Clément Berthière, Benoit Estienne, Jean-Marie Stéphan, William Witczak-Krempa

SciPost Phys. 19, 122 (2025) · published 7 November 2025 | Toggle abstract · pdf

Fluctuations of observables provide unique insights into the nature of physical systems, and their study stands as a cornerstone of both theoretical and experimental science. Generalized fluctuations, or cumulants, provide information beyond the mean and variance of an observable. In this paper, we develop a systematic method to determine the asymptotic behavior of cumulants of local observables as the region becomes large. Our analysis reveals that the expansion is closely tied to the geometric characteristics of the region and its boundary, with coefficients given by convex moments of the connected correlation function: the latter is integrated against intrinsic volumes of convex polytopes built from the coordinates, which can be interpreted as average shadows. A particular application of our method shows that, in two dimensions, the leading behavior of odd cumulants of conserved quantities is topological, specifically depending on the Euler characteristic of the region. We illustrate these results with the paradigmatic strongly-interacting system of two-dimensional quantum Hall state at filling fraction $1/2$, by performing Monte-Carlo calculations of the skewness (third cumulant) of particle number in the Laughlin state.

Zhen Huang, Denis Golež, Hugo U. R. Strand, Jason Kaye

SciPost Phys. 19, 121 (2025) · published 7 November 2025 | Toggle abstract · pdf

We present an efficient separation of variables algorithm for the evaluation of imaginary time Feynman diagrams appearing in the bold pseudo-particle strong coupling expansion of the Anderson impurity model. The algorithm uses a fitting method based on AAA rational approximation and numerical optimization to obtain a sum-of-exponentials expansion of the hybridization function, which is then used to decompose the diagrams. A diagrammatic formulation of the algorithm leads to an automated procedure for diagrams of arbitrary order and topology. We also present methods of stabilizing the self-consistent solution of the pseudo-particle Dyson equation. The result is a low-cost and high-order accurate impurity solver for quantum embedding methods using general multi-orbital hybridization functions at low temperatures, appropriate for low-to-intermediate expansion orders. In addition to other benchmark examples, we use our solver to perform a dynamical mean-field theory study of a minimal model of the strongly correlated compound Ca$_2$RuO$_4$, describing the anti-ferromagnetic transition and the in- and out-of-plane anisotropy induced by spin-orbit coupling.

Kshitij Sharma, Himanshu Sahu, Subroto Mukerjee

SciPost Phys. 19, 120 (2025) · published 7 November 2025 | Toggle abstract · pdf

In this study, we explore the interplay between $\mathcal{PT}$-symmetry and quantum chaos in a non-Hermitian dynamical system. We consider an extension of the standard diagnostics of quantum chaos, namely the complex level spacing ratio and out-of-time-ordered correlators (OTOCs), to study the $\mathcal{PT}$-symmetric quantum kicked rotor model. The kicked rotor has long been regarded as a paradigmatic dynamic system to study classical and quantum chaos. By introducing non-Hermiticity in the quantum kicked rotor, we uncover new phases and transitions that are absent in the Hermitian system. From the study of the complex level spacing ratio, we locate three regimes – one which is integrable and $\mathcal{PT}$-symmetry, another which is chaotic with $\mathcal{PT}$-symmetry and a third which is chaotic but with broken $\mathcal{PT}$-symmetry. We find that the complex level spacing ratio can distinguish between all three phases. Since calculations of the OTOC can be related to those of the classical Lyapunov exponent in the semi-classical limit, we investigate its nature in these regimes and at the phase boundaries. In the phases with $\mathcal{PT}$-symmetry, the OTOC exhibits behaviour akin to what is observed in the Hermitian system in both the integrable and chaotic regimes. Moreover, in the $\mathcal{PT}$-symmetry broken phase, the OTOC demonstrates additional exponential growth stemming from the complex nature of the eigenvalue spectrum at later times. We derive the analytical form of the late-time behaviour of the OTOC. By defining a normalized OTOC to mitigate the effects caused by $\mathcal{PT}$-symmetry breaking, we show that the OTOC exhibits singular behaviour at the transition from the $\mathcal{PT}$-symmetric chaotic phase to the $\mathcal{PT}$-symmetry broken, chaotic phase.

Benoit Estienne, Yacine Ikhlef, Andrei Rotaru

SciPost Phys. 19, 119 (2025) · published 6 November 2025 | Toggle abstract · pdf

We present a general method for calculating Rényi entropies in the ground state of a one-dimensional critical system with mixed open boundaries, for an interval starting at one of its ends. Technically, we consider the case when the boundary operator implementing the change of boundary conditions is degenerate under the Virasoro algebra. By exploiting the null-vectors conditions, we derive the ordinary differential equations that govern the scaling functions associated to the entropies. In particular, we provide an explicit formula for the second Rényi entropy. Additionally, we identify and compute the leading finite-size corrections to compare our theoretical results with numerical data for the Ising and three-state Potts critical chains.

Ivo H. A. Knottnerus, Yu Chih Tseng (曾于誌), Alexander Urech, Robert J. C. Spreeuw, Florian Schreck

SciPost Phys. 19, 118 (2025) · published 31 October 2025 | Toggle abstract · pdf

We present fast parallel rearrangement of single atoms in optical tweezers into arbitrary geometries by updating holograms displayed by an ultra fast spatial light modulator. Using linear interpolation of the tweezer position and the optical phase between the start and end arrays, we can calculate and display holograms every few ms, limited by technology. To show the versatility of our method, we sort the same atomic sample into multiple geometries with success probabilities of $0.996(2)$ per rearrangement cycle. This makes the method a useful tool for rearranging large atom arrays for quantum computation and quantum simulation.