Publications

Order by: publication date number of citations

• 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.

• Learning lattice quantum field theories with equivariant continuous flows

  Mathis Gerdes, Pim de Haan, Corrado Rainone, Roberto Bondesan, Miranda C. N. Cheng

  SciPost Phys. 15, 238 (2023) · published 13 December 2023 | Toggle abstract · pdf

  We propose a novel machine learning method for sampling from the high-dimensional probability distributions of Lattice Field Theories, which is based on a single neural ODE layer and incorporates the full symmetries of the problem. We test our model on the $\phi^4$ theory, showing that it systematically outperforms previously proposed flow-based methods in sampling efficiency, and the improvement is especially pronounced for larger lattices. Furthermore, we demonstrate that our model can learn a continuous family of theories at once, and the results of learning can be transferred to larger lattices. Such generalizations further accentuate the advantages of machine learning methods.

  4 citations

• Transient superconductivity in three-dimensional Hubbard systems by combining matrix-product states and self-consistent mean-field theory

  Svenja Marten, Gunnar Bollmark, Thomas Köhler, Salvatore R. Manmana, Adrian Kantian

  SciPost Phys. 15, 236 (2023) · published 12 December 2023 | Toggle abstract · pdf

  We combine matrix-product-state (MPS) and mean-field (MF) methods to model the real-time evolution of a three-dimensional (3D) extended Hubbard system formed from one-dimensional (1D) chains arrayed in parallel with weak coupling in-between them. This approach allows us to treat much larger 3D systems of correlated fermions out-of-equilibrium over a much more extended real-time domain than previous numerical approaches. We deploy this technique to study the evolution of the system as its parameters are tuned from a charge-density wave phase into the superconducting regime, which allows us to investigate the formation of transient non-equilibrium superconductivity. In our ansatz, we use MPS solutions for chains as input for a self-consistent time-dependent MF scheme. In this way, the 3D problem is mapped onto an effective 1D Hamiltonian that allows us to use the MPS efficiently to perform the time evolution, and to measure the BCS order parameter as a function of time. Our results confirm previous findings for purely 1D systems that for such a scenario a transient superconducting state can occur.

• 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.

• Spin rotons and supersolids in binary antidipolar condensates

  Wyatt Kirkby, Thomas Bland, Francesca Ferlaino, Russell N. Bisset

  SciPost Phys. Core 6, 084 (2023) · published 4 December 2023 | Toggle abstract · pdf

  We present a theoretical study of a mixture of antidipolar and nondipolar Bose-Einstein condensates confined to an infinite tube. We predict the presence of a spin roton and its associated instability, which triggers a continuous unmodulated-to-supersolid phase transition. We characterize the phase diagram of the binary system, ranging from the quasi-1D to the radial Thomas-Fermi (elongated 3D) regimes. We also present the dynamic formation of supersolids following a quench from the uniform miscible phase, which maintains phase coherence across the system.

  1 citation

• Gauging tensor networks with belief propagation

  Joseph Tindall, Matt Fishman

  SciPost Phys. 15, 222 (2023) · published 1 December 2023 | Toggle abstract · pdf

  Effectively compressing and optimizing tensor networks requires reliable methods for fixing the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new algorithm for gauging tensor networks using belief propagation, a method that was originally formulated for performing statistical inference on graphical models and has recently found applications in tensor network algorithms. We show that this method is closely related to known tensor network gauging methods. It has the practical advantage, however, that existing belief propagation implementations can be repurposed for tensor network gauging, and that belief propagation is a very simple algorithm based on just tensor contractions so it can be easier to implement, optimize, and generalize. We present numerical evidence and scaling arguments that this algorithm is faster than existing gauging algorithms, demonstrating its usage on structured, unstructured, and infinite tensor networks. Additionally, we apply this method to improve the accuracy of the widely used simple update gate evolution algorithm.

  1 citation