Welcome to LSQuant, a novel initiative dedicated to the promotion, dissemination and developments of large-scale quantum transport methodologies. These methods, elaborated and optimized during the two decades, have proven to be key enabling simulation tools, not only to unveil complex transport phenomena in quantum materials but also guiding experimental and industrial research by supporting the interpretation of measured data or suggesting new directions for improvement of given technologies in nanoelectronics, spintronic, flexible and organic electronics and thermal management. To take these methods to the next level, it has become essential to engage new users and developers and associate a broader community to support and implement efficient versions of these codes to either explore new emerging scientific horizons in quantum physics, or solve concrete real-life high technology problems. LSQuant is designed to tackle such challenges and accelerate the promotion and the development of user-friendly algorithms and user interfaces, the training of new generations of users, and to provide more widespread access of such computational tools for the sake of societal progress.

Supremacy of Linear Scaling quantum Transport schemes

Predictive computational modelling is a fundamental tool for studying electronic, optical, and thermal properties in complex forms of disordered condensed like nanostructures, organic composes, topological materials, etc. Linear scaling (or order-N) numerical methods are possibly the best solutions for studying quantum transport in realistic models of disordered matter given that they allow for simulating system size containing billions of atoms. Such methods enable for instance computing the charge mobility of disordered polycrystalline graphene samples of a 1 micron squared in one week, whereas "alternative algorithms" involving matrix inversion or diagonalization of a gigantic matrix would require a billion years!

We first refer the interested readers to study the recent review published in Physics Reports, where we have technically described and compared various alternative order-N computational methods which have been used extensively to explore quantum transport phenomena in disordered media. In this review article, focus is made on the zero-frequency electrical conductivities derived within the Kubo-Greenwood and Kubo-Streda formalisms, and illustrations of the capabilities of these methods to tackle the quasi-ballistic, diffusive, and localization regimes of quantum transport in the non-interacting limit are provided. The fundamental issue of computational cost versus accuracy of various proposed numerical schemes is addressed in depth. Afterwards, the usefulness of these methods is illustrated with various examples of transport in disordered materials, such as polycrystalline and defected graphene models, 3D metals and Dirac semimetals, carbon nanotubes, and organic semiconductors. Finally, we extend the review to the study of spin dynamics and topological transport, for which efficient approaches for calculating charge, spin, and valley Hall conductivities are described.

This review paper contains the essentials technical aspects of our current methodology and is thus a first document to read and study for interested researchers.

This website will provide an open platform for current and future users to exchange about most recent developments concerning linear scaling quantum transport methods and their applications and will launch activities and partnerships to engage students, researchers and engineers.

Sections of LSQuant under development will include short tutorials, open source codes and sections opened to partnerships

- General recursive methods & KPM
- Time-evolution of quantum states for arbitrary Hamiltonians
- Kubo-Greenwood (σxx)
- Kubo-Bastin Conductivity (σxy)
Spin transport physics (Spin dynamics, spin Hall effects, Spin –Orbit torques)
Landauer Büttiker & link to Kwant using KPM
- Molecular dynamics and quantum transport with vibrational disorder
- Time-evolution of Many-body quantum states
- Quantum dynamics with Non Hermitian Hamiltonians
- High-throughput quantum transport calculations using LSQUANT workflow
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