Publications

Order by: publication date number of citations

• Holographic quantum scars

  Diego Liska, Vladimir Gritsev, Ward Vleeshouwers, Jiří Minář

  SciPost Phys. 15, 106 (2023) · published 20 September 2023 | Toggle abstract · pdf

  We discuss a construction of quantum many-body scars in the context of holography. We consider two-dimensional conformal field theories and use their dynamical symmetries, naturally realized through the Virasoro algebra, to construct scarred states. By studying their Loschmidt amplitude, we evaluate the states' periodic properties. A geometrical interpretation allows us to compute the expectation value of the stress tensor and entanglement entropy of these scarred states. We show that their holographic dual is related by a diffeomorphism to empty AdS, even for energies above the black hole threshold. We also demonstrate that expectation values in the scarred states are generally non-thermal and that their entanglement entropy grows with the energy as $\log(E)$ in contrast to $\sqrt{E}$ for the typical (bulk) states. Furthermore, we identify fixed points on the CFT plane associated with divergent or vanishing entanglement entropy in the limit where the scarred states have infinite energy.

  8 citations

• Accuracy of restricted Boltzmann machines for the one-dimensional $J_1-J_2$ Heisenberg model

  Luciano Loris Viteritti, Francesco Ferrari, Federico Becca

  SciPost Phys. 12, 166 (2022) · published 19 May 2022 | Toggle abstract · pdf

  Neural networks have been recently proposed as variational wave functions for quantum many-body systems [G. Carleo and M. Troyer, Science 355, 602 (2017)]. In this work, we focus on a specific architecture, known as Restricted Boltzmann Machine (RBM), and analyse its accuracy for the spin-1/2 $J_1-J_2$ antiferromagnetic Heisenberg model in one spatial dimension. The ground state of this model has a non-trivial sign structure, especially for $J_2/J_1>0.5$, forcing us to work with complex-valued RBMs. Two variational Ans\"atze are discussed: one defined through a fully complex RBM, and one in which two different real-valued networks are used to approximate modulus and phase of the wave function. In both cases, translational invariance is imposed by considering linear combinations of RBMs, giving access also to the lowest-energy excitations at fixed momentum $k$. We perform a systematic study on small clusters to evaluate the accuracy of these wave functions in comparison to exact results, providing evidence for the supremacy of the fully complex RBM. Our calculations show that this kind of Ans\"atze is very flexible and describes both gapless and gapped ground states, also capturing the incommensurate spin-spin correlations and low-energy spectrum for $J_2/J_1>0.5$. The RBM results are also compared to the ones obtained with Gutzwiller-projected fermionic states, often employed to describe quantum spin models [F. Ferrari, A. Parola, S. Sorella and F. Becca, Phys. Rev. B 97, 235103 (2018)]. Contrary to the latter class of variational states, the fully-connected structure of RBMs hampers the transferability of the wave function from small to large clusters, implying an increase of the computational cost with the system size.

  8 citations

• Deconstructing S-Duality

  Kyle Aitken, Andreas Karch, Brandon Robinson

  SciPost Phys. 4, 032 (2018) · published 19 June 2018 | Toggle abstract · pdf

  We use the technique of deconstruction to lift dualities from 2+1 to 3+1 dimensions. In this work we demonstrate the basic idea by deriving S-duality of maximally supersymmetric electromagnetism in 3+1 dimensions from mirror symmetry in 2+1. We also study the deconstruction of a non-supersymmetric duality in 3+1 dimensions using Abelian bosonization in 2+1 dimensions.

  8 citations

• What's anomalous in LHC jets?

  Thorsten Buss, Barry M. Dillon, Thorben Finke, Michael Krämer, Alessandro Morandini, Alexander Mück, Ivan Oleksiyuk, Tilman Plehn

  SciPost Phys. 15, 168 (2023) · published 17 October 2023 | Toggle abstract · pdf

  Searches for anomalies are a significant motivation for the LHC and help define key analysis steps, including triggers. We discuss specific examples how LHC anomalies can be defined through probability density estimates, evaluated in a physics space or in an appropriate neural network latent space, and discuss the model-dependence in choosing an appropriate data parameterisation. We illustrate this for classical k-means clustering, a Dirichlet variational autoencoder, and invertible neural networks. For two especially challenging scenarios of jets from a dark sector we evaluate the strengths and limitations of each method.

  8 citations

• Gravitational Regge bounds

  Kelian Häring, Alexander Zhiboedov

  SciPost Phys. 16, 034 (2024) · published 26 January 2024 | Toggle abstract · pdf

  We review the basic assumptions and spell out the detailed arguments that lead to the bound on the Regge growth of gravitational scattering amplitudes. The minimal extra ingredient compared to the gapped case - in addition to unitarity, analyticity, subexponentiality, and crossing - is the assumption that scattering at large impact parameters is controlled by known semi-classical physics. We bound the Regge growth of amplitudes both with the fixed transferred momentum and smeared over it. Our basic conclusion is that gravitational scattering amplitudes admit dispersion relations with two subtractions. For a sub-class of smeared amplitudes, black hole formation reduces the number of subtractions to one. Finally, using dispersion relations with two subtractions we derive bounds on the local growth of relativistic scattering amplitudes. Schematically, the local bound states that the amplitude cannot grow faster than $s^2$. The results obtained in the paper are valid for $d> 4$ for which the $2\to2$ scattering amplitude is well-defined.

  8 citations

• Scaling at quantum phase transitions above the upper critical dimension

  A. Langheld, J. A. Koziol, P. Adelhardt, S. C. Kapfer, K. P. Schmidt

  SciPost Phys. 13, 088 (2022) · published 10 October 2022 | Toggle abstract · pdf

  The hyperscaling relation and standard finite-size scaling (FSS) are known to break down above the upper critical dimension due to dangerous irrelevant variables. We establish a coherent formalism for FSS at quantum phase transitions above the upper critical dimension following the recently introduced Q-FSS formalism for thermal phase transitions. Contrary to long-standing belief, the correlation sector is affected by dangerous irrelevant variables. The presented formalism recovers a generalized hyperscaling relation and FSS form. Using this new FSS formalism, we determine the full set of critical exponents for the long-range transverse-field Ising chain in all criticality regimes ranging from the nearest-neighbor to the long-range mean field regime. For the same model, we also explicitly confirm the effect of dangerous irrelevant variables on the characteristic length scale.

  8 citations

• Adaptive numerical solution of Kadanoff-Baym equations

  Francisco Meirinhos, Michael Kajan, Johann Kroha, Tim Bode

  SciPost Phys. Core 5, 030 (2022) · published 27 May 2022 | Toggle abstract · pdf

  A time-stepping scheme with adaptivity in both the step size and the integration order is presented in the context of non-equilibrium dynamics described via Kadanoff-Baym equations. The accuracy and effectiveness of the algorithm are analysed by obtaining numerical solutions of exactly solvable models. We find a significant reduction in the number of time-steps compared to fixed-step methods. Due to the at least quadratic scaling of Kadanoff-Baym equations, reducing the amount of steps can dramatically increase the accessible integration time, opening the door for the study of long-time dynamics in interacting systems. A selection of illustrative examples is provided, among them interacting and open quantum systems as well as classical stochastic processes. An open-source implementation of our algorithm in the scientific-computing language Julia is made available.

  8 citations

• On 2d CFTs that interpolate between minimal models

  Sylvain Ribault

  SciPost Phys. 6, 075 (2019) · published 25 June 2019 | Toggle abstract · pdf

  We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational, correlation functions of these CFTs may tend to correlation functions of minimal models, or diverge, or have finite limits which can be logarithmic. These results are based on analytic relations between four-point structure constants and residues of conformal blocks.

  8 citations

• Unsupervised mapping of phase diagrams of 2D systems from infinite projected entangled-pair states via deep anomaly detection

  Korbinian Kottmann, Philippe Corboz, Maciej Lewenstein, Antonio Acín

  SciPost Phys. 11, 025 (2021) · published 9 August 2021 | Toggle abstract · pdf

  We demonstrate how to map out the phase diagram of a two dimensional quantum many body system with no prior physical knowledge by applying deep \textit{anomaly detection} to ground states from infinite projected entangled pair state simulations. As a benchmark, the phase diagram of the 2D frustrated bilayer Heisenberg model is analyzed, which exhibits a second-order and two first-order quantum phase transitions. We show that in order to get a good qualitative picture of the transition lines, it suffices to use data from the cost-efficient simple update optimization. Results are further improved by post-selecting ground-states based on their energy at the cost of contracting the tensor network once. Moreover, we show that the mantra of ``more training data leads to better results'' is not true for the learning task at hand and that, in principle, one training example suffices for this learning task. This puts the necessity of neural network optimizations for these learning tasks in question and we show that, at least for the model and data at hand, a simple geometric analysis suffices.

  8 citations

• Generalized eigenproblem without fermion doubling for Dirac fermions on a lattice

  M. J. Pacholski, G. Lemut, J. Tworzydło, C. W. J. Beenakker

  SciPost Phys. 11, 105 (2021) · published 14 December 2021 | Toggle abstract · pdf

  The spatial discretization of the single-cone Dirac Hamiltonian on the surface of a topological insulator or superconductor needs a special "staggered" grid, to avoid the appearance of a spurious second cone in the Brillouin zone. We adapt the Stacey discretization from lattice gauge theory to produce a generalized eigenvalue problem, of the form ${\mathcal H}\psi=E {\mathcal P}\psi$, with Hermitian tight-binding operators ${\mathcal H}$, ${\mathcal P}$, a locally conserved particle current, and preserved chiral and symplectic symmetries. This permits the study of the spectral statistics of Dirac fermions in each of the four symmetry classes A, AII, AIII, and D.

  7 citations