Publications

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Critical dynamics and cyclic memory retrieval in non-reciprocal Hopfield networks

Shuyue Xue, Mohammad Maghrebi, George I. Mias, Carlo Piermarocchi

SciPost Phys. 19, 100 (2025) · published 16 October 2025 | · pdf

We study Hopfield networks with non-reciprocal coupling inducing switches between memory patterns. Dynamical phase transitions occur between phases of no memory retrieval, retrieval of multiple point-attractors, and limit-cycles. The limit cycle phase is bounded by a Hopf bifurcation line and a fold bifurcation line. Autocorrelation scales as $\tilde{C}(\tau/N^\zeta)$, with $\zeta = 1/2$ on the Hopf line and $\zeta = 1/3$ on the fold line. Perturbations of strength $F$ on the Hopf line exhibit response times scaling as $|F|^{-2/3}$, while they induce switches in a controlled way within times scaling as $|F|^{-1/2}$ in the fold line. A Master Equation approach numerically verifies the critical behavior predicted analytically. We discuss how these networks could model biological processes near a critical threshold of cyclic instability evolving through multi-step transitions.
Single-gap isotropic $s-$wave superconductivity in single crystals AuSn$_4$

Sunil Ghimire, Kamal R. Joshi, Elizabeth H. Krenkel, Makariy A. Tanatar, Marcin Kończykowski, Romain Grasset, Paul C. Canfield, Ruslan Prozorov

SciPost Phys. 17, 116 (2024) · published 21 October 2024 | · pdf

London, $\lambda_L (T)$, and Campbell, $\lambda_{C} (T)$, penetration depths were measured in single crystals of a topological superconductor candidate AuSn$_4$. At low temperatures, $\lambda_L (T)$ is exponentially attenuated and, if fitted with the power law, $\lambda(T) \sim T^n$, gives exponents $n>4$, indistinguishable from the isotropic single $s-$wave gap Bardeen-Cooper-Schrieffer (BCS) asymptotic. The superfluid density fits perfectly in the entire temperature range to the BCS theory. The superconducting transition temperature, $T_c = 2.40 ± 0.05$ K, does not change after 2.5 MeV electron irradiation, indicating the validity of the Anderson theorem for isotropic $s-$wave superconductors. Campbell penetration depth before and after electron irradiation shows no hysteresis between the zero-field cooling (ZFC) and field cooling (FC) protocols, consistent with the parabolic pinning potential. Interestingly, the critical current density estimated from the original Campbell theory decreases after irradiation, implying that a more sophisticated theory involving collective effects is needed to describe vortex pinning in this system. In general, our thermodynamic measurements strongly suggest that the bulk response of the AuSn$_4$ crystals is fully consistent with the isotropic $s-$wave weak-coupling BCS superconductivity.
Andreev bound states at boundaries of polarized 2D Fermi superfluids with s-wave pairing and spin-orbit coupling

Kadin Thompson, Joachim Brand, Ulrich Zuelicke

SciPost Phys. 14, 115 (2023) · published 16 May 2023 | · pdf

A topological superfluid phase characterized by an emergent chiral-p-wave pair potential is expected to form in a two-dimensional Fermi superfluid subject to s-wave pairing, spin-orbit coupling and a large-enough Zeeman splitting. Andreev bound states appear at phase boundaries, including Majorana zero modes whose existence is assured by the bulk-boundary correspondence principle. Here we study the physical properties of these subgap-energy bound states at step-like interfaces using the spin-resolved Bogoliubov-de$\,$Gennes mean-field formalism and assuming small spin-orbit coupling. Extending a recently developed spin-projection technique based on Feshbach partitioning [SciPost Phys. 5, 016 (2018)] combined with the Andreev approximation allows us to obtain remarkably simple analytical expressions for the bound-state energies as well as the majority and minority spin components of their wave functions. Besides the vacuum boundary, where a majority-spin Majorana excitation is encountered, we also consider the boundary between the topological and a nontopological superfluid phase that can appear in a coexistence scenario due to the first-order topological phase transition predicted for this system. At this superfluid-superfluid interface, we find a localized chiral Majorana mode hosted by the minority-spin sector. Our theory further predicts majority-spin subgap-energy bound states similar to those found at a Josephson junction between same-chirality p-wave superfluids. Their presence affects the Majorana mode due to a coupling of minority and majority spin sectors only in the small energy range where their spectra overlap. Our results may inform experimental efforts aimed at realizing and characterizing unconventional Majorana quasiparticles.
Rademacher expansion of modular integrals

Marco Maria Baccianti, Jeevan Chandra, Lorenz Eberhardt, Thomas Hartman, Sebastian Mizera

SciPost Phys. 19, 103 (2025) · published 20 October 2025 | · pdf

We develop a method to evaluate integrals of non-holomorphic modular functions over the fundamental domain of the torus with modular parameter $\tau$ analytically. It proceeds in two steps: first the integral is transformed to a Lorentzian contour by the same strategy that leads to the Lorentzian inversion formula in CFT, and then we apply a two-dimensional version of the Rademacher expansion. This computes the integral in terms of an expansion sensitive to the singular behaviour of the integrand near all the Lorentzian cusps $\tau \to i ∞$, $\bar{\tau} \to x ∈ \mathbb{Q}$. We apply this technique to a variety of examples such as the evaluation of string one-loop partition functions, where it leads to the first analytic formula for the cosmological constants of the bosonic string and the $\mathrm{SO}(16) × \mathrm{SO}(16)$ string.
Boundary chaos: Spectral form factor

Felix Fritzsch, Tomaž Prosen

SciPost Phys. 17, 142 (2024) · published 22 November 2024 | · pdf

Random matrix spectral correlations is a defining feature of quantum chaos. Here, we study such correlations in a minimal model of chaotic many-body quantum dynamics where interactions are confined to the system's boundary, dubbed boundary chaos, in terms of the spectral form factor and its fluctuations. We exactly calculate the latter in the limit of large local Hilbert space dimension $q$ for different classes of random boundary interactions and find it to coincide with random matrix theory, possibly after a non-zero Thouless time. The latter effect is due to a drastic enhancement of the spectral form factor, when integer time and system size fulfill a resonance condition. We compare our semiclassical (large $q$) results with numerics at small local Hilbert space dimension ($q=2,3$) and observe qualitatively similar features as in the semiclassical regime.
Quench dynamics of entanglement from crosscap states

Konstantinos Chalas, Pasquale Calabrese, Colin Rylands

SciPost Phys. 19, 132 (2025) · published 19 November 2025 | · pdf

The linear growth of entanglement after a quench from a state with short-range correlations is a universal feature of many body dynamics. It has been shown to occur in integrable and chaotic systems undergoing either Hamiltonian, Floquet or circuit dynamics and has also been observed in experiments. The entanglement dynamics emerging from long-range correlated states is far less studied, although no less viable using modern quantum simulation experiments. In this work, we investigate the dynamics of the bipartite entanglement entropy and mutual information from initial states which have long-range entanglement with correlation between antipodal points of a finite and periodic system. Starting from these crosscap states, we study both brickwork quantum circuits and Hamiltonian dynamics and find distinct patterns of behaviour depending on the type of dynamics and whether the system is integrable or chaotic. Specifically, we study both dual unitary and random unitary quantum circuits as well as free and interacting fermion Hamiltonians. For integrable systems, we find that after a time delay the entanglement experiences a linear in time decrease followed by a series of revivals, while, in contrast, chaotic systems exhibit constant entanglement entropy. On the other hand, both types of systems experience an immediate linear decrease of the mutual information in time. In chaotic systems this then vanishes, whereas integrable systems instead experience a series of revivals. We show how the quasiparticle and membrane pictures of entanglement dynamics can be modified to describe this behaviour, and derive explicitly the quasiparticle picture in the case of free fermion models which we then extend to all integrable systems.
The effect of dephasing and spin-lattice relaxation during the switching processes in quantum antiferromagnets

Asliddin Khudoyberdiev, Götz S. Uhrig

SciPost Phys. 19, 117 (2025) · published 29 October 2025 | · pdf

The control of antiferromagnetic order can pave the way to large storage capacity as well as fast manipulation of stored data. Here achieving a steady-state of sublattice magnetization after switching is crucial to prevent loss of stored data. The present theoretical approach aims to obtain instantaneous stable states of the order after reorienting the Néel vector in open quantum antiferromagnets using time-dependent Schwinger boson mean-field theory. The Lindblad formalism is employed to couple the system to the environment. The quantum theoretical approach comprises differences in the effects of dephasing, originating from destructive interference of different wave vectors, and spin-lattice relaxation. We show that the spin-lattice relaxation results in an exponentially fast convergence to the steady-state after full ultrafast switching.
Emergent criticality in a constrained boson model

Anirudha Menon, Anwesha Chattopadhyay, Krishnendu Sengupta, Arnab Sen

SciPost Phys. 19, 055 (2025) · published 25 August 2025 | · pdf

We show, via explicit computation on a constrained bosonic model, that the presence of subsystem symmetries can lead to a quantum phase transition (QPT) where the critical point exhibits an emergent enhanced symmetry. Such a transition separates a unique gapped ground state from a gapless one; the latter phase exhibits a broken $Z_2$ symmetry which we tie to the presence of the subsystem symmetries in the model. The intermediate critical point separating these phases exhibits an additional emergent $Z_2$ symmetry which we identify. This emergence leads to a critical theory which seems to be different from those in the Ising universality class. Instead, within the data obtained from finite-size scaling analysis, we find the critical theory to be not inconsistent with Ashkin-Teller universality in the sense that the transitions of the model reproduces a critical line with variable correlation length exponent $\nu$ but constant central charge $c$ close to unity. We verify this scenario via explicit exact-diagonalization computations, provide an effective Landau-Ginzburg theory for such a transition, and discuss the connection of our model to the PXP model describing Rydberg atom arrays.
Extracting quantum-critical properties from directly evaluated enhanced perturbative continuous unitary transformations

L. Schamriß, M. R. Walther, K. P. Schmidt

SciPost Phys. 17, 094 (2024) · published 26 September 2024 | · pdf

Directly evaluated enhanced perturbative continuous unitary transformations (deepCUTs) are used to calculate non-perturbatively extrapolated numerical data for the ground-state energy and the energy gap. The data coincide with numerical evaluations of the truncated perturbative series and provide robust extrapolations beyond the perturbative regime. We develop a general scheme to extract quantum-critical properties from the deepCUT data based on critical scaling and a strict correspondence between the truncation used for deepCUT and the length scale of correlations at the critical point. We apply our approach to transverse-field Ising models (TFIMs) as paradigmatic systems for quantum phase transitions of various universality classes depending on the lattice geometry and the choice of antiferromagnetic or ferromagnetic coupling. In particular, we focus on the quantum phase diagram of the bilayer antiferromagnetic TFIM on the triangular lattice with an Ising-type interlayer coupling. Without a field, the model is known to host a classically disordered ground state, and in the limit of decoupled layers it exhibits the 3d-XY 'order by disorder' transition of the corresponding single-layer model. Our starting point for the unknown parts of the phase diagram is a high-order perturbative calculation about the limit of isolated dimers where the model is in a gapped phase.
Quasiparticle disintegration in fermionic superfluids

Senne Van Loon, Jacques Tempere, Hadrien Kurkjian

SciPost Phys. 12, 108 (2022) · published 28 March 2022 | · pdf

We study the fermionic quasiparticle spectrum in a zero-temperature superfluid Fermi gas, and in particular how it is modified by different disintegration processes. On top of the disintegration by emission of a collective boson ($1\to2$, subject of a previous study, PRL 124, 073404), we consider here disintegration events where three quasiparticles are emitted ($1\to3$). We show that both disintegration processes are described by a $t$-matrix self-energy (as well as some highly off-resonant vacuum processes), and we characterize the associated disintegration continua. At strong coupling, we show that the quasiparticle spectrum is heavily distorted near the $1\to3$ disintegration threshold. Near the dispersion minimum, where the quasiparticles remain well-defined, the main effect of the off-shell disintegration processes is to shift the location of the minimum by a value that corresponds to the Hartree shift in the BCS limit. With our approximation of the self-energy, the correction to the energy gap with respect to the mean-field result however remains small, in contrast with experimental measurements.

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