Publications

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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 | · 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.

2 citations
xSPDE3: Extensible software for stochastic ordinary and partial differential equations

Simon Kiesewetter, Ria R. Joseph, Peter D. Drummond

SciPost Phys. Codebases 17 (2023) · published 2 October 2023 | · pdf

The xSPDE toolbox treats stochastic partial and ordinary differential equations, with applications in biology, chemistry, engineering, medicine, physics and quantum technologies. It computes statistical averages, including time-step and/or sampling error estimation. xSPDE can provide higher order convergence, Fourier spectra and probability densities. The toolbox has graphical output and $\chi^{2}$ statistics, as well as weighted, projected, or forward-backward equations. It can generate input-output quantum spectra. All equations may have independent periodic, Dirichlet, and Neumann or Robin boundary conditions in any dimension, for any vector field component, and at either end of any interval.

2 citations
SOLAX: A Python solver for fermionic quantum systems with neural network support

Louis Thirion, Philipp Hansmann, Pavlo Bilous

SciPost Phys. Codebases 51 (2025) · published 20 February 2025 | · pdf

Numerical modeling of fermionic many-body quantum systems presents similar challenges across various research domains, necessitating universal tools, including state-of-the-art machine learning techniques. Here, we introduce SOLAX, a Python library designed to compute and analyze fermionic quantum systems using the formalism of second quantization. SOLAX provides a modular framework for constructing and manipulating basis sets, quantum states, and operators, facilitating the simulation of electronic structures and determining many-body quantum states in finite-size Hilbert spaces. The library integrates machine learning capabilities to mitigate the exponential growth of Hilbert space dimensions in large quantum clusters. The core low-level functionalities are implemented using the recently developed Python library JAX. Demonstrated through its application to the Single Impurity Anderson Model, SOLAX offers a flexible and powerful tool for researchers addressing the challenges of many-body quantum systems across a broad spectrum of fields, including atomic physics, quantum chemistry, and condensed matter physics.

2 citations
Codebase release 4.0 for QSpace

Andreas Weichselbaum

SciPost Phys. Codebases 40-r4.0 (2024) · published 14 November 2024 | · src

This is the documentation for the tensor library QSpace (v4.0) that provides a toolbox to exploit 'quantum symmetry spaces' in tensor network states in the quantum many-body context. QSpace permits arbitrary combinations of symmetries including the Abelian symmetries $\mathbb{Z}_n$ and $U(1)$ , as well as all non-Abelian symmetries represented by the simple classical Lie algebras: $A_n$ , $B_n$ , $C_n$ , and $D_n$ , or respectively, the special unitary group SU( $n$ ), the odd orthogonal group SO( $2n+1$ ), the symplectic group Sp( $2n$ ), and the even orthogonal group SO( $2n$ ). The code (C++ embedded via the MEX interface into Matlab) is available (https://bitbucket.org/qspace4u) under the Apache 2.0 license. QSpace is designed as a bottom-up approach for non-Abelian symmetries. It starts from the defining representation and the respective Lie algebra. By explicitly computing and tabulating generalized Clebsch-Gordan coefficient tensors, QSpace is versatile in its operations across all symmetries. At the level of an application, much of the symmetry-related details are hidden within the QSpace C++ core libraries. Hence when developing tensor network algorithms with QSpace, these can be coded (nearly) as if there are no symmetries at all, despite being able to fully exploit general non-Abelian symmetries.

2 citations
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 | · 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.

2 citations
Consistent, multidimensional differential histogramming and summary statistics with YODA 2

Andy Buckley, Louie Corpe, Matthew Filipovich, Christian Gutschow, Nick Rozinsky, Simon Thor, Yoran Yeh, Jamie Yellen

SciPost Phys. Codebases 45 (2025) · published 16 January 2025 | · pdf

Histogramming is often taken for granted, but the power and compactness of partially aggregated, multidimensional summary statistics, and their fundamental connection to differential and integral calculus make them formidable statistical objects, especially when very large data volumes are involved. But expressing these concepts robustly and efficiently in high-dimensional parameter spaces and for large data samples is a highly non-trivial challenge – doubly so if the resulting library is to remain usable by scientists as opposed to software engineers. In this paper we summarise the core principles required for consistent generalised histogramming, and use them to motivate the design principles and implementation mechanics of the re-engineered YODA histogramming library, a key component of physics data–model comparison and statistical interpretation in collider physics.

2 citations
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 | · 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.

2 citations
Codebase release 1.0 for Worm Algorithm for Bose-Hubbard and XXZ Models

Nicolas Sadoune, Lode Pollet

SciPost Phys. Codebases 9-r1.0 (2022) · published 29 November 2022 | · src

We present a novel and open-source implementation of the worm algorithm, which is an algorithm to simulate Bose-Hubbard and sign-positive spin models using a path-integral representation of the partition function. The code can deal with arbitrary lattice structures and assumes spin-exchange terms, or bosonic hopping amplitudes, between nearest-neighbor sites, and local or nearest-neighbor interactions of the density-density type. We explicitly demonstrate the near-linear scaling of the algorithm with respect to the system volume and the inverse temperature and analyze the autocorrelation times in the vicinity of a $U(1)$ second order phase transition. The code is written in such a way that extensions to other lattice models as well as closely-related sign-positive models can be done straightforwardly on top of the provided framework.

2 citations
QArray: A GPU-accelerated constant capacitance model simulator for large quantum dot arrays

Barnaby van Straaten, Joseph Hickie, Lucas Schorling, Jonas Schuff, Federico Fedele, Natalia Ares

SciPost Phys. Codebases 35 (2024) · published 21 October 2024 | · pdf

Semiconductor quantum dot arrays are a leading architecture for the development of quantum technologies. Over the years, the constant capacitance model has served as a fundamental framework for simulating, understanding, and navigating the charge stability diagrams of small quantum dot arrays. However, while the size of the arrays keeps growing, solving the constant capacitance model becomes computationally prohibitive. This paper presents an open-source software package able to compute a $100 × 100$ pixels charge stability diagram of a 16-dot array in less than a second. Smaller arrays can be simulated in milliseconds - faster than they could be measured experimentally, enabling the creation of diverse datasets for training machine learning models and the creation of digital twins that can interface with quantum dot devices in real-time. Our software package implements its core functionalities in the systems programming language Rust and the high-performance numerical computing library JAX. The Rust implementation benefits from advanced optimisations and parallelisation, enabling the users to take full advantage of multi-core processors. The JAX implementation allows for GPU acceleration.

2 citations
kdotpy: k·p theory on a lattice for simulating semiconductor band structures

Wouter Beugeling, Florian Bayer, Christian Berger, Jan Böttcher, Leonid Bovkun, Christopher Fuchs, Maximilian Hofer, Saquib Shamim, Moritz Siebert, Li-Xian Wang, Ewelina M. Hankiewicz, Tobias Kießling, Hartmut Buhmann, Laurens W. Molenkamp

SciPost Phys. Codebases 47 (2025) · published 28 January 2025 | · pdf

The software project kdotpy provides a Python application for simulating electronic band structures of semiconductor devices with k·p theory on a lattice. The application implements the widely used Kane model, capable of reliable predictions of transport and optical properties for a large variety of topological and non-topological materials with a zincblende crystal structure. The application automates the tedious steps of simulating band structures. The user inputs the relevant physical parameters on the command line, for example materials and dimensions of the device, magnetic field, and temperature. The program constructs the appropriate matrix Hamiltonian on a discretized lattice of spatial coordinates and diagonalizes it. The physical observables are extracted from the eigenvalues and eigenvectors and saved as output. The program is highly customizable with a large set of configuration options and material parameters.

2 citations

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