Publications

Order by: publication date number of citations

• Comparative analysis of tight-binding models for transition metal dichalcogenides

  Bert Jorissen, Lucian Covaci, Bart Partoens

  SciPost Phys. Core 7, 004 (2024) · published 6 February 2024 | Toggle abstract · pdf

  We provide a comprehensive analysis of the prominent tight-binding (TB) models for transition metal dichalcogenides (TMDs) available in the literature. We inspect the construction of these TB models, discuss their parameterization used and conduct a thorough comparison of their effectiveness in capturing important electronic properties. Based on these insights, we propose a novel TB model for TMDs designed for enhanced computational efficiency. Utilizing $MoS_2$ as a representative case, we explain why specific models offer a more accurate description. Our primary aim is to assist researchers in choosing the most appropriate TB model for their calculations on TMDs.

  1 citation

• DFT2kp: Effective kp models from ab-initio data

  João Victor V. Cassiano, Augusto de Lelis Araújo, Paulo E. Faria Junior, Gerson J. Ferreira

  SciPost Phys. Codebases 25 (2024) · published 5 February 2024 | Toggle abstract · pdf

  The $k\cdot p$ method, combined with group theory, is an efficient approach to obtain the low energy effective Hamiltonians of crystalline materials. Although the Hamiltonian coefficients are written as matrix elements of the generalized momentum operator $\pi= p+ p_{SOC}$ (including spin-orbit coupling corrections), their numerical values must be determined from outside sources, such as experiments or ab initio methods. Here, we develop a code to explicitly calculate the Kane (linear in crystal momentum) and Luttinger (quadratic in crystal momentum) parameters of $k\cdot p$ effective Hamiltonians directly from ab initio wavefunctions provided by Quantum ESPRESSO. Additionally, the code analyzes the symmetry transformations of the wavefunctions to optimize the final Hamiltonian. This is an optional step in the code, where it numerically finds the unitary transformation $U$ that rotates the basis towards an optimal symmetry-adapted representation informed by the user. Throughout the paper, we present the methodology in detail and illustrate the capabilities of the code applying it to a selection of relevant materials. Particularly, we show a "hands-on" example of how to run the code for graphene (with and without spin-orbit coupling). The code is open source and available at https://gitlab.com/dft2kp/dft2kp.

  1 citation

• Codebase release 0.0 for DFT2kp

  João Victor V. Cassiano, Augusto de Lelis Araújo, Paulo E. Faria Junior, Gerson J. Ferreira

  SciPost Phys. Codebases 25-r0.0 (2024) · published 5 February 2024 | Toggle abstract · src

  The $k\cdot p$ method, combined with group theory, is an efficient approach to obtain the low energy effective Hamiltonians of crystalline materials. Although the Hamiltonian coefficients are written as matrix elements of the generalized momentum operator $\pi= p+ p_{SOC}$ (including spin-orbit coupling corrections), their numerical values must be determined from outside sources, such as experiments or ab initio methods. Here, we develop a code to explicitly calculate the Kane (linear in crystal momentum) and Luttinger (quadratic in crystal momentum) parameters of $k\cdot p$ effective Hamiltonians directly from ab initio wavefunctions provided by Quantum ESPRESSO. Additionally, the code analyzes the symmetry transformations of the wavefunctions to optimize the final Hamiltonian. This is an optional step in the code, where it numerically finds the unitary transformation $U$ that rotates the basis towards an optimal symmetry-adapted representation informed by the user. Throughout the paper, we present the methodology in detail and illustrate the capabilities of the code applying it to a selection of relevant materials. Particularly, we show a "hands-on" example of how to run the code for graphene (with and without spin-orbit coupling). The code is open source and available at https://gitlab.com/dft2kp/dft2kp.

  1 citation

• Codebase release 0.1 for MatsubaraFunctions.jl

  Dominik Kiese, Anxiang Ge, Nepomuk Ritz, Jan von Delft, Nils Wentzell

  SciPost Phys. Codebases 24-r0.1 (2024) · published 11 January 2024 | Toggle abstract · src

  The Matsubara Green's function formalism stands as a powerful technique for computing the thermodynamic characteristics of interacting quantum many-particle systems at finite temperatures. In this manuscript, our focus centers on introducing MatsubaraFunctions.jl, a Julia library that implements data structures for generalized n-point Green's functions on Matsubara frequency grids. The package's architecture prioritizes user-friendliness without compromising the development of efficient solvers for quantum field theories in equilibrium. Following a comprehensive introduction of the fundamental types, we delve into a thorough examination of key facets of the interface. This encompasses avenues for accessing Green's functions, techniques for extrapolation and interpolation, as well as the incorporation of symmetries and a variety of parallelization strategies. Examples of increasing complexity serve to demonstrate the practical utility of the library, supplemented by discussions on strategies for sidestepping impediments to optimal performance.

  1 citation

• MatsubaraFunctions.jl: An equilibrium Green's function library in the Julia programming language

  Dominik Kiese, Anxiang Ge, Nepomuk Ritz, Jan von Delft, Nils Wentzell

  SciPost Phys. Codebases 24 (2024) · published 11 January 2024 | Toggle abstract · pdf

  The Matsubara Green's function formalism stands as a powerful technique for computing the thermodynamic characteristics of interacting quantum many-particle systems at finite temperatures. In this manuscript, our focus centers on introducing MatsubaraFunctions.jl, a Julia library that implements data structures for generalized n-point Green's functions on Matsubara frequency grids. The package's architecture prioritizes user-friendliness without compromising the development of efficient solvers for quantum field theories in equilibrium. Following a comprehensive introduction of the fundamental types, we delve into a thorough examination of key facets of the interface. This encompasses avenues for accessing Green's functions, techniques for extrapolation and interpolation, as well as the incorporation of symmetries and a variety of parallelization strategies. Examples of increasing complexity serve to demonstrate the practical utility of the library, supplemented by discussions on strategies for sidestepping impediments to optimal performance.

  1 citation

• Neural network quantum states analysis of the Shastry-Sutherland model

  Matěj Mezera, Jana Menšíková, Pavel Baláž, Martin Žonda

  SciPost Phys. Core 6, 088 (2023) · published 22 December 2023 | Toggle abstract · pdf

  We utilize neural network quantum states (NQS) to investigate the ground state properties of the Heisenberg model on a Shastry-Sutherland lattice using the variational Monte Carlo method. We show that already relatively simple NQSs can be used to approximate the ground state of this model in its different phases and regimes. We first compare several types of NQSs with each other on small lattices and benchmark their variational energies against the exact diagonalization results. We argue that when precision, generality, and computational costs are taken into account, a good choice for addressing larger systems is a shallow restricted Boltzmann machine NQS. We then show that such NQS can describe the main phases of the model in zero magnetic field. Moreover, NQS based on a restricted Boltzmann machine correctly describes the intriguing plateaus forming in magnetization of the model as a function of increasing magnetic field.

• Pyqcm: An open-source Python library for quantum cluster methods

  Théo N. Dionne, Alexandre Foley, Moïse Rousseau, David Sénéchal

  SciPost Phys. Codebases 23 (2023) · published 20 December 2023 | Toggle abstract · pdf

  Pyqcm is a Python/C++ library that implements a few quantum cluster methods with an exact diagonalization impurity solver. Quantum cluster methods are used in the study of strongly correlated electrons to provide an approximate solution to Hubbard-like models. The methods covered by this library are Cluster Perturbation Theory (CPT), the Variational Cluster Approach (VCA) and Cellular (or Cluster) Dynamical Mean Field Theory (CDMFT). The impurity solver (the technique used to compute the cluster's interacting Green function) is exact diagonalization from sparse matrices, using the Lanczos algorithm and variants thereof. The core library is written in C++ for performance, but the interface is in Python, for ease of use and inter-operability with the numerical Python ecosystem. The library is distributed under the GPL license.

  1 citation

• Codebase release 2.2 for Pyqcm

  Théo N. Dionne, Alexandre Foley, Moïse Rousseau, David Sénéchal

  SciPost Phys. Codebases 23-r2.2 (2023) · published 20 December 2023 | Toggle abstract · src

  Pyqcm is a Python/C++ library that implements a few quantum cluster methods with an exact diagonalization impurity solver. Quantum cluster methods are used in the study of strongly correlated electrons to provide an approximate solution to Hubbard-like models. The methods covered by this library are Cluster Perturbation Theory (CPT), the Variational Cluster Approach (VCA) and Cellular (or Cluster) Dynamical Mean Field Theory (CDMFT). The impurity solver (the technique used to compute the cluster's interacting Green function) is exact diagonalization from sparse matrices, using the Lanczos algorithm and variants thereof. The core library is written in C++ for performance, but the interface is in Python, for ease of use and inter-operability with the numerical Python ecosystem. The library is distributed under the GPL license.

  1 citation

• Reconstructing the potential configuration in a high-mobility semiconductor heterostructure with scanning gate microscopy

  Gaëtan J. Percebois, Antonio Lacerda-Santos, Boris Brun, Benoit Hackens, Xavier Waintal, Dietmar Weinmann

  SciPost Phys. 15, 242 (2023) · published 15 December 2023 | Toggle abstract · pdf

  The weak disorder potential seen by the electrons of a two-dimensional electron gas in high-mobility semiconductor heterostructures leads to fluctuations in the physical properties and can be an issue for nanodevices. In this paper, we show that a scanning gate microscopy (SGM) image contains information about the disorder potential, and that a machine learning approach based on SGM data can be used to determine the disorder. We reconstruct the electric potential of a sample from its experimental SGM data and validate the result through an estimate of its accuracy.

• Non-parametric learning critical behavior in Ising partition functions: PCA entropy and intrinsic dimension

  Rajat K. Panda, Roberto Verdel, Alex Rodriguez, Hanlin Sun, Ginestra Bianconi, Marcello Dalmonte

  SciPost Phys. Core 6, 086 (2023) · published 14 December 2023 | Toggle abstract · pdf

  We provide and critically analyze a framework to learn critical behavior in classical partition functions through the application of non-parametric methods to data sets of thermal configurations. We illustrate our approach in phase transitions in 2D and 3D Ising models. First, we extend previous studies on the intrinsic dimension of 2D partition function data sets, by exploring the effect of volume in 3D Ising data. We find that as opposed to 2D systems for which this quantity has been successfully used in unsupervised characterizations of critical phenomena, in the 3D case its estimation is far more challenging. To circumvent this limitation, we then use the principal component analysis (PCA) entropy, a "Shannon entropy" of the normalized spectrum of the covariance matrix. We find a striking qualitative similarity to the thermodynamic entropy, which the PCA entropy approaches asymptotically. The latter allows us to extract-through a conventional finite-size scaling analysis with modest lattice sizes-the critical temperature with less than 1% error for both 2D and 3D models while being computationally efficient. The PCA entropy can readily be applied to characterize correlations and critical phenomena in a huge variety of many-body problems and suggests a (direct) link between easy-to-compute quantities and entropies.