Publications

Order by: publication date number of citations

• Codebase release 1.3 for GrassmannTN

  Atis Yosprakob

  SciPost Phys. Codebases 20-r1.3 (2023) · published 16 November 2023 | Toggle abstract · src

  We present GrassmannTN, a Python package for the computation of the Grassmann tensor network. The package is built to assist in the numerical computation without the need to input the fermionic sign factor manually. It prioritizes coding readability by designing every tensor manipulating function around the tensor subscripts. The computation of the Grassmann tensor renormalization group and Grassmann isometries using GrassmannTN are given as the use case examples.

  1 citation

• Codebase release 1.3 for SymTensor

  Yang Gao, Phillip Helms, Garnet Kin-Lic Chan, Edgar Solomonik

  SciPost Phys. Codebases 10-r1.3 (2023) · published 24 February 2023 | Toggle abstract · src

  Tensor contractions are ubiquitous in computational chemistry and physics, where tensors generally represent states or operators and contractions express the algebra of these quantities. In this context, the states and operators often preserve physical conservation laws, which are manifested as group symmetries in the tensors. These group symmetries imply that each tensor has block sparsity and can be stored in a reduced form. For nontrivial contractions, the memory footprint and cost are lowered, respectively, by a linear and a quadratic factor in the number of symmetry sectors. State-of-the-art tensor contraction software libraries exploit this opportunity by iterating over blocks or using general block-sparse tensor representations. Both approaches entail overhead in performance and code complexity. With intuition aided by tensor diagrams, we present a technique, irreducible representation alignment, which enables efficient handling of Abelian group symmetries via only dense tensors, by using contraction-specific reduced forms. This technique yields a general algorithm for arbitrary group symmetric contractions, which we implement in Python and apply to a variety of representative contractions from quantum chemistry and tensor network methods. As a consequence of relying on only dense tensor contractions, we can easily make use of efficient batched matrix multiplication via Intel's MKL and distributed tensor contraction via the Cyclops library, achieving good efficiency and parallel scalability on up to 4096 Knights Landing cores of a supercomputer.

  1 citation

• Phenomenological XXZ model for the competition between superconductivity and charge order in cuprates

  Giulia Venditti, Ilaria Maccari, Jose Lorenzana, Sergio Caprara

  SciPost Phys. 15, 230 (2023) · published 7 December 2023 | Toggle abstract · pdf

  We argue that there is a special doping point in the phase diagram of cuprates, such that the condensation of holes into a charge-ordered and a superconducting phase are degenerate in energy but with an energy barrier in between. We present Monte Carlo simulations of a phenomenological XXZ model for this problem without and with quenched disorder in two dimensions. While in the clean case charge order and superconductivity are separated by a first-order line which is nearly independent of temperature, in the presence of quenched disorder charge order is fragmented into domains separated by superconducting filaments reminiscent of the supersolid behaviour in $^4$He. Assuming weak interlayer couplings, the resulting phase diagram of the three-dimensional system is in good agreement with the experiments.

  1 citation

• 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.

  1 citation

• 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

• 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.

  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

• 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

• 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