# Overview of KITE

KITE is a user-friendly open source software suite for simulating electronic structure and quantum transport properties of large-scale molecular and condensed systems with up to tens of billions of atomic orbitals ($$N\sim 10^{10}$$). In a nutshell, KITE takes real-space tight-binding models of arbitrary complexity as an input that can be promptly defined by the user through its versatile Python interface. Then, its memory-efficient and heavily-parallelised C++ code employs extremely accurate Chebyshev spectral expansions1 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 time-evolution of electronic wave-packets. 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, ad-atoms, mechanical strain and external magnetic fields. Some illustrative examples may be found in KITE’s presentation paper2. See the Tutorial section for a quick-start 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 Kubo-Greenwood formula);
• First and second-order optical (AC) Conductivities;
• Spin Dynamics by time-evolution of gaussian wave-packets.

These calculations can now be applied to arbitrary two- and three-dimensional tight-binding models that have:

• Generic multi-orbital local (on-site) and bond disorder;
• User-defined 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 large-RAM "single-shot" recursive algorithm that enabled for the first time the efficient evaluation of zero-temperature DC conductivity of huge tight-binding systems (containing billions of atomic orbitals) entirely in real space. At that time, this method proved essential to numerically demonstrate that zero-energy modes in graphene with dilute vacancy defects enjoy from a finite (non-zero) conductivity in the large system limit, thereby overcoming Anderson localization 3.

In the following years, the usefulness of the above method in generic disordered lattices5 has been extended to studies of the linear conductivity tensor at finite temperature/frequency6 7 (proposed by L. Covaci and T. G. Rappoport in collaboration with José H. García (ICN2)) and the non-linear optical response (proposed by S. M. João and J. M. Viana Parente Lopes8). It was the conjunction of all these proposals that put forward the joint venture that led to the pre-release of KITE in 2018 and its official release in 2020 2.

From its inception, KITE was built to handle real-space models of realistic complexity and sizes. Thereby, its architecture allies a versatile and user-friendly $$\texttt{python}$$ 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 syntax9 that allows the user to input an arbitrary (2D or 3D) lattice model decorated with a myriad of non-periodic perturbations, such as on-site disorder, personalized structural defects, and strain. The model hamiltonian is then passed to the $$\texttt{C++}$$ code ($$\texttt{KITEx}$$) that implements a matrix-free Chebyshev iteration combining a domain-decomposition of the lattice with a "tile-by-tile" matrix-vector multiplication strategy in order to minimize memory-transfer overheads and thus boost parallelization and calculational efficiency2. Such an approach has allowed the spectral calculations to be carried out for unheard-of huge system sizes 10 11, by exploiting modern large-RAM multi-core computers. Finally, a convenient post-processing tool ($$\texttt{KITE-tools}$$), developed by S. M. João, was also included in the package thereby turning KITE into a ready-to-use tool for practical applications.

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

2. KITE: high-performance 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)

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

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

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

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

7. Numerical calculation of the Casimir-Polder 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)

8. Basis-independent spectral methods for non-linear optical response in arbitrary tight-binding models, S. M. João and J. M. Viana Parente Lopes, J. Phys.: Condens. Mat. 32 (12), 125901 (2019)

9. Pybinding V0.9.4: a python package for tight-binding calculations, D. Moldovan, M. Anđelković, and F. M. Peeters, Zenodo (2017)

10. High-resolution real-space evaluation of the self-energy operator of disordered lattices: Gade singularity, spin–orbit effects and p-wave superconductivity, S. M. João, J. M. Viana Parente Lopes, and A. Ferreira, J. Phys. Mater. 5 045002 (2022)

11. 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)