MagneticTB

A Mathematica program package MagneticTB, which can generate the tight-binding model for arbitrary magnetic space group. The only input parameters in MagneticTB are the (magnetic) space group number and the orbital information in each Wyckoff positions. Some useful functions including getting the matrix expression for symmetry operators, manipulating the energy band structure by parameters and interfacing with other software are also developed.

Installation

Unzip the "MagneticTB-main.zip" file and copy the MagneticTB directory to any of the following four paths:

• FileNameJoin[{$UserBaseDirectory, "Applications"}]
• FileNameJoin[{$BaseDirectory, "Applications"}]
• FileNameJoin[{$InstallationDirectory, "AddOns", "Packages"}]
• FileNameJoin[{$InstallationDirectory, "AddOns", "Applications"}]

Then one can use the package after running Needs["MagneticTB`"]. The version of Mathematica should higher or equal to 11.0.

Capabilities of MagneticTB

• Construct the tight-binding model for arbitrary magnetic space group
• Get the matrix expression for symmetry operators
• Interface with other software
• Manipulate the energy band structure by parameters
• Calculate the band co-representations of tight-binding model

See Comput. Phys. Commun. 270, 108153 (2022) (arXiv:2012.08871) for detail (please cite this paper if you use our code for your research).

Examples

See Examples.

Release Notes

v1.00b

• Add a new example for Charge-4 Weyl point in double magnetic space group PRB 105, 104426 (2022)(arXiv:2112.10479).

v1.00c

• Add Chinese manual.
• Fix a bug for displaying the lattice vector of monoclinic lattice.

v1.01 2022/07/22

• Fixed an issue where in very rare cases the order of basis functions would change due to the automatic unitarization.

v1.02 2022/12/1

• MagneticTB now has the capability to calculate the band co-representations of a tight-binding model!

  • Before using this capability, SpaceGroupIrep and MSGCorep package needed to be installed.

  • Add two functions getMSGElemFromMSGCorep and getTBBandCorep, both two funcitons are depending on the MSGCorep package.

  • getMSGElemFromMSGCorep[{N1, N2}] gives the magnetic space group element from MSGCorep package, where N1.N2 is the BNS magnetic space group number.

  • getTBBandCorep[BNSNo, Hamiltonian, paramaters, kset], give the co-representations of tight-binding model, where BNSNo is the BNS magnetic space group number, Hamiltonian is the Hamiltonian generated by MagneticTB, parameters is the parameter in the tight-binding model, kset is the list contains several k points.

  • For Orthorhombic and Monoclinic lattices, if you want to calculate the co-representations of tight-binding model please use getMSGElemFromMSGCorep to get the magnetic space group elements rather than msgop. For other lattices both msgop and getMSGElemFromMSGCorep should OK.

  • See Examples/Co-representationOfTBModel.nb for concrete example.

  • Please also consider to cite MSGCorep package (arXiv:2211.10740) if you are using this capability.

v1.02b 2023/2/14

• Add an example for getting the TB parameters by hand, see Examples/ObtainTheTBParametersByHand.nb.
• Add English manual.

v.1.03 2023/2/17

• Using a greedy algorithm to automatically find the generators of a space group, significantly improves computational efficiency.