Publications

Order by: publication date number of citations

• Learning knot invariants across dimensions

  Jessica Craven, Mark Hughes, Vishnu Jejjala, Arjun Kar

  SciPost Phys. 14, 021 (2023) · published 21 February 2023 | Toggle abstract · pdf

  We use deep neural networks to machine learn correlations between knot invariants in various dimensions. The three-dimensional invariant of interest is the Jones polynomial $J(q)$, and the four-dimensional invariants are the Khovanov polynomial $\text{Kh}(q,t)$, smooth slice genus $g$, and Rasmussen's $s$-invariant. We find that a two-layer feed-forward neural network can predict $s$ from $\text{Kh}(q,-q^{-4})$ with greater than $99\%$ accuracy. A theoretical explanation for this performance exists in knot theory via the now disproven knight move conjecture, which is obeyed by all knots in our dataset. More surprisingly, we find similar performance for the prediction of $s$ from $\text{Kh}(q,-q^{-2})$, which suggests a novel relationship between the Khovanov and Lee homology theories of a knot. The network predicts $g$ from $\text{Kh}(q,t)$ with similarly high accuracy, and we discuss the extent to which the machine is learning $s$ as opposed to $g$, since there is a general inequality $|s| \leq 2g$. The Jones polynomial, as a three-dimensional invariant, is not obviously related to $s$ or $g$, but the network achieves greater than $95\%$ accuracy in predicting either from $J(q)$. Moreover, similar accuracy can be achieved by evaluating $J(q)$ at roots of unity. This suggests a relationship with $SU(2)$ Chern—Simons theory, and we review the gauge theory construction of Khovanov homology which may be relevant for explaining the network's performance.

  5 citations

• Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain

  Yuan Miao, Enej Ilievski, Oleksandr Gamayun

  SciPost Phys. 10, 086 (2021) · published 22 April 2021 | Toggle abstract · pdf

  Using the algebro-geometric approach, we study the structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain. We outline how classical nonlinear spin waves governed by the anisotropic Landau-Lifshitz equation arise as coherent macroscopic low-energy fluctuations of the ferromagnetic ground state. Special emphasis is devoted to the simplest types of solutions, describing precessional motion and elliptic magnetisation waves. The internal magnon structure of classical spin waves is resolved by performing the semi-classical quantisation using the Riemann-Hilbert problem approach. We present an expression for the overlap of two semi-classical eigenstates and discuss how correlation functions at the semi-classical level arise from classical phase-space averaging.

  5 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 | 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.

  5 citations

• Detecting nematic order in STM/STS data with artificial intelligence

  Jeremy B. Goetz, Yi Zhang, Michael J. Lawler

  SciPost Phys. 8, 087 (2020) · published 15 June 2020 | Toggle abstract · pdf

  Detecting the subtle yet phase defining features in Scanning Tunneling Microscopy and Spectroscopy data remains an important challenge in quantum materials. We meet the challenge of detecting nematic order from local density of states data with supervised machine learning and artificial neural networks for the difficult scenario without sharp features such as visible lattice Bragg peaks or Friedel oscillation signatures in the Fourier transform spectrum. We train the artificial neural networks to classify simulated data of isotropic and anisotropic two-dimensional metals in the presence of disorder. The supervised machine learning succeeds only with at least one hidden layer in the ANN architecture, demonstrating it is a higher level of complexity than nematic order detected from Bragg peaks which requires just two neurons. We apply the finalized ANN to experimental STM data on CaFe2As2, and it predicts nematic symmetry breaking with 99% confidence (probability 0.99), in agreement with previous analysis. Our results suggest ANNs could be a useful tool for the detection of nematic order in STM data and a variety of other forms of symmetry breaking.

  5 citations

• Laser-induced heating for the experimental study of critical Casimir forces with optical trapping

  Ignacio A. Martinez, Artyom Petrosyan, Sergio Ciliberto

  SciPost Phys. 15, 247 (2023) · published 20 December 2023 | Toggle abstract · pdf

  Critical Casimir interactions represent a perfect example of bath-induced forces at mesoscales. These forces may have a relevant role in the living systems as well as a role in the design of nanomachines fueled by environmental fluctuations. Since the thermal fluctuations are enhanced in the vicinity of a demixing point of a second-order phase transition, we can modulate the magnitude and range of these Casimir-like forces by slight changes in the temperature. Here, we consider two optical trapped colloidal beads inside a binary mixture. The Casimir interaction is controlled by warming the mixture by laser-induced heating, whose local application ensures high reproducibility. Once this two-particle system is warmed, the critical behavior of different observables allows the system to become its self-thermometer. We use this experimental scheme for analyzing the energetics of a critical colloidal system under a non-equilibrium-driven protocol. We quantify how the injected work can be dissipated to the environment as heat or stored as free energy. Indeed, our system allows us to use the fluctuation theorems framework for analyzing the performance of this critically driven toy model. Our work paves the way for future experimental studies on the non-equilibrium features of bath-induced forces and the design of critically driven nanosystems.

  5 citations

• Tunnelling to holographic traversable wormholes

  Suzanne Bintanja, Ben Freivogel, Andrew Rolph

  SciPost Phys. 16, 066 (2024) · published 5 March 2024 | Toggle abstract · pdf

  We study nonperturbative effects of quantum gravity in a system consisting of a coupled pair of holographic CFTs. The AdS$_4$/CFT$_3$ system has three possible ground states: two copies of empty AdS, a pair of extremal AdS black holes, and an eternal AdS traversable wormhole. We give a recipe for calculating transition rates via gravitational instantons and test it by calculating the emission rate of radiation shells from a black hole. We calculate the nucleation rate of a traversable wormhole between a pair of AdS-RN black holes in the canonical and microcanonical ensembles. Our results give predictions of nonpertubative quantum gravity that can be tested in a holographic simulation.

  5 citations

• Rank one HCIZ at high temperature: interpolating between classical and free convolutions

  Pierre Mergny, Marc Potters

  SciPost Phys. 12, 022 (2022) · published 14 January 2022 | Toggle abstract · pdf

  We study the rank one Harish-Chandra-Itzykson-Zuber integral in the limit where $\frac{N \beta}{2} \to c $, called the high temperature regime and show that it can be used to construct a promising one-parameter interpolation, with parameter $c$ between the classical and the free convolution. This $c$-convolution has a simple interpretation in terms of another associated family of distribution indexed by $c$, called the Markov-Krein transform: the $c$-convolution of two distributions corresponds to the classical convolution of their Markov-Krein transforms. We derive first cumulants-moments relations, a central limit theorem, a Poisson limit theorem and shows several numerical examples of $c$-convoluted distributions.

  5 citations

• Renormalisation group effects in SMEFT for di-Higgs production

  Gudrun Heinrich, Jannis Lang

  SciPost Phys. 18, 113 (2025) · published 31 March 2025 | Toggle abstract · pdf

  We study the effects of renormalisation group running for the Wilson coefficients of dimension-6 operators contributing to Higgs boson pair production in gluon fusion within Standard Model Effective Field Theory (SMEFT). The running of these Wilson coefficients has been implemented in the NLO QCD code ggHH_SMEFT, which is publicly available within the Powheg-Box-V2 framework.

  5 citations

• Analysis of the buildup of spatiotemporal correlations and their bounds outside of the light cone

  Nils O. Abeling, Lorenzo Cevolani, Stefan Kehrein

  SciPost Phys. 5, 052 (2018) · published 26 November 2018 | Toggle abstract · pdf

  In non-relativistic quantum theories the Lieb-Robinson bound defines an effective light cone with exponentially small tails outside of it. In this work we use it to derive a bound for the time evolution of the correlation function of two local disjoint observables if the initial state has a power-law decay. We show that the exponent of the power-law of the bound is identical to the initial (equilibrium) decay. We explicitly verify this result by studying the full dynamics of the susceptibilities and correlations in the exactly solvable Luttinger model after a sudden quench from the non-interacting to the interacting model.

  5 citations

• Tau-decay determination of the strong coupling

  Antonio Pich

  SciPost Phys. Proc. 1, 036 (2019) · published 21 February 2019 | Toggle abstract · pdf

  We review the current status of the determination of the strong coupling from tau decay. Using the most recent release of the ALEPH data, a very comprehensive phenomenological analysis has been performed, exploring all strategies previously considered in the literature and several complementary approaches. Once their actual uncertainties are properly assessed, the results from all adopted methodologies are in excellent agreement, leading to a very robust and reliable value of the strong coupling, $\alpha_s^{(n_f=3)}(m_\tau^2) = 0.328\pm 0.013$, which implies $\alpha_s^{(n_f=5)}(M_Z^2) = 0.1197\pm 0.0015$.

  5 citations