Line Calculations¶
This module contains the functions and data / result containers for calculating the Wilson loop / Wannier charge centers on a line in \(\mathbf{k}\)space.

class
z2pack.line.
EigenstateLineData
(*args, **kwargs)[source]¶ Data container for a line constructed from periodic eigenstates \(u_{n, \mathbf{k}} \rangle\). This has all attributes that
OverlapLineData
has, and the following additional ones:eigenstates
: The eigenstates of the Hamiltonian, given as a list of arrays which contain the eigenstates as row vectors.

class
z2pack.line.
LineResult
(data, stateful_ctrl, convergence_ctrl)[source]¶ Container for the data, state and convergence status of a line calculation. The attributes / properties of the data object (
WccLineData
orEigenstateLineData
) can be accessed directly from theLineResult
object.
property
convergence_report
¶ Convergence report (as a dict) for the result. The keys of the dictionary indicate the type of convergence test, and the values are booleans which are
True
if the test converged.

property

class
z2pack.line.
OverlapLineData
(*args, **kwargs)[source]¶ Data container for Line Data constructred from overlap matrices. This has all attributes that
WccLineData
has, and the following additional ones:overlaps
: A list containing the overlap matrix for each step of kpoints, as numpy array.wilson
: An array containing the Wilson loop (product of overlap matrices) for the line. The Wilson loop is given in the basis of the eigenstates at the start / end of the line.wilson_eigenstates
: Eigenstates of the Wilson loop, given as a list of 1D  arrays.

class
z2pack.line.
WccLineData
(*args, **kwargs)[source]¶ Data container for a line constructed directly from the WCC. The following attributes and properties can be accessed:
wcc
: A list of Wannier charge centers.pol
: The total polarization (sum of WCC) along the line.gap_pos
: The position of the largest gap between any two WCC.gap_size
: The size of the largest gap between any two WCC.
Note
The WCC are given in reduced coordinates, which means the possible values range from 0 to 1. The same is true for all values derived from the WCC.

z2pack.line.
run
(*, system, line, pos_tol=0.01, iterator=range(8, 27, 2), save_file=None, init_result=None, load=False, load_quiet=True, serializer='auto')¶ Calculates the Wannier charge centers for a given system and line, automatically converging w.r.t. the number of kpoints along the line.
 Parameters
system (
z2pack.system.EigenstateSystem
orz2pack.system.OverlapSystem
.) – System for which the WCC should be calculated.line – Line along which the WCC should be calculated. The argument should be a callable which parametrizes the line \(\mathbf{k}(t)\), in reduced coordinates. It should take one argument (
float
) and return a list offloat
describing the point in kspace. Note that the line must be closed, that is \(\mathbf{k}(0) = \mathbf{k}(1) + \mathbf{G}\), where \(\mathbf{G}\) is an inverse lattice vector.pos_tol (float) – The maximum movement of a WCC for the iteration w.r.t. the number of kpoints in a single string to converge. The iteration can be turned off by setting
pos_tol=None
.iterator – Generator for the number of points in a kpoint string. The iterator should also take care of the maximum number of iterations. It is needed even when
pos_tol=None
, to provide a starting value.save_file (str) – Path to a file where the result should be stored.
init_result (
LineResult
) – Initial result which is loaded at the start of the calculation.load (bool) – Determines whether the initial result is loaded from
save_file
.load_quiet (bool) – Determines whether errors / inexistent files are ignored when loading from
save_file
serializer (module) – Serializer which is used to save the result to file. Valid options are
msgpack
,json
andpickle
. By default (serializer='auto'
), the serializer is inferred from the file ending. If this fails,msgpack
is used.
 Returns
LineResult
instance.
Example usage:
system = ... # Refer to the various ways of creating a System instance. result = z2pack.line.run( system=system, line=lambda t: [t, 0, 0] # Line along kx for ky, kz = 0. ) print(result.wcc) # Prints the list of WCC.