbraccia, Sandro Scandolo, Gabriele Sclauzero, Ari P Seitsonen, Alexander Smogunov, Paolo Umari, and Renata M Wentzcovitch, QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter, 21 (2009), pp. 395502{395520.

40 references, page 1 of 3
Abstract
Comment: 26 pages, 10 figures
Subjects
free text keywords: Ecological Modelling, Modelling and Simulation, General Physics and Astronomy, General Chemistry, Computer Science Applications, Physics - Computational Physics, Mathematics - Numerical Analysis, Physics - Chemical Physics, 65Z05, 82D25, 65F30, 65K10, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA], [PHYS.PHYS.PHYS-CHEM-PH]Physics [physics]/Physics [physics]/Chemical Physics [physics.chem-ph]
40 references, page 1 of 3

[1] P-A. Absil, R. Mahony, and R. Sepulchre, Optimization algorithms on matrix manifolds, Princeton University Press, 2009.

[2] J. Bezanson, A. Edelman, S. Karpinski, and V.B. S., Julia: A fresh approach to numerical computing, SIAM Review, 59 (2017), pp. 65{98.

[3] E. I. Blount, Formalisms of band theory, Solid State Phys., 13 (1962), pp. 305{373.

[4] D. R. Bowler and T. Miyazaki, O(N) methods in electronic structure calculations, Rep. Prog. Phys., 75 (2012), p. 036503.

[5] C. Brouder, G. Panati, M. Calandra, C. Mourougane, and N. Marzari, Exponential localization of Wannier functions in insulators, Phys. Rev. Lett., 98 (2007), p. 046402. [OpenAIRE]

[6] E. Cances, A. Levitt, G. Panati, and G. Stoltz, Robust determination of maximallylocalized Wannier functions, Phys. Rev. B, 95 (2017), p. 075114. [OpenAIRE]

[7] H. Cornean, D. Gontier, A. Levitt, and D. Monaco, Localised wannier functions in metallic systems. in preparation, 2017.

[8] A. Damle and L. Lin, Disentanglement via entanglement: A uni ed method for wannier localization, arXiv:1703.06958, (2017). [OpenAIRE]

[9] A. Damle, L. Lin, and L. Ying, Compressed representation of Kohn{Sham orbitals via selected columns of the density matrix, J. Chem. Theory Comput., 11 (2015), pp. 1463{1469.

[10] Anil Damle, Lin Lin, and Lexing Ying, Scdm-k: Localized orbitals for solids via selected columns of the density matrix, J. Comput. Phys., 334 (2017), pp. 1 { 15.

[11] M. Dauge, Elliptic boundary value problems on corner domains: smoothness and asymptotics of solutions, vol. 1341, Springer, 2006. [OpenAIRE]

[12] W. E, T. Li, and J. Lu, Localized bases of eigensubspaces and operator compression, Proc. Natl. Acad. Sci., 107 (2010), pp. 1273{1278.

[13] A. Edelman, T.A. Arias, and S.T. Smith, The geometry of algorithms with orthogonality constraints, SIAM journal on Matrix Analysis and Applications, 20 (1998), pp. 303{353.

[14] J. M. Foster and S. F. Boys, Canonical con gurational interaction procedure, Rev. Mod. Phys., 32 (1960), p. 300.

[15] Paolo Giannozzi, Stefano Baroni, Nicola Bonini, Matteo Calandra, Roberto Car, Carlo Cavazzoni, Davide Ceresoli, Guido L Chiarotti, Matteo Cococcioni, Ismaila Dabo, Andrea Dal Corso, Stefano de Gironcoli, Stefano Fabris, Guido Fratesi, Ralph Gebauer, Uwe Gerstmann, Christos Gougoussis, Anton Kokalj, Michele Lazzeri, Layla Martin-Samos, Nicola Marzari, Francesco Mauri, Riccardo Mazzarello, Stefano Paolini, Alfredo Pasquarello, Lorenzo Paulatto, Carlo Sbraccia, Sandro Scandolo, Gabriele Sclauzero, Ari P Seitsonen, Alexander Smogunov, Paolo Umari, and Renata M Wentzcovitch, QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter, 21 (2009), pp. 395502{395520.

40 references, page 1 of 3
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