SciPost Phys. Core 5, 048 (2022) ·
published 10 October 2022

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Topological crystalline insulators are phases of matter where the crystalline symmetries solely protect the topology. In this work, we explore the effect of manybody interactions in a subclass of topological crystalline insulators, namely the mirrorsymmetry protected topological crystalline insulator. Employing a prototypical mirrorsymmetric quasionedimensional model, we demonstrate the emergence of a mirrorsymmetry protected topological phase and its robustness in the presence of shortrange interactions. When longerrange interactions are introduced, we find an interactioninduced topological phase transition between the mirrorsymmetry protected topological order and a trivial charge density wave. The results are obtained using densitymatrix renormalization group and quantum MonteCarlo simulations in applicable limits.
David F. Rentería Estrada, Roger J. HernándezPinto, German F. R. Sborlini, Pia Zurita
SciPost Phys. Core 5, 049 (2022) ·
published 31 October 2022

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In the context of highenergy physics, a reliable description of the partonlevel kinematics plays a crucial role for understanding the internal structure of hadrons and improving the precision of the calculations. In protonproton collisions, this represents a challenging task since extracting such information from experimental data is not straightforward. With this in mind, we propose to tackle this problem by studying the production of one hadron and a direct photon in protonproton collisions, including up to NexttoLeading Order Quantum Chromodynamics and LeadingOrder Quantum Electrodynamics corrections. Using MonteCarlo integration, we simulate the collisions and analyze the events to determine the correlations among measurable and partonic quantities. Then, we use these results to feed three different Machine Learning algorithms that allow us to find the momentum fractions of the partons involved in the process, in terms of suitable combinations of the final state momenta. Our results are compatible with previous findings and suggest a powerful application of MachineLearning to model highenergy collisions at the partoniclevel with highprecision.
Charanjit Kaur Khosa, Veronica Sanz, Michael Soughton
SciPost Phys. Core 5, 050 (2022) ·
published 2 November 2022

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In this paper we propose ways to incorporate Machine Learning training outputs into a study of statistical significance. We describe these methods in supervised classification tasks using a CNN and a DNN output, and unsupervised learning based on a VAE. As use cases, we consider two physical situations where Machine Learning are often used: high$p_T$ hadronic activity, and boosted Higgs in association with a massive vector boson.
SciPost Phys. Core 5, 051 (2022) ·
published 1 December 2022

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The Spectral Form Factor (SFF) is a convenient tool for the characterization of eigenvalue statistics of systems with discrete spectra, and thus serves as a proxy for quantum chaoticity. This work presents an analytical calculation of the SFF of the ChernSimons Matrix Model (CSMM), which was first introduced to describe the intermediate level statistics of disordered electrons at the mobility edge. The CSMM is characterized by a parameter $ 0 \leq q\leq 1$, where the Circular Unitary Ensemble (CUE) is recovered for $q\to 0$. The CSMM was later found as a matrix model description of $U(N)$ ChernSimons theory on $S^3$, which is dual to a topological string theory characterized by string coupling $g_s=\log q$. The spectral form factor is proportional to a colored HOMFLY invariant of a $(2n,2)$torus link with its two components carrying the fundamental and antifundamental representations, respectively. We check that taking $N \to \infty$ whilst keeping $q<1$ reduces the connected SFF to an exact linear ramp of unit slope, confirming the main result from arXiv:2012.11703 for the specific case of the CSMM. We then consider the `t Hooft limit, where $N \to \infty$ and $q \to 1^$ such that $y = q^N $ remains finite. As we take $q\to 1^$, this constitutes the opposite extreme of the CUE limit. In the `t Hooft limit, the connected SFF turns into a remarkable sequence of polynomials which, as far as the authors are aware, have not appeared in the literature thus far. A gap opens in the spectrum and, after unfolding by a constant rescaling, the connected SFF approximates a linear ramp of unit slope for all $y$ except $y \approx 1$, where the connected SFF goes to zero. We thus find that, although the CSMM was introduced to describe intermediate statistics and the `t Hooft limit is the opposite limit of the CUE, we still recover WignerDyson universality for all $y$ except $y\approx 1$.
SciPost Phys. Core 5, 052 (2022) ·
published 2 December 2022

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In lattice field theory, Monte Carlo simulation algorithms get highly affected by critical slowing down in the critical region, where autocorrelation time increases rapidly. Hence the cost of generation of lattice configurations near the critical region increases sharply. In this paper, we use a Conditional Generative Adversarial Network (CGAN) for sampling lattice configurations. We train the CGAN on the dataset consisting of Hybrid Monte Carlo (HMC) samples in regions away from the critical region, i.e., in the regions where the HMC simulation cost is not so high. Then we use the trained CGAN model to generate independent samples in the critical region. We perform both interpolation and extrapolation to the critical region. Thus, the overall computational cost is reduced. We test our approach for GrossNeveu model in 1+1 dimension. We find that the observable distributions obtained from the proposed CGAN model match with those obtained from HMC simulations, while circumventing the problem of critical slowing down.
Isidora Araya Day, Anton R. Akhmerov, Dániel Varjas
SciPost Phys. Core 5, 053 (2022) ·
published 15 December 2022

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We show that topological defects in quadrupole insulators do not host quantized fractional charges, contrary to what their Wannier representation indicates. In particular, we test the charge quantization hypothesis based on the Wannier representation of a disclination and a parametric defect. Since disclinations necessarily strain the lattice and parametric defects require closed curves in parameter space, both defects break fourfold rotation symmetry, even away from their origin. The Wannier representation of the defects is thus determined by local reflection symmetries. Contrary to the hypothesis, we find that the local charge density decays as $\sim 1/r^2$ with distance, leading to a diverging defect charge. Because topological defects are incompatible with fourfold rotation symmetry, we conclude that defect charge quantization is protected by sublattice symmetry, and not higher order topology.