Publications

Order by: publication date number of citations

• divERGe implements various Exact Renormalization Group examples

  Jonas B. Profe, Dante M. Kennes, Lennart Klebl

  SciPost Phys. Codebases 26 (2024) · published 8 February 2024 | Toggle abstract · pdf

  We present divERGe, an open source, high-performance C/C++/Python library for functional renormalization group (FRG) calculations on lattice fermions. The versatile model interface is tailored to real materials applications and seamlessly integrates with existing, standard tools from the ab-initio community. The code fully supports multi-site, multi-orbital, and non-SU(2) models in all of the three included FRG variants: TU$^2$FRG, N-patch FRG, and grid FRG. With this, the divERGe library paves the way for widespread application of FRG as a tool in the study of competing orders in quantum materials.

  1 citation

• A simple coin for a 2d entangled walk

  Ahmadullah Zahed, Kallol Sen

  SciPost Phys. Core 6, 048 (2023) · published 10 July 2023 | Toggle abstract · pdf

  We analyze the effect of a simple coin operator, built out of Bell pairs, in a 2d Discrete Quantum Random Walk (DQRW) problem. The specific form of the coin enables us to find analytical and closed form solutions to the recursion relations of the DQRW. The coin induces entanglement between the spin and position degrees of freedom, which oscillates with time and reaches a constant value asymptotically. We probe the entangling properties of the coin operator further, by two different measures. First, by integrating over the space of initial tensor product states, we determine the Entangling Power of the coin operator. Secondly, we compute the Generalized Relative Rényi Entropy between the corresponding density matrices for the entangled state and the initial pure unentangled state. Both the Entangling Power and Generalized Relative Rényi Entropy behaves similar to the entanglement with time. Finally, in the continuum limit, the specific coin operator reduces the 2d DQRW into two 1d massive fermions coupled to synthetic gauge fields, where both the mass term and the gauge fields are built out of the coin parameters.

  1 citation

• Dual applications of Chebyshev polynomials method: Efficiently finding thousands of central eigenvalues for many-spin systems

  Haoyu Guan, Wenxian Zhang

  SciPost Phys. 11, 103 (2021) · published 8 December 2021 | Toggle abstract · pdf

  Computation of a large group of interior eigenvalues at the middle spectrum is an important problem for quantum many-body systems, where the level statistics provides characteristic signatures of quantum chaos. We propose an exact numerical method, dual applications of Chebyshev polynomials (DACP), to simultaneously find thousands of central eigenvalues, where the level space decreases exponentially with the system size. To disentangle the near-degenerate problem, we employ twice the Chebyshev polynomials, to construct an exponential semicircle filter as a preconditioning step and to generate a large set of proper basis states in the desired subspace. Numerical calculations on Ising spin chain and spin glass shards confirm the correctness and efficiency of DACP. As numerical results demonstrate, DACP is $30$ times faster than the state-of-the-art shift-invert method for the Ising spin chain while $8$ times faster for the spin glass shards. In contrast to the shift-invert method, the computation time of DACP is only weakly influenced by the required number of eigenvalues, which renders it a powerful tool for large scale eigenvalues computations. Moreover, the consumed memory also remains a small constant (5.6 GB) for spin-$1/2$ systems consisting of up to $20$ spins, making it desirable for parallel computing.

  1 citation

• Device-independent and semi-device-independent entanglement certification in broadcast Bell scenarios

  Emanuel-Cristian Boghiu, Flavien Hirsch, Pei-Sheng Lin, Marco Túlio Quintino, Joseph Bowles

  SciPost Phys. Core 6, 028 (2023) · published 11 April 2023 | Toggle abstract · pdf

  It has recently been shown that by broadcasting the subsystems of a bipartite quantum state, one can activate Bell nonlocality and significantly improve noise tolerance bounds for device-independent entanglement certification. In this work we strengthen these results and explore new aspects of this phenomenon. First, we prove new results related to the activation of Bell nonlocality. We construct Bell inequalities tailored to the broadcast scenario, and show how broadcasting can lead to even stronger notions of Bell nonlocality activation. In particular, we exploit these ideas to show that bipartite states admitting a local hidden-variable model for general measurements can lead to genuine tripartite nonlocal correlations. We then study device-independent entanglement certification in the broadcast scenario, and show through semidefinite programming techniques that device-independent entanglement certification is possible for the two-qubit Werner state in essentially the entire range of entanglement. Finally, we extend the concept of EPR steering to the broadcast scenario, and present novel examples of activation of the two-qubit isotropic state. Our results pave the way for broadcast-based device-independent and semi-device-independent protocols.

  1 citation

• Topological interpretation of color exchange invariants: hexagonal lattice on a torus

  Olivier Cépas, Peter M. Akhmetiev

  SciPost Phys. 10, 042 (2021) · published 18 February 2021 | Toggle abstract · pdf

  We explain a correspondence between some invariants in the dynamics of color exchange in a 2d coloring problem, which are polynomials of winding numbers, and linking numbers in 3d. One invariant is visualized as linking of lines on a special surface with Arf-Kervaire invariant one, and is interpreted as resulting from an obstruction to transform the surface into its chiral image with special continuous deformations. We also consider additional constraints on the dynamics and see how the surface is modified.

  1 citation

• Transport and magnetic properties in the Nd diluted system Y$_{1-x}$Nd$_{x}$Co$_{2}$Zn$_{20}$

  Rikako Yamamoto, Yasuyuki Shimura, Kazunori Umeo, Toshiro Takabatake, Takahiro Onimaru

  SciPost Phys. Proc. 11, 010 (2023) · published 5 June 2023 | Toggle abstract · pdf

  We report the electrical resistivity, specific heat, and magnetization measurements of Y$_{1-x}$Nd$_{x}$Co$_{2}$Zn$_{20}$ for $0.017 \leq x \leq 0.95$. The Schottky-type specific heat peak at around 13 K for all the samples is reproduced by the crystalline electric field model with the $\Gamma_{6}$ doublet ground state of a Nd$^{3+}$ ion. The magnetization and magnetic susceptibility data of the samples for $x \leq 0.06$ are well reproduced by the calculation without intersite magnetic interactions among Nd moments. Therefore, the dilute Nd system Y$_{1-x}$Nd$_{x}$Co$_{2}$Zn$_{20}$ for $x \leq 0.06$ is a good candidate to study on-site interaction of the $\Gamma_{6}$ doublet ground state of 4$f$ electrons with conduction electrons.

  1 citation

• Anomaly of $(2+1)$-dimensional symmetry-enriched topological order from $(3+1)$-dimensional topological quantum field theory

  Weicheng Ye, Liujun Zou

  SciPost Phys. 15, 004 (2023) · published 10 July 2023 | Toggle abstract · pdf

  Symmetry acting on a (2+1)$D$ topological order can be anomalous in the sense that they possess an obstruction to being realized as a purely (2+1)$D$ on-site symmetry. In this paper, we develop a (3+1)$D$ topological quantum field theory to calculate the anomaly indicators of a (2+1)$D$ topological order with a general symmetry group $G$, which may be discrete or continuous, Abelian or non-Abelian, contain anti-unitary elements or not, and permute anyons or not. These anomaly indicators are partition functions of the (3+1)$D$ topological quantum field theory on a specific manifold equipped with some $G$-bundle, and they are expressed using the data characterizing the topological order and the symmetry actions. Our framework is applied to derive the anomaly indicators for various symmetry groups, including $\mathbb{Z}_2\times\mathbb{Z}_2$, $\mathbb{Z}_2^T\times\mathbb{Z}_2^T$, $SO(N)$, $O(N)^T$, $SO(N)\times \mathbb{Z}_2^T$, etc, where $\mathbb{Z}_2$ and $\mathbb{Z}_2^T$ denote a unitary and anti-unitary order-2 group, respectively, and $O(N)^T$ denotes a symmetry group $O(N)$ such that elements in $O(N)$ with determinant $-1$ are anti-unitary. In particular, we demonstrate that some anomaly of $O(N)^T$ and $SO(N)\times \mathbb{Z}_2^T$ exhibit symmetry-enforced gaplessness, i.e., they cannot be realized by any symmetry-enriched topological order. As a byproduct, for $SO(N)$ symmetric topological orders, we derive their $SO(N)$ Hall conductance.

  1 citation

• New machine learning techniques for simulation-based inference: InferoStatic nets, kernel score estimation, and kernel likelihood ratio estimation

  Kyoungchul Kong, Konstantin T. Matchev, Stephen Mrenna, Prasanth Shyamsundar

  SciPost Phys. Codebases 14 (2023) · published 7 July 2023 | Toggle abstract · pdf

  We propose an intuitive, machine-learning approach to multiparameter inference, dubbed the InferoStatic Networks (ISN) method, to model the score and likelihood ratio estimators in cases when the probability density can be sampled but not computed directly. The ISN uses a backend neural network that models a scalar function called the inferostatic potential $\varphi$. In addition, we introduce new strategies, respectively called Kernel Score Estimation (KSE) and Kernel Likelihood Ratio Estimation (KLRE), to learn the score and the likelihood ratio functions from simulated data. We illustrate the new techniques with some toy examples and compare to existing approaches in the literature. We mention en passant some new loss functions that optimally incorporate latent information from simulations into the training procedure.

  1 citation

• Codebase release 0.2 for Pychastic

  Radost Waszkiewicz, Maciej Bartczak, Kamil Kolasa, Maciej Lisicki

  SciPost Phys. Codebases 11-r0.2 (2023) · published 3 April 2023 | Toggle abstract · src

  In the last decade, Python-powered physics simulations ecosystem has been growing steadily, allowing greater interoperability, and becoming an important tool in numerical exploration of physical phenomena, particularly in soft matter systems. Driven by the need for fast and precise numerical integration in colloidal dynamics, here we formulate the problem of Brownian Dynamics (BD) in a mathematically consistent formalism of the Itō calculus, and develop a Python package to assist numerical computations. We show that, thanks to the automatic differentiation packages, the classical truncated Taylor-Itō integrators can be implemented without the burden of computing the derivatives of the coefficient functions beforehand. Furthermore, we show how to circumvent the difficulties of BD simulations such as calculations of the divergence of the mobility tensor in the diffusion equation and discontinuous trajectories encountered when working with dynamics on $S^2$ and $SO(3)$. The resulting Python package, Pychastic, is capable of performing BD simulations including hydrodynamic interactions at speeds comparable to dedicated implementations in lower-level programming languages, but with a much simpler end-user interface.

  1 citation

• Masses of vector and pseudovector hybrid mesons in a chiral symmetric model

  Walaa I. Eshraim

  SciPost Phys. Proc. 6, 014 (2022) · published 31 May 2022 | Toggle abstract · pdf

  We enlarge the chiral model, the so-called extended Linear Sigma Model (eLSM), by including the low-lying hybrid nonet with exotic quantum numbers $J^{PC}=1^{-+}$ and the nonet of their chiral partners with $J^{PC}=1^{+-}$ to a global $U(3)_r \times U(3)_l$ chiral symmetry. We use the assignment of the $\pi_1^{hyb}= \pi_1(1600)$ as input to determine the unknown parameters. Then, we compute the lightest vector and pseudovector hybrid masses that could guide ongoing and upcoming experiments in searching for hybrids.

  1 citation