Publications

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• Rényi complexity in mean-field disordered systems

  Nina Javerzat, Eric Bertin, Misaki Ozawa

  SciPost Phys. 18, 124 (2025) · published 10 April 2025 | Toggle abstract · pdf

  Configurational entropy, or complexity, plays a critical role in characterizing disordered systems such as glasses, yet its measurement often requires significant computational resources. Recently, Rényi entropy, a one-parameter generalization of Shannon entropy, has gained attention across various fields of physics due to its simpler functional form, making it more practical for measurements. In this paper, we compute the Rényi version of complexity for prototypical mean-field disordered models, including the random energy model, its generalization, referred to as the random free energy model, and the $p$-spin spherical model. We first demonstrate that the Rényi complexity with index $m$ is related to the free energy difference for a generalized annealed Franz-Parisi potential with $m$ clones. Detailed calculations show that for models having one-step replica symmetry breaking (RSB), the Rényi complexity vanishes at the Kauzmann transition temperature $T_K$, irrespective of $m>1$, while RSB solutions are required even in the liquid phase. This study strengthens the link between Rényi entropy and the physics of disordered systems and provides theoretical insights for its practical measurements.

• Interaction quenches in Bose gases studied with a time-dependent hypernetted-chain Euler-Lagrange method

  Mathias Gartner, David Miesbauer, Michael Kobler, Julia Freund, Giuseppe Carleo, Robert E. Zillich

  SciPost Phys. 18, 123 (2025) · published 9 April 2025 | Toggle abstract · pdf

  We present a new variational method to study the dynamics of a closed bosonic many-body system, the time-dependent hypernetted-chain Euler-Lagrange method, tHNC. Based on the Jastrow ansatz, it accounts for quantum fluctuations in a non-perturbative way. The tHNC method scales well with the number of dimensions, as demonstrated by our results on one-, two-, and three-dimensional systems. We apply the tHNC method to interaction quenches, i.e. sudden changes of the interaction strength, in homogeneous Bose gases. When the quench is strong enough that the final state has roton excitations (as found and predicted for dipolar and Rydberg-dressed Bose-Einstein condensates, respectively), the pair distribution function exhibits stable oscillations. For validation, we compare tHNC results with time-dependent variational Monte Carlo results in one and two dimensions.

• Emptiness instanton in quantum polytropic gas

  Alexander G. Abanov, Dimitri M. Gangardt

  SciPost Phys. 18, 122 (2025) · published 9 April 2025 | Toggle abstract · pdf

  The emptiness formation problem is addressed for a one-dimensional quantum polytropic gas characterized by an arbitrary polytropic index $\gamma$, which defines the equation of state $P \sim \rho^\gamma$, where $P$ is the pressure and $\rho$ is the density. The problem involves determining the probability of the spontaneous formation of an empty interval in the ground state of the gas. In the limit of a macroscopically large interval, this probability is dominated by an instanton configuration. By solving the hydrodynamic equations in imaginary time, we derive the analytic form of the emptiness instanton. This solution is expressed as an integral representation analogous to those used for correlation functions in Conformal Field Theory. Prominent features of the spatiotemporal profile of the instanton are obtained directly from this representation.

• Lattice T-duality from non-invertible symmetries in quantum spin chains

  Salvatore D. Pace, Arkya Chatterjee, Shu-Heng Shao

  SciPost Phys. 18, 121 (2025) · published 8 April 2025 | Toggle abstract · pdf

  Dualities of quantum field theories are challenging to realize in lattice models of qubits. In this work, we explore one of the simplest dualities, T-duality of the compact boson CFT, and its realization in quantum spin chains. In the special case of the XX model, we uncover an exact lattice T-duality, which is associated with a non-invertible symmetry that exchanges two lattice U(1) symmetries. The latter symmetries flow to the momentum and winding U(1) symmetries with a mixed anomaly in the CFT. However, the charge operators of the two U(1) symmetries do not commute on the lattice and instead generate the Onsager algebra. We discuss how some of the anomalies in the CFT are nonetheless still exactly realized on the lattice and how the lattice U(1) symmetries enforce gaplessness. We further explore lattice deformations preserving both U(1) symmetries and find a rich gapless phase diagram with special $\mathrm{Spin}(2k)_1$ WZW model points and whose phase transitions all have dynamical exponent $z>1$.

  10 citations

• Universal aspects of high-temperature relaxation dynamics in random spin models

  Tian-Gang Zhou, Wei Zheng, Pengfei Zhang

  SciPost Phys. 18, 120 (2025) · published 8 April 2025 | Toggle abstract · pdf

  Universality is a crucial concept in modern physics, allowing us to capture the essential features of a system's behavior using a small set of parameters. In this work, we unveil universal spin relaxation dynamics in anisotropic random Heisenberg models with infinite-range interactions at high temperatures. Starting from a polarized state, the total magnetization can relax monotonically or decay with long-lived oscillations, determined by the sign of a universal single function $A=-\xi_1^2+\xi_2^2-4\xi_2\xi_3+\xi_3^2$. Here $(\xi_1,\xi_3,\xi_3)$ characterizes the anisotropy of the Heisenberg interaction. Furthermore, the oscillation shows up only for $A>0$, with frequency $\Omega \propto \sqrt{A}$. This result is derived from the Kadanoff-Baym equation under the melon diagram approximation, which is consistent with numerical solutions. Furthermore, we verify our theory and approximation using exact diagonalization, albeit for a small system size of $N=8$. Our study sheds light on the universal aspect of quantum many-body dynamics beyond low energy limit.

  1 citation

• Universal and non-universal large deviations in critical systems

  Ivan Balog, Bertrand Delamotte, Adam Rançon

  SciPost Phys. 18, 119 (2025) · published 2 April 2025 | Toggle abstract · pdf

  Rare events play a crucial role in understanding complex systems. Characterizing and analyzing them in scale-invariant situations is challenging due to strong correlations. In this work, we focus on characterizing the tails of probability distribution functions (PDFs) for these systems. Using a variety of methods, perturbation theory, functional renormalization group, hierarchical models, large $n$ limit, and Monte Carlo simulations, we investigate universal rare events of critical $O(n)$ systems. Additionally, we explore the crossover from universal to nonuniversal behavior in PDF tails, extending Cramér's series to strongly correlated variables. Our findings highlight the universal and nonuniversal aspects of rare event statistics. We also discuss the ubiquity of this power-law corrections to the leading compressed-exponential decay in these tails in and out-of-equilibrium.

  3 citations

• Exact full-RSB SAT/UNSAT transition in infinitely wide two-layer neural networks

  Brandon L. Annesi, Enrico M. Malatesta, Francesco Zamponi

  SciPost Phys. 18, 118 (2025) · published 2 April 2025 | Toggle abstract · pdf

  We analyze the problem of storing random pattern-label associations using two classes of continuous non-convex weights models, namely the perceptron with negative margin and an infinite-width two-layer neural network with non-overlapping receptive fields and generic activation function. Using a full-RSB Ansatz we compute the exact value of the SAT/UNSAT transition. Furthermore, in the case of the negative perceptron we show that the overlap distribution of typical states displays an overlap gap (a disconnected support) in certain regions of the phase diagram defined by the value of the margin and the density of patterns to be stored. This implies that some recent theorems that ensure convergence of Approximate Message Passing (AMP) based algorithms to capacity are not applicable. Finally, we show that Gradient Descent is not able to reach the maximal capacity, irrespectively of the presence of an overlap gap for typical states. This finding, similarly to what occurs in binary weight models, suggests that gradient-based algorithms are biased towards highly atypical states, whose inaccessibility determines the algorithmic threshold.

  4 citations

• Full event particle-level unfolding with variable-length latent variational diffusion

  Alexander Shmakov, Kevin Greif, Michael James Fenton, Aishik Ghosh, Pierre Baldi, Daniel Whiteson

  SciPost Phys. 18, 117 (2025) · published 1 April 2025 | Toggle abstract · pdf

  The measurements performed by particle physics experiments must account for the imperfect response of the detectors used to observe the interactions. One approach, unfolding, statistically adjusts the experimental data for detector effects. Recently, generative machine learning models have shown promise for performing unbinned unfolding in a high number of dimensions. However, all current generative approaches are limited to unfolding a fixed set of observables, making them unable to perform full-event unfolding in the variable dimensional environment of collider data. A novel modification to the variational latent diffusion model (VLD) approach to generative unfolding is presented, which allows for unfolding of high- and variable-dimensional feature spaces. The performance of this method is evaluated in the context of semi-leptonic $t\bar{t}$ production at the Large Hadron Collider.

  10 citations

• Photon counting statistics in Gaussian bosonic networks

  Kalle Sulo Ukko Kansanen, Pedro Portugal, Christian Flindt, Peter Samuelsson

  SciPost Phys. 18, 116 (2025) · published 1 April 2025 | Toggle abstract · pdf

  The statistics of transmitted photons in microwave cavities play a foundational role in microwave quantum optics and its technological applications. By utilizing quantum mechanical phase-space methods, we here develop a general theory of the photon counting statistics in Gaussian bosonic networks consisting of driven cavities with beamsplitter interactions and two-mode-squeezing. The dynamics of the network can be captured by a Lyapunov equation for the covariance matrix of the cavity fields, which generalizes to a Riccati equation, when counting fields are included. By solving the Riccati equation, we obtain the statistics of emitted and absorbed photons as well as the time-dependent correlations encoded in waiting time distributions and second-order coherence functions. To illustrate our theoretical framework, we first apply it to a simple linear network consisting of two coupled cavities, for which we evaluate the photon cross-correlations and discuss connections between the photon emission statistics and the entanglement between the cavities. We then consider a bosonic circulator consisting of three coupled cavities, for which we investigate how a synthetic flux may affect the direction of the photon flow, similarly to recent experiments. Our general framework paves the way for systematic investigations of the photon counting statistics in Gaussian bosonic networks.

• How to escape atypical regions in the symmetric binary perceptron: A journey through connected-solutions states

  Damien Barbier

  SciPost Phys. 18, 115 (2025) · published 31 March 2025 | Toggle abstract · pdf

  We study the binary symmetric perceptron model, and in particular its atypical solutions. While the solution-space of this problem is dominated by isolated configurations, it is also solvable for a certain range of constraint density $\alpha$ and threshold $\kappa$. We provide in this paper a statistical measure probing sequences of solutions, where two consecutive elements shares a strong overlap. After simplifications, we test its predictions by comparing it to Monte-Carlo simulations. We obtain good agreement and show that connected states with a Markovian correlation profile can fully decorrelate from their initialization only for $\kappa>\kappa_{\rm no-mem.\, state}$ ($\kappa_{\rm no-mem.\, state}\sim \sqrt{0.91\log(N)}$ for $\alpha=0.5$ and $N$ being the dimension of the problem). For $\kappa<\kappa_{\rm no-mem.\, state}$, we show that decorrelated sequences still exist but have a non-trivial correlations profile. To study this regime we introduce an Ansatz for the correlations that we label as the nested Markov chain.

  1 citation