Implementation of Stengel-Spaldin Functional in Wannierization

[sjhong6230]

The main differences for this pull request are shown below.

• Implemented the Stengel-Spaldin functional [1] in Wannierization.

• Added use_ss_functional parameter. Uses Stengel-Spaldin functional if true, and Marzari-Vanderbilt for false.

• Changed some arrays to allocatable in disentangle.f90 and kmesh.f90 for the many k-points computation. (If not, a stack overflow occurs.) (Since this is for personal local tests, it is unnecessary.)

Since the functional sums over k-points before b-vector summation, I needed to order the b-vector information before Wannierization. This sorting is implemented in the kmesh_sort subroutine in kmesh.f90, and only used for wannier90.x (not postw90.x).

The main changes are in wannierise.f90 file. wann_phases, wann_omega, and wann_domega subroutines are changed. guiding_centres=T case is also considered.

Documentations, tests, and tutorials are added by slightly modifying the silicon tutorial. Also, test data are modified for restart and bvec tests.

Since this is my first pull request in Wannier90, there might be many errors and mistakes. Please feel free to comment.

[1] https://journals.aps.org/prb/abstract/10.1103/PhysRevB.73.075121

[sjhong6230]

Results of personal local tests

• bands.pdf : Comparison of interpolated bands for Marzari-Vanderbilt and Stengel-Spaldin functionals

• convergence.pdf : Convergence tests for Marzari-Vanderbilt and Stengel-Spaldin functionals

• supercell.pdf : Size-consistency tests. Only Stengel-Spaldin functional is size-consistent.

[sjhong6230]

TODO after this PR is merged.

• Changing the order of Fourier transform and WS distance method for implementation of translation invariant formulas.

• Implementation of translation invariant formulas for all operators in get_oper.f90

[sjhong6230]

Note: The default value of use_ss_functional is false.