Overview of KITE
KITE is a userfriendly open source software suite for simulating 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 tightbinding models of arbitrary complexity as an input that can be promptly defined by the user through its versatile Python 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), response functions (linear and nonlinear conductivities) or even dynamical effects arising from the timeevolution of electronic wavepackets. KITE’s scope is not limited to periodic systems but, instead, its true power in unveiled through the study of more realistic lattice models, which may include randomly distributed dilute impurities, structural defects, adatoms, mechanical strain and external magnetic fields. Some illustrative examples may be found in KITE’s presentation paper^{2}. See the Tutorial section for a quickstart guide.
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 tensor (using the KuboGreenwood formula);
 First and secondorder optical (AC) Conductivities;
 Spin Dynamics by timeevolution of gaussian wavepackets.
These calculations can now be applied to arbitrary two and threedimensional tightbinding models 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 (University of York, UK) 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 that enabled for the first time the efficient evaluation of zerotemperature DC conductivity of huge tightbinding systems (containing billions of atomic orbitals) entirely in real space. At that time, this method proved essential to numerically demonstrate that zeroenergy modes in graphene with dilute vacancy defects enjoy from a finite (nonzero) conductivity in the large system limit, thereby overcoming Anderson localization ^{3}.
In the following years, the usefulness of the above method in generic disordered lattices^{5} has been extended to studies of the linear conductivity tensor at finite temperature/frequency^{6} ^{7} (proposed by L. Covaci and T. G. Rappoport in collaboration with José H. García (ICN2)) 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 prerelease of KITE in 2018 and its official release in 2020 ^{2}.
From its inception, KITE was built to handle realspace models of realistic complexity and sizes. Thereby, its architecture allies a versatile and userfriendly \(\texttt{python}\) interface, with a highly efficient \(\texttt{C++}\) 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, and strain. The model hamiltonian is then passed to the \(\texttt{C++}\) code (\(\texttt{KITEx}\)) that implements a matrixfree Chebyshev iteration combining 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 has allowed the spectral calculations to be carried out for unheardof huge system sizes ^{10} ^{11}, by exploiting 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, A.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). ↩

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

Highresolution realspace evaluation of the selfenergy operator of disordered lattices: Gade singularity, spin–orbit effects and pwave superconductivity, S. M. João, J. M. Viana Parente Lopes, and A. Ferreira, J. Phys. Mater. 5 045002 (2022). ↩

Anomalous Transport Signatures in Weyl Semimetals with Point Defects, J. P. Santos Pires, S. M. João, A. Ferreira, B. Amorim, and J. M. Viana Parente Lopes, Phys. Rev. Lett. 129, 196601 (2022). ↩