Publications

Order by: publication date number of citations

• YASTN: Yet another symmetric tensor networks; A Python library for Abelian symmetric tensor network calculations

  Marek M. Rams, Gabriela Wójtowicz, Aritra Sinha, Juraj Hasik

  SciPost Phys. Codebases 52 (2025) · published 26 February 2025 | Toggle abstract · pdf

  We present an open-source tensor network Python library for quantum many-body simulations. At its core is an Abelian-symmetric tensor, implemented as a sparse block structure managed by a logical layer on top of a dense multidimensional array backend. This serves as the basis for higher-level tensor network algorithms operating on matrix product states and projected entangled pair states. An appropriate backend, such as PyTorch, gives direct access to automatic differentiation (AD) for cost-function gradient calculations and execution on GPU and other supported accelerators. We show the library performance in simulations with infinite projected entangled-pair states, such as finding the ground states with AD and simulating thermal states of the Hubbard model via imaginary time evolution. For these challenging examples, we identify and quantify sources of the numerical advantage exploited by the symmetric-tensor implementation.

  8 citations

• Codebase release 1.2 for YASTN

  Marek M. Rams, Gabriela Wójtowicz, Aritra Sinha, Juraj Hasik

  SciPost Phys. Codebases 52-r1.2 (2025) · published 26 February 2025 | Toggle abstract · src

  We present an open-source tensor network Python library for quantum many-body simulations. At its core is an Abelian-symmetric tensor, implemented as a sparse block structure managed by a logical layer on top of a dense multidimensional array backend. This serves as the basis for higher-level tensor network algorithms operating on matrix product states and projected entangled pair states. An appropriate backend, such as PyTorch, gives direct access to automatic differentiation (AD) for cost-function gradient calculations and execution on GPU and other supported accelerators. We show the library performance in simulations with infinite projected entangled-pair states, such as finding the ground states with AD and simulating thermal states of the Hubbard model via imaginary time evolution. For these challenging examples, we identify and quantify sources of the numerical advantage exploited by the symmetric-tensor implementation.

  4 citations

• Codebase release 1.0 for SOLAX

  Louis Thirion, Philipp Hansmann, Pavlo Bilous

  SciPost Phys. Codebases 51-r1.0 (2025) · published 20 February 2025 | Toggle abstract · src

  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.

  1 citation

• 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 | Toggle abstract · 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

• Pymablock: An algorithm and a package for quasi-degenerate perturbation theory

  Isidora Araya Day, Sebastian Miles, Hugo K. Kerstens, Daniel Varjas, Anton R. Akhmerov

  SciPost Phys. Codebases 50 (2025) · published 12 February 2025 | Toggle abstract · pdf

  A common technique in the study of complex quantum-mechanical systems is to reduce the number of degrees of freedom in the Hamiltonian by using quasi-degenerate perturbation theory. While the Schrieffer-Wolff transformation achieves this and constructs an effective Hamiltonian, its scaling is suboptimal, it is limited to two subspaces, and implementing it efficiently is both challenging and error-prone. We introduce an algorithm for constructing an equivalent effective Hamiltonian as well as a Python package, Pymablock, that implements it. Our algorithm combines an optimal asymptotic scaling and the ability to handle any number of subspaces with a range of other improvements. The package supports numerical and analytical calculations of any order and it is designed to be interoperable with any other packages for specifying the Hamiltonian. We demonstrate how the package handles constructing a k.p model, analyses a superconducting qubit, and computes the low-energy spectrum of a large tight-binding model. We also compare its performance with reference calculations and demonstrate its efficiency.

  4 citations

• Codebase release 2.1 for Pymablock

  Isidora Araya Day, Sebastian Miles, Hugo K. Kerstens, Daniel Varjas, Anton R. Akhmerov

  SciPost Phys. Codebases 50-r2.1 (2025) · published 12 February 2025 | Toggle abstract · src

  A common technique in the study of complex quantum-mechanical systems is to reduce the number of degrees of freedom in the Hamiltonian by using quasi-degenerate perturbation theory. While the Schrieffer-Wolff transformation achieves this and constructs an effective Hamiltonian, its scaling is suboptimal, it is limited to two subspaces, and implementing it efficiently is both challenging and error-prone. We introduce an algorithm for constructing an equivalent effective Hamiltonian as well as a Python package, Pymablock, that implements it. Our algorithm combines an optimal asymptotic scaling and the ability to handle any number of subspaces with a range of other improvements. The package supports numerical and analytical calculations of any order and it is designed to be interoperable with any other packages for specifying the Hamiltonian. We demonstrate how the package handles constructing a k.p model, analyses a superconducting qubit, and computes the low-energy spectrum of a large tight-binding model. We also compare its performance with reference calculations and demonstrate its efficiency.

  2 citations

• Codebase release 0.2 for Carlo.jl

  Lukas Weber

  SciPost Phys. Codebases 49-r0.2 (2025) · published 7 February 2025 | Toggle abstract · src

  Carlo.jl is a Monte Carlo simulation framework written in Julia. It provides MPI-parallel scheduling (including parallel tempering), organized storage of input, checkpoint, and output files, as well as statistical postprocessing. With a minimalist design, it aims to aid the development of high-quality Monte Carlo codes, especially for demanding applications in condensed matter and statistical physics. This hands-on user guide shows how to implement a simple code with Carlo.jl, how to run an existing stochastic series expansion code based on Carlo.jl, and provides benchmarks to show its efficacy.

  1 citation

• Carlo.jl: A general framework for Monte Carlo simulations in Julia

  Lukas Weber

  SciPost Phys. Codebases 49 (2025) · published 7 February 2025 | Toggle abstract · pdf

  Carlo.jl is a Monte Carlo simulation framework written in Julia. It provides MPI-parallel scheduling (including parallel tempering), organized storage of input, checkpoint, and output files, as well as statistical postprocessing. With a minimalist design, it aims to aid the development of high-quality Monte Carlo codes, especially for demanding applications in condensed matter and statistical physics. This hands-on user guide shows how to implement a simple code with Carlo.jl, how to run an existing stochastic series expansion code based on Carlo.jl, and provides benchmarks to show its efficacy.

  2 citations

• DanceQ: High-performance library for number conserving bases

  Robin Schäfer, David J. Luitz

  SciPost Phys. Codebases 48 (2025) · published 5 February 2025 | Toggle abstract · pdf

  The complexity of quantum many-body problems scales exponentially with the size of the system, rendering any finite-size scaling analysis a formidable challenge. This is particularly true for methods based on the full representation of the wave function, where one simply accepts the enormous Hilbert space dimensions and performs linear algebra operations, e.g., for finding the ground state of the Hamiltonian. If the system satisfies an underlying symmetry where an operator with a degenerate spectrum commutes with the Hamiltonian, it can be block-diagonalized, thus reducing the complexity at the expense of additional bookkeeping. At the most basic level required for Krylov space techniques (like the Lanczos algorithm), it is necessary to implement a matrix-vector product of a block of the Hamiltonian with arbitrary block-wavefunctions, potentially without holding the Hamiltonian block in memory. An efficient implementation of this operation requires the calculation of the position of an arbitrary basis vector in the canonical ordering of the basis of the block. We present here an elegant and powerful, multi-dimensional approach to this problem for the $U(1)$ symmetry appearing in problems with particle number conservation. Our divide-and-conquer algorithm uses multiple subsystems and hence generalizes previous approaches to make them scalable. In addition to the theoretical presentation of our algorithm, we provide DanceQ, a flexible and modern – header only – C++20 implementation to manipulate, enumerate, and map to its index any basis state in a given particle number sector as open source software under https://DanceQ.gitlab.io/danceq.

  2 citations

• Codebase release 1.0 for DanceQ

  Robin Schäfer, David J. Luitz

  SciPost Phys. Codebases 48-r1.0 (2025) · published 5 February 2025 | Toggle abstract · src

  The complexity of quantum many-body problems scales exponentially with the size of the system, rendering any finite-size scaling analysis a formidable challenge. This is particularly true for methods based on the full representation of the wave function, where one simply accepts the enormous Hilbert space dimensions and performs linear algebra operations, e.g., for finding the ground state of the Hamiltonian. If the system satisfies an underlying symmetry where an operator with a degenerate spectrum commutes with the Hamiltonian, it can be block-diagonalized, thus reducing the complexity at the expense of additional bookkeeping. At the most basic level required for Krylov space techniques (like the Lanczos algorithm), it is necessary to implement a matrix-vector product of a block of the Hamiltonian with arbitrary block-wavefunctions, potentially without holding the Hamiltonian block in memory. An efficient implementation of this operation requires the calculation of the position of an arbitrary basis vector in the canonical ordering of the basis of the block. We present here an elegant and powerful, multi-dimensional approach to this problem for the $U(1)$ symmetry appearing in problems with particle number conservation. Our divide-and-conquer algorithm uses multiple subsystems and hence generalizes previous approaches to make them scalable. In addition to the theoretical presentation of our algorithm, we provide DanceQ, a flexible and modern – header only – C++20 implementation to manipulate, enumerate, and map to its index any basis state in a given particle number sector as open source software under https://DanceQ.gitlab.io/danceq.

  2 citations