LINVARIANT

LINVARIANT is a first-principles-based model effective Hamiltonian software package for the atomistic simulations of realistic materials. The goals are to reach large scales and keep being predictive.

INVARIANT is a property of a mathematical object (or a class of mathematical objects) that remains unchanged after operations or transformations of a certain type are applied to the objects.

L is to memorize famous physicist Lev Davidovich Landau (22 January 1908 – 1 April 1968). 

• LINVARIANT takes care of multi-physics systems such as lattice, electron, spin, and their interactions.

• LINVARIANT is capable of generating both microscopic and phenomenological models.

• LINVARIANT learns/analysis the symmetry of the interaction forms and generates their DFT training accordingly.

• LINVARIANT solves the models with many numerical solvers, such as MC, MD, Exact diagonalization, Minimization, etc.

• For large-scale calculations, LINVARIANT exports FORTRAN code from symbolic models.

Features:

models:

• Lattice models for structural phase transitions, such as Landau-Ginzburg-Devonshire models.

• Magnetic models for (non-)collinear spins, such as the extended Heisenberg model.

• Electronic models, such as the Tight-Binding model written in Wannier orbitals.

• Full models with couplings among lattice, orbitals, and spins.

• Models in zero-, one-, two, and three-dimension.

solvers:

• (1) Finite Element Method (FEM), (2) Minimization, (3) molecular dynamics (MD), (4) Monte Carlo (MC), and (5) Finite Differences nonlinear solver on the large-scale continuous model

• Parallel tempering algorithm is available with both MC and MD

fitting:

• Basis (ionic): phonon/irreducible representation/atomistic basis

• Basis (electronic): pseudo-atomic/Wannier basis

• searching crystal structures by machine learning of the energy invariants

• walking around (sampling) the potential energy surface by machine learning the symmetry of the energetic coupling terms.

auxiliary:

• Write Fortran (numerical) using mathematica (symbolic)

• interface to VASP, Quantum Espresso, and OpenMX

• interface to WANNIER90

• mpi and openmp parallelization

• dynamics under external electric field

• Jij of Heisenberg model from DFT by Liechtenstein formalism

• Fij (force constants) from tight-binding models (atomistic Green's function method)

• Electron/phonon bands unfolding

• phonon/magnon calculations from DFT input

• X ray diffraction simulation

• Nudged Elastic Bands (NEB) and Growing String Method (GSM) to explore the phase transition, dynamics, and domain wall structures

• Mollwide projection

examples:

• Boracite, Perovskite (To be added: Spinel, Rutile, Pyrochlore)

Todo:

• implement the k dot p model builder

• adding transport property calculations

• including electron-phonon coupling (EPC) beyond first-order w.r.t. phonons.

Publications used LINVARIANT:

• Deterministic control of ferroelectric polarization by ultrafast laser pulses, Nat. Commun. 13, 2566 (2022)

• Microscopic origin of the electric Dzyaloshinskii-Moriya interaction, Phys. Rev. B 106, 224101 (2022).

• Dzyaloshinskii-Moriya-like interaction in ferroelectrics and anti-ferroelectrics, Nat. Mater. 20, 341 (2021)

• Domain wall-localized phonons in BiFeO3: spectrum and selection rules, npj Comput. Mater. 6, 48 (2020)

• Improper ferroelectricities in 134-type AA’3B4O12 perovskites, Phys. Rev. B 101, 214441 (2020).