Overview of KITE
KITE is a general purpose opensource tightbinding software for accurate realspace simulations of electronic structure and quantum transport properties of largescale molecular and condensed systems with up to tens of billions of atomic orbitals (\(N\sim 10^{10}\)). In a nutshell, KITE takes realspace lattice models (tightbinding hamiltonians) of arbitrary complexity as an input that can be promptly defined by the user through its versatile Pybinding interface. Then, its memoryefficient and heavilyparallelised C++ code employs extremely accurate Chebyshev spectral expansions^{1} in order to extract static electronic properties (DoS, LDoS and spectral functions), perturbative response functions (linear and nonlinear conductivities) or even dynamical effects arising from the timeevolution of electronic wavepackets entirely in realspace. Since it is based upon realspace hamiltonians, KITE’s scope is not limited to periodic singleparticle hamiltonians but, instead, its true power in unveiled through the study of more realistic models which may include disordered potentials, dilute impurities, structural defects, adatoms, mechanical strain and even external magnetic fields. Some illustrative examples may be found in the KITE’s presentation paper^{2}. See the Tutorial section for a quickstart guide to the main features of KITE v1.1.
KITE's latest release (version 1.1) contains the following functionalities:
 Average density of states (DOS) and local DOS;
 \(\mathbf{k}\)space Spectral Functions and ARPES Response;
 Linear DC conductivity (using the KuboGreenwood formula);
 First and SecondOrder Optical (AC) Conductivities;
 SpinRelaxation by TimeEvolution of Gaussian Wavepackets.
These calculations can now be applied to arbitrary two and threedimensional tightbinding hamiltonians that have:
 Generic multiorbital local (onsite) and bond disorder;
 Userdefined local potential profile and structural disorder;
 Different boundary conditions (periodic, open and twisted);
 Applied perpendicular magnetic field (limited use in 3D);
For more details about the current release refer to the documentation section.
A Short Background Story¶
The seeds for KITE’s project were laid in 2014, when an exact spectral expansion of the broadened lattice Green's function was discovered by Aires Ferreira in collaboration with Eduardo R. Mucciolo (University of Central Florida)^{3} and, independently, by A. Braun and P. Schmitteckert (Karlsruhe Institute of Technology)^{4}. Aires Ferreira then developed a largeRAM "singleshot" recursive algorithm (with the technical assistance of M. D. Costa, National University of Singapore) that enabled the efficient evaluation of zerotemperature DC conductivity of huge tightbinding systems (more than 10 billion orbitals) entirely in realspace. At that time, this method proved essential to numerically show that the DC conductivity of graphene indeed attains finite value in the presence of dilute vacancies^{3}.
In the following years, the usefulness of the above method in generic disordered lattices[5] with small coordination number \([Z=O(1)]\) became ever more clear by the development of similar techniques to evaluate generic response functions, most notably the linear conductivity tensor at finite temperature/frequency (proposed by L. Covaci and T. G. Rappoport in collaboration with José H. García (ICN2)^{6} ^{7}) and the nonlinear optical response (proposed by S. M. João and J. M. Viana Parente Lopes^{8}). It was the conjunction of all these proposals that put forward the joint venture that led to the first release of KITE in 2018^{2}.
From its beginnings, KITE was sought to handle realspace lattice models of arbitrary complexity and realistically large sizes. Thereby, its architecture allies a versatile and userfriendly \(\texttt{python}\) interface, with a highly efficient and CPUscalable \(\texttt{C++}\) code (developed by J. M. Viana Parente Lopes) that handles the heavy spectral computations. The interface is based on Pybinding’s syntax^{9} that allows the user to input an arbitrary (2D or 3D) lattice model decorated with a myriad of nonperiodic perturbations, such as onsite disorder, personalized structural defects, strain, etc... This model hamiltonian is then passed to the \(\texttt{C++}\) highperformance code (\(\texttt{KITEx}\)) that implements a matrixfree Chebyshev iteration which combines a domaindecomposition of the lattice with a "tilebytile" matrixvector multiplication strategy in order to minimize memorytransfer overheads and thus boost parallelization and calculational efficiency^{2}. Such an approach allows the spectral calculations to be carried out for unheardof huge system sizes, particularly by using modern largeRAM multicore computers. Finally, a convenient postprocessing tool (\(\texttt{KITEtools}\)), developed by S. M. João, was also included in the package thereby turning KITE into a readytouse tool for practical applications.

Kernel polynomial method, A. Weiße, G. Wellein, A. Alvermann and H. Fehske, Rev. Mod. Phys. 78, 275 (2016). ↩

KITE: highperformance accurate modelling of electronic structure and response functions of large molecules, disordered crystals and heterostructures, S. M. João, M. Anđelković, L. Covaci, T. G. Rappoport, João M. Viana Parente Lopes, and A. Ferreira, R. Soc. open sci. 7, 191809 (2020). ↩↩↩

Critical delocalization of chiral zero energy modes in graphene, A. Ferreira and E. Mucciolo, Phys. Rev. Lett. 115, 106601 (2015). ↩↩

Numerical evaluation of Green's functions based on the Chebyshev expansion, A. Braun and P. Schmitteckert, Phys. Rev. B 90, 165112 (2014). ↩

Efficient multiscale lattice simulations of strained and disordered graphene, N. Leconte, A. Ferreira, and J. Jung. Semiconductors and Semimetals 95, 35 (2016). ↩

RealSpace Calculation of the Conductivity Tensor for Disordered Topological Matter, J. H. García, L. Covaci, and T. G. Rappoport, Phys. Rev. Lett. 114, 116602 (2015). ↩

Numerical calculation of the CasimirPolder interaction between a graphene sheet with vacancies and an atom, T. P. Cysne, T. G. Rappoport, Aires Ferreira, J. M. Viana Parente Lopes, and N. M. R. Peres, Phys. Rev. B 94, 235405 (2016) ↩

Basisindependent spectral methods for nonlinear optical response in arbitrary tightbinding models, S. M. João and J. M. Viana Parente Lopes, J. Phys.: Condens. Mat. 32 (12), 125901 (2019) ↩

D. Moldovan, M. Anđelković, F. M. Peeters, Pybinding V0.9.4: a python package for tightbinding calculations Zenodo (2017) ↩