Construction of maximally localized Wannier functions

doi:10.1007/s11467-016-0628-8

Front. Phys.

2017, Vol. 12

Issue (5) : 127102 https://doi.org/10.1007/s11467-016-0628-8

RESEARCH ARTICLE

Construction of maximally localized Wannier functions

Junbo Zhu (竺俊博)¹,Zhu Chen (陈竹)²,Biao Wu (吴飙)^1,^3,^4,⁵(

)

¹. International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
². Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
³. Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
⁴. Wilczek Quantum Center, College of Science, Zhejiang University of Technology, Hangzhou 310014, China
⁵. Synergetic Innovation Center for Quantum Effects and Applications (SICQEA), Hunan Normal University, Changsha 410081, China

Download: PDF(874 KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

We present a general method for constructing maximally localized Wannier functions. It consists of three steps: (i) picking a localized trial wave function, (ii) performing a full band projection, and (iii) orthonormalizing with the Löwdin method. Our method is capable of producing maximally localized Wannier functions without further minimization, and it can be applied straightforwardly to random potentials without using supercells. The effectiveness of our method is demonstrated for both simple bands and composite bands.

Keywords Wannier function random potential cold atomic gases

Corresponding Author(s): Biao Wu (吴飙)

Issue Date: 25 November 2016

Cite this article:

Junbo Zhu (竺俊博),Zhu Chen (陈竹),Biao Wu (吴飙). Construction of maximally localized Wannier functions[J]. Front. Phys. , 2017, 12(5): 127102.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-016-0628-8
https://academic.hep.com.cn/fop/EN/Y2017/V12/I5/127102

1	G. H. Wannier, The structure of electronic excitation levels in insulating crystals, Phys. Rev. 52, 191 (1937) https://doi.org/10.1103/PhysRev.52.191
2	R. Resta, Macroscopic polarization in crystalline dielectrics: The geometric phase approach, Rev. Mod. Phys. 66, 899 (1994) https://doi.org/10.1103/RevModPhys.66.899
3	R. D. King-Smith and D. Vanderbilt, Theory of polarization of crystalline solids, Phys. Rev. B 47, 1651 (1993) https://doi.org/10.1103/PhysRevB.47.1651
4	S. Goedecker, Linear scaling electronic structure methods, Rev. Mod. Phys. 71, 1085 (1999) https://doi.org/10.1103/RevModPhys.71.1085
5	G. Galli, Linear scaling methods for electronic structure calculations and quantum molecular dynamics simulations, Current Opinion in Solid State and Materials Science 1(6), 864 (1996) https://doi.org/10.1016/S1359-0286(96)80114-8
6	D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Cold bosonic atoms in optical lattices, Phys. Rev. Lett. 81, 3108 (1998) https://doi.org/10.1103/PhysRevLett.81.3108
7	M. White, M. Pasienski, D. McKay, S. Q. Zhou, D. Ceperley, and B. DeMarco, Strongly interacting bosons in a disordered optical lattice, Phys. Rev. Lett. 102, 055301 (2009) https://doi.org/10.1103/PhysRevLett.102.055301
8	S. Q. Zhou and D. M. Ceperley, Construction of localized wave functions for a disordered optical lattice and analysis of the resulting Hubbard model parameters, Phys. Rev. A 81, 013402 (2010) https://doi.org/10.1103/PhysRevA.81.013402
9	N. Marzari and D. Vanderbilt, Maximally localized generalized Wannier functions for composite energy bands, Phys. Rev. B 56, 12847 (1997) https://doi.org/10.1103/PhysRevB.56.12847
10	W. Kohn, Analytic properties of Bloch waves and Wannier functions, Phys. Rev. 115, 809 (1959) https://doi.org/10.1103/PhysRev.115.809
11	H. Teichler, Best Localized Symmetry-Adapted Wannier Functions of the Diamond Structure, Phys. Status Solidi B 43, 307 (1971) https://doi.org/10.1002/pssb.2220430132
12	N. Marzari, A. A. Mostofi, J. R. Yates, I. Souza, and D. Vanderbilt, Maximally localized Wannier functions: Theory and applications, Rev. Mod. Phys. 84, 1419 (2012) https://doi.org/10.1103/RevModPhys.84.1419
13	H. D. Cornean, I. Herbst, and G. Nenciu, On the construction of composite Wannier functions, arXiv: 1506.07435 (2015)
14	J. I. Mustafa, S. Coh, M. L. Cohen, and S. G. Louie, Automated construction of maximally localized Wannier functions: Optimized projection functions method, Phys. Rev. B 92, 165134 (2015), arXiv: 1508.04148 (2015)
15	E. Cancès, A. Levitt, G. Panati, and G. Stoltz, Robust determination of maximally-localized Wannier functions, arXiv: 1605.07201 (2016)
16	P. O. Löwdin, On the non-orthogonality problem connected with the use of atomic wave functions in the theory of molecules and crystals, J. Chem. Phys. 18, 365 (1950) https://doi.org/10.1063/1.1747632
17	W. Kohn, Construction of Wannier functions and applications to energy bands, Phys. Rev. B 7, 4388 (1973) https://doi.org/10.1103/PhysRevB.7.4388
18	J. G. Aiken, J. A. Erdos, and J. A. Goldstein, You have full text access to this content On Löwdin orthogonalization, Int. J. Quantum Chem. 18, 1101 (1980) https://doi.org/10.1002/qua.560180416
19	A. Nenciu and G. Nenciu, Existence of exponentially localized Wannier functions for nonperiodic systems, Phys. Rev. B 47, 10112 (1993) https://doi.org/10.1103/PhysRevB.47.10112
20	W. Kohn and J. R. Onffroy, Wannier functions in a simple nonperiodic system, Phys. Rev. B 8, 2485 (1973) https://doi.org/10.1103/PhysRevB.8.2485
21	S. Kivelson, Wannier functions in one-dimensional disordered systems: Application to fractionally charged solitons, Phys. Rev. B 26, 4269 (1982) https://doi.org/10.1103/PhysRevB.26.4269
22	J. Zhu, Z. Chen, and B. Wu, Construction of Wannier functions in disordered systems, arXiv: 1512.02043 (2015)

[1]	Yong Xu. Topological gapless matters in three-dimensional ultracold atomic gases[J]. Front. Phys. , 2019, 14(4): 43402-.
[2]	Haiping LIN (林海平), Janosch M. C. RAUBA, Kristian S. THYGESEN, Karsten W. JACOBSEN, Michelle Y. SIMMONS, Werner A. HOFER. First-principles modelling of scanning tunneling microscopy using non-equilibrium Green’s functions[J]. Front Phys Chin, 2010, 5(4): 369-379.

Viewed

Full text

Abstract

Cited

Shared

Discussed