Publications

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Exact finite-size scaling of the maximum likelihood spectra in the quenched and annealed Sherrington-Kirkpatrick spin glass

Ding Wang, Lei-Han Tang

SciPost Phys. 17, 106 (2024) · published 8 October 2024 | · pdf

Fine resolution of the discrete eigenvalues at the spectral edge of an $N× N$ random matrix is required in many applications. Starting from a finite-size scaling ansatz for the Stieltjes transform of the maximum likelihood spectrum, we demonstrate that the scaling function satisfies a first-order ODE of the Riccati type. Further transformation yields a linear second-order ODE for the characteristic function, whose nodes determine leading eigenvalues. Using this technique, we examine in detail the spectral crossover of the annealed Sherrington-Kirkpatrick (SK) spin glass model, where a gap develops below a critical temperature. Our analysis provides analytic predictions for the finite-size scaling of the spin condensation phenomenon in the annealed SK model, validated by Monte Carlo simulations. Deviation of scaling amplitudes from their predicted values is observed in the critical region due to eigenvalue fluctuations. More generally, rescaling the spectral axis, adjusted to the distance of neighboring eigenvalues, offers a powerful approach to handling singularities in the infinite size limit.
Quantum chaos, randomness and universal scaling of entanglement in various Krylov spaces

Hai-Long Shi, Augusto Smerzi, Luca Pezzè

SciPost Phys. 19, 102 (2025) · published 17 October 2025 | · pdf

Multipartite entanglement is a crucial resource for advancing quantum technologies, with considerable research efforts directed toward achieving its rapid and scalable generation. In this work, we derive an analytical expression for the time-averaged quantum Fisher information (QFI), enabling the detection of scalable multipartite entanglement dynamically generated by all quantum chaotic systems governed by Dyson's ensembles. Our approach integrates concepts of randomness and quantum chaos, demonstrating that the QFI is universally determined by the structure and dimension of the Krylov space that confines the chaotic dynamics. In particular, the QFI ranges from $N^2/3$ for $N$ qubits in the permutation-symmetric subspace (e.g. for chaotic kicked top models with long-range interactions), to $N$ when the dynamics extend over the full Hilbert space with or without bit reversal symmetry or parity symmetry (e.g. in chaotic models with short-range Ising-like interactions). In the former case, the QFI reveals multipartite entanglement among $N/3$ qubits and highlights the power of chaotic collective spin systems in generating scalable multipartite entanglement. Interestingly this result can be related to isotropic substructures in the Wigner distribution of chaotic states and demonstrates the efficacy of quantum chaos for Heisenberg-scaling quantum metrology. Finally, our general expression for the QFI agrees with that obtained for random states and, differently from out-of-time-order-correlators, it can also distinguish chaotic from integrable unstable spin dynamics.
Topological states in double monolayer graphene

Ying-Hai Wu

SciPost Phys. 13, 094 (2022) · published 12 October 2022 | · pdf

Motivated by the experiments on double monolayer graphene that observe a variety of fractional quantum Hall states [Liu et al., Nat. Phys. 15, 893 (2019); Li et al., Nat. Phys. 15, 898 (2019)], we study the special setting in which two monolayers have different areas. It has not been considered before and allows us to construct a class of exotic topological states. The elementary excitations of these states do not carry fractional charges but obey fractional statistics. This is in sharp contrast to all previously studied cases, where the two properties are intimately connected and serve as hallmarks of fractional quantum Hall states. Numerical calculations are performed to demonstrate that some states can be realized with realistic parameters.
Analytical expression for $\pi$-ton vertex contributions to the optical conductivity

Juraj Krsnik, Anna Kauch, Karsten Held

SciPost Phys. 18, 138 (2025) · published 25 April 2025 | · pdf

Vertex corrections from the transversal particle-hole channel, so-called $\pi$-tons, are generic in models for strongly correlated electron systems and can lead to a displaced Drude peak (DDP). Here, we derive the analytical expression for these $\pi$-tons, and how they affect the optical conductivity as a function of correlation length $\xi$, fermion lifetime $\tau$, temperature $T$, and coupling strength to spin or charge fluctuations $g$. In particular, for $T\rightarrow T_c$, the critical temperature for antiferromagnetic or charge ordering, the dc vertex correction is algebraic $\sigma_{VERT}^{dc}\propto \xi \sim (T-T_c)^{-\nu}$ in one dimension and logarithmic $\sigma_{VERT}^{dc}\propto \ln\xi \sim \nu \ln (T-T_c)$ in two dimensions. Here, $\nu$ is the critical exponent for the correlation length. If we have the exponential scaling $\xi \sim e^{1/T}$ of an ideal two-dimensional system, the DDP becomes more pronounced with increasing $T$ but fades away at low temperatures where only a broadening of the Drude peak remains, as it is observed experimentally, with the dc resistivity exhibiting a linear $T$ dependence at low temperatures. Further, we find the maximum of the DPP to be given by the inverse lifetime: $\omega_{DDP} \sim 1/\tau$. These characteristic dependencies can guide experiments to evidence $\pi$-tons in actual materials.
Free growth under tension

Chenyun Yao, Jens Elgeti

SciPost Phys. 19, 097 (2025) · published 15 October 2025 | · pdf

Ever since the ground breaking work of Trepat et al. in 2009, we know that cell colonies growing on a substrate can be under tensile mechanical stress. The origin of tension has so far been attributed to cellular motility forces being oriented outward of the colony. Works in the field mainly revolve around how this orientation of the forces can be explained, ranging from velocity alignment to self-sorting due to self-propulsion. In this work, we demonstrate that tension in growing colonies can also be explained without cellular motility forces! Using a combination of well established tissue growth simulation technique and analytical modelling, we show how tension can arise as a consequence of simple mechanics of growing tissues. Combining these models with a minimalistic motility model shows how colonies can expand while under even larger tension. Furthermore, our results and analytical models provide novel analysis procedures to identify the underlying mechanics.
New examples of Abelian D4D2D0 indices

Joseph McGovern

SciPost Phys. 20, 015 (2026) · published 20 January 2026 | · pdf

We apply the methods of [S. Alexandrov et al., Commun. Number Theory Phys. 18, 49 (2024)] to compute generating series of D4D2D0 indices with a single unit of D4 charge for several compact Calabi-Yau threefolds, assuming modularity of these indices. Our examples include a $\mathbb{Z}_7$ quotient of Rødland's pfaffian threefold, a $\mathbb{Z}_5$ quotient of Hosono-Takagi's double quintic symmetroid threefold, the $\mathbb{Z}_3$ quotient of the bicubic intersection in $\mathbb{P}^5$, and the $\mathbb{Z}_5$ quotient of the quintic hypersurface in $\mathbb{P}^4$. For these examples we compute GV invariants to the highest genus that available boundary conditions make possible, and for the case of the quintic quotient alone this is sufficiently many GV invariants for us to make one nontrivial test of the modularity of these indices. As discovered in [S. Alexandrov et al., Commun. Number Theory Phys. 18, 49 (2024)], the assumption of modularity allows us to compute terms in the topological string genus expansion beyond those obtainable with previously understood boundary data. We also consider five multiparameter examples with $h^{1,1}>1$, for which only a single index needs to be computed for modularity to fix the rest. We propose a modification of the formula in [S. Alexandrov et al., Adv. Theor. Math. Phys. 27, 683 (2023)] that incorporates torsion to solve these models. Our new examples are only tractable because they have sufficiently small triple intersection and second Chern numbers, which happens because all of our examples are suitable quotient manifolds. In an appendix we discuss some aspects of quotient threefolds and their Wall data.
Mechanical stability of resonant Bose-Fermi mixtures

Christian Gualerzi, Leonardo Pisani, Pierbiagio Pieri

SciPost Phys. 19, 039 (2025) · published 14 August 2025 | · pdf

We investigate the mechanical stability of Bose-Fermi mixtures at zero temperature in the presence of a tunable Feshbach resonance, which induces a competition between boson condensation and boson-fermion pairing when the boson density is smaller than the fermion density. Using a many-body diagrammatic approach validated by fixed-node Quantum Monte Carlo calculations and supported by recent experimental observations, we determine the minimal amount of boson-boson repulsion required to guarantee the stability of the mixture across the entire range of boson-fermion interactions from weak to strong coupling. Our stability phase diagrams indicate that mixtures with boson-to-fermion mass ratios near two, such as the $^{87}$Rb-$^{40}$K system, exhibit optimal stability conditions. Moreover, by applying our results to a recent experiment with a $^{23}$Na-$^{40}$K mixture, we find that the boson-boson repulsion was insufficient to ensure stability, suggesting that the experimental timescale was short enough to avoid mechanical collapse. On the other hand, we also show that even in the absence of boson-boson repulsion, Bose-Fermi mixtures become intrinsically stable beyond a certain coupling strength, preceding the quantum phase transition associated with the vanishing of the bosonic condensate. We thus propose an experimental protocol for observing this quantum phase transition in a mechanically stable configuration.
Random matrices and the free energy of Ising-like models with disorder

Nils Gluth, Thomas Guhr, Alfred Hucht

SciPost Phys. 17, 122 (2024) · published 30 October 2024 | · pdf

We consider an Ising model with quenched surface disorder, the disorder average of the free energy is the main object of interest. Explicit expressions for the free energy distribution are difficult to obtain if the quenched surface spins take values of $± 1$. Thus, we choose a different approach and model the surface disorder by Gaussian random matrices. The distribution of the free energy is calculated. We chose skew-circulant random matrices and analytically compute the characteristic function of the free energy distribution. From the characteristic function we numerically calculate the distribution and show that it becomes log-normal for sufficiently large dimensions of the disorder matrices, and in the limit of infinitely large matrices tends to a Gaussian. Furthermore, we establish a connection to the central limit theorem.
Conformal maps and superfluid vortex dynamics on curved and bounded surfaces: The case of an elliptical boundary

Matteo Caldara, Andrea Richaud, Pietro Massignan, Alexander L. Fetter

SciPost Phys. 17, 039 (2024) · published 8 August 2024 | · pdf

Recent advances in cold-atom platforms have made real-time dynamics accessible, renewing interest in the motion of superfluid vortices in two-dimensional domains. Here we show that the energy and the trajectories of arbitrary vortex configurations may be computed on a complicated (curved or bounded) surface, provided that one knows a conformal map that links the latter to a simpler domain (like the full plane, or a circular boundary). We also prove that Hamilton's equations based on the vortex energy agree with the complex dynamical equations for the vortex dynamics, demonstrating that the vortex trajectories are constant-energy curves. We use these ideas to study the dynamics of vortices in a two-dimensional incompressible superfluid with an elliptical boundary, and we derive an analytical expression for the complex potential describing the hydrodynamic flow throughout the fluid. For a vortex inside an elliptical boundary, the orbits are nearly self-similar ellipses.
Entanglement Rényi entropies in celestial holography

Federico Capone, Andy O’Bannon, Ronnie Rodgers, Somyadip Thakur

SciPost Phys. 19, 042 (2025) · published 15 August 2025 | · pdf

Celestial holography is the conjecture that scattering amplitudes in $(d+2)$-dimensional asymptotically Minkowski spacetimes are dual to correlators of a $d$-dimensional conformal field theory (CFT) on the celestial sphere, called the celestial CFT (CCFT). In a CFT, we can calculate sub-region entanglement Rényi entropies (EREs), including entanglement entropy (EE), from correlators of twist operators, via the replica trick. We argue that CCFT twist operators are holographically dual to cosmic branes in the $(d+2)$-dimensional spacetime, and that their correlators are holographically dual to the $(d+2)$-dimensional partition function (the vacuum-to-vacuum scattering amplitude) in the presence of these cosmic branes. We hence compute the EREs of a spherical sub-region of the CCFT's conformal vacuum, finding the form dictated by conformal symmetry, including a universal contribution determined by the CCFT's sphere partition function (odd $d$) or Weyl anomaly (even $d$). We find that this universal contribution vanishes when $d=4$ mod $4$, and otherwise is proportional to $i$ times the $d^{\textrm{th}}$ power of the $(d+2)$-dimensional long-distance cutoff in Planck units.

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