Publications

Order by: publication date number of citations

• NISQ algorithm for the matrix elements of a generic observable

  Rebecca Erbanni, Kishor Bharti, Leong-Chuan Kwek, Dario Poletti

  SciPost Phys. 15, 180 (2023) · published 30 October 2023 | Toggle abstract · pdf

  The calculation of off-diagonal matrix elements has various applications in fields such as nuclear physics and quantum chemistry. In this paper, we present a noisy intermediate scale quantum algorithm for estimating the diagonal and off-diagonal matrix elements of a generic observable in the energy eigenbasis of a given Hamiltonian without explicitly preparing its eigenstates. By means of numerical simulations we show that this approach finds many of the matrix elements for the one and two qubits cases. Specifically, while in the first case, one can initialize the ansatz parameters over a broad interval, in the latter the optimization landscape can significantly slow down the speed of convergence and one should therefore be careful to restrict the initialization to a smaller range of parameters.

  1 citation

• Plea for the use of the exact Stirling formula in statistical mechanics

  Didier Lairez

  SciPost Phys. Lect. Notes 76 (2023) · published 30 October 2023 | Toggle abstract · pdf

  In statistical mechanics, the generally called Stirling approximation is actually an approximation of Stirling's formula. In this article, it is shown that the term that is dropped is in fact the one that takes fluctuations into account. The use of the Stirling's exact formula forces us to reintroduce them into the already proposed solutions of well-know puzzles such as the extensivity paradox or the Gibbs' paradox of joining two volumes of identical gas. This amendment clearly results in a gain in consistency and rigor of these solutions.

  1 citation

• Exact multi-instantons in topological string theory

  Jie Gu, Marcos Mariño

  SciPost Phys. 15, 179 (2023) · published 26 October 2023 | Toggle abstract · pdf

  Topological string theory has multi-instanton sectors which lead to non-perturbative effects in the string coupling constant and control the large order behavior of the perturbative genus expansion. As proposed by Couso, Edelstein, Schiappa and Vonk, these sectors can be described by a trans-series extension of the BCOV holomorphic anomaly equations. In this paper we find exact, closed form solutions for these multi-instanton trans-series in the case of local Calabi-Yau manifolds. The resulting multi-instanton amplitudes turn out to be very similar to the eigenvalue tunneling amplitudes of matrix models. Their form suggests that the flat coordinates of the Calabi-Yau manifold are naturally quantized in units of the string coupling constant, as postulated in large $N$ dualities. Based on our results we obtain a general picture for the resurgent structure of the topological string in the local case, which we illustrate with explicit calculations for local $\mathbb{P}^2$.

  5 citations

• Four lectures on Euler integrals

  Saiei-Jaeyeong Matsubara-Heo, Sebastian Mizera, Simon Telen

  SciPost Phys. Lect. Notes 75 (2023) · published 26 October 2023 | Toggle abstract · pdf

  These lecture notes provide a self-contained introduction to Euler integrals, which are frequently encountered in applications. In particle physics, they arise as Feynman integrals or string amplitudes. Our four selected topics demonstrate the diverse mathematical techniques involved in the study of Euler integrals, including polyhedral geometry, very affine varieties, differential equations, and computational algebra.

  3 citations

• Visualizing near-coexistence of massless Dirac electrons and ultra-massive saddle point electrons

  Abhay Kumar Nayak, Jonathan Reiner, Hengxin Tan, Huixia Fu, Henry Ling, Chandra Shekhar, Claudia Felser, Tamar (Tami) Pereg-Barnea, Binghai Yan, Haim Beidenkopf, Nurit Avraham

  SciPost Phys. 15, 178 (2023) · published 25 October 2023 | Toggle abstract · pdf

  Strong singularities in the electronic density of states amplify correlation effects and play a key role in determining the ordering instabilities in various materials. Recently high order van Hove singularities (VHSs) with diverging power-law scaling have been classified in single-band electron models. We show that the 110 surface of Bismuth exhibits high order VHS with an usually high density of states divergence $\sim (E)^{-0.7}$. Detailed mapping of the surface band structure using scanning tunneling microscopy and spectroscopy combined with first-principles calculations show that this singularity occurs in close proximity to Dirac bands located at the center of the surface Brillouin zone. The enhanced power-law divergence is shown to originate from the anisotropic flattening of the Dirac band just above the Dirac node. Such near-coexistence of massless Dirac electrons and ultra-massive saddle points enables to study the interplay of high order VHS and Dirac fermions.

  1 citation

• Dark matter from the centre of SU(N)

  Michele Frigerio, Nicolas Grimbaum-Yamamoto, Thomas Hambye

  SciPost Phys. 15, 177 (2023) · published 25 October 2023 | Toggle abstract · pdf

  A dark sector with non-abelian gauge symmetry provides a sound framework to justify stable dark matter (DM) candidates. We consider scalar fields charged under a $SU(N)$ gauge group, and show that the centre of $SU(N)$, the discrete subgroup $Z_N$ also known as $N$-ality, can ensure the stability of scalar DM particles. We analyse in some details two minimal DM models of this class, based on $SU(2)$ and $SU(3)$, respectively. These models have non-trivial patterns of spontaneous symmetry breaking, leading to distinctive phenomenological implications. For the $SU(2)$ model these include a specific interplay of two DM states, with the same interactions but different masses, and several complementary DM annihilation regimes, either within the dark sector or through the Higgs portal. The $SU(3)$ model predicts dark radiation made of a pair of dark photons with a unique gauge coupling, as well as regimes where DM semi-annihilations become dominant and testable.

  4 citations

• Resolving phase transitions with discontinuous Galerkin methods

  Eduardo Grossi, Nicolas Wink

  SciPost Phys. Core 6, 071 (2023) · published 25 October 2023 | Toggle abstract · pdf

  We demonstrate the applicability and advantages of Discontinuous Galerkin (DG) schemes in the context of the Functional Renormalization Group (fRG). We investigate the $O(N)$-model in the large $N$ limit. It is shown that the flow equation for the effective potential can be cast into a conservative form. We discuss results for the Riemann problem, as well as initial conditions leading to a first and second order phase transition. In particular, we unravel the mechanism underlying first order phase transitions, based on the formation of a shock in the derivative of the effective potential.

  4 citations

• Flavoured $(g-2)_\mu$ with dark lepton seasoning

  Harun Acaroğlu, Prateek Agrawal, Monika Blanke

  SciPost Phys. 15, 176 (2023) · published 24 October 2023 | Toggle abstract · pdf

  As a joint explanation for the dark matter (DM) problem and the muon $(g-2)$ anomaly, we propose a simplified model of lepton-flavoured complex scalar DM with couplings to both the left- and right-handed leptons of the Standard Model (SM). Both interactions are governed by the same new flavour-violating coupling matrix $\lambda$, however we allow for a relative scaling of the coupling strength. The SM is further extended by two fermion representations, transforming as an $SU(2)_L$ doublet and singlet, respectively, and mediating these interactions. The fermions additionally couple to the SM Higgs doublet via a new Yukawa coupling. To study the model's phenomenology we first investigate constraints from collider searches, flavour experiments, precision tests of the SM, the DM relic density, and direct as well as indirect detection experiments individually. We then perform a combined analysis by demanding that all mentioned constraints are satisfied simultaneously. We use the results of this combined analysis and examine if the model is capable of accommodating the $(g-2)_\mu$ anomaly within its viable parameter space without introducing fine-tuned lepton masses. For all benchmark scenarios we consider, we find that the central value of $\Delta a_\mu^\text{exp}$ can be reached without generating too large corrections to the lepton masses. We hence conclude that this model qualifies as a viable and attractive lepton-flavoured DM model that at the same time solves the $(g-2)_\mu$ anomaly.

  2 citations

• Exact entanglement in the driven quantum symmetric simple exclusion process

  Denis Bernard, Ludwig Hruza

  SciPost Phys. 15, 175 (2023) · published 20 October 2023 | Toggle abstract · pdf

  Entanglement properties of driven quantum systems can potentially differ from the equilibrium situation due to long range coherences. We confirm this observation by studying a suitable toy model for mesoscopic transport: the open quantum symmetric simple exclusion process (QSSEP). We derive exact formulae for its mutual information between different subsystems in the steady state and show that it satisfies a volume law. Surprisingly, the QSSEP entanglement properties only depend on data related to its transport properties and we suspect that such a relation might hold for more general mesoscopic systems. Exploiting the free probability structure of QSSEP, we obtain these results by developing a new method to determine the eigenvalue spectrum of sub-blocks of random matrices from their so-called local free cumulants - a mathematical result on its own with potential applications in the theory of random matrices. As an illustration of this method, we show how to compute expectation values of observables in systems satisfying the Eigenstate Thermalization Hypothesis (ETH) from the local free cumulants.

  4 citations

• Local operator entanglement in spin chains

  Eric Mascot, Masahiro Nozaki, Masaki Tezuka

  SciPost Phys. Core 6, 070 (2023) · published 20 October 2023 | Toggle abstract · pdf

  Understanding how and whether local perturbations can affect the entire quantum system is a fundamental step in understanding non-equilibrium phenomena such as thermalization. This knowledge of non-equilibrium phenomena is applicable for quantum computation, as many quantum computers employ non-equilibrium processes for computations. In this paper, we investigate the evolution of bi- and tripartite operator mutual information of the time-evolution operator and the Pauli spin operators in the one-dimensional Ising model with magnetic field and the disordered Heisenberg model to study the properties of quantum circuits. In the Ising model, the early-time evolution qualitatively follows an effective light cone picture, and the late-time value is well described by Page's value for a random pure state. In the Heisenberg model with strong disorder, we find that many-body localization prevents the information from propagating and being delocalized. We also find an effective Ising Hamiltonian that describes the time evolution of bi- and tripartite operator mutual information for the Heisenberg model in the large disorder regime.

  1 citation