Publications

Order by: publication date number of 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.

  3 citations

• Practical realization of chiral nonlinearity for strong topological protection

  Xinxin Guo, Lucien Jezequel, Mathieu Padlewski, Hervé Lissek, Pierre Delplace, Romain Fleury

  SciPost Phys. 18, 034 (2025) · published 27 January 2025 | Toggle abstract · pdf

  Nonlinear topology has been much less inquired compared to its linear counterpart. Existing advances have focused on nonlinearities of limited magnitudes and fairly homogeneous types. As such, the realizations have rarely been concerned with the requirements for nonlinearity. Here we explore nonlinear topological protection by determining nonlinear rules and demonstrate their relevance in real-world experiments. We take advantage of chiral symmetry and identify the condition for its continuation in general nonlinear environments. Applying it to one-dimensional topological lattices, we show possible evolution paths for zero-energy edge states that preserve topologically nontrivial phases regardless of the specifics of the chiral nonlinearities. Based on an acoustic prototype design with non-local nonlinearities, we theoretically, numerically, and experimentally implement the nonlinear topological edge states that persist in all nonlinear degrees and directions without any frequency shift. Our findings unveil a broad family of nonlinearities compatible with topological non-triviality, establishing a solid ground for future drilling in the emergent field of nonlinear topology.

  3 citations

• On quantum melting of superfluid vortex crystals: From Lifshitz scalar to dual gravity

  Dung Xuan Nguyen, Sergej Moroz

  SciPost Phys. 17, 164 (2024) · published 11 December 2024 | Toggle abstract · pdf

  Despite a long history of studies of vortex crystals in rotating superfluids, their melting due to quantum fluctuations is poorly understood. Here we develop a fracton-elasticity duality to investigate a two-dimensional vortex lattice within the fast rotation regime, where the Lifshitz model of the collective Tkachenko mode serves as the leading-order low-energy effective theory. We incorporate topological defects and discuss several quantum melting scenarios triggered by their proliferation. Furthermore, we lay the groundwork for a dual non-linear emergent gravity description of the superfluid vortex crystals.

  3 citations

• Finite-size corrections to the energy spectra of gapless one-dimensional systems in the presence of boundaries

  Yifan Liu, Haruki Shimizu, Atsushi Ueda, Masaki Oshikawa

  SciPost Phys. 17, 099 (2024) · published 2 October 2024 | Toggle abstract · pdf

  We present the finite-size scaling theory of one-dimensional quantum critical systems in the presence of boundaries. While the finite-size spectrum in the conformal limit, namely of a conformal field theory with conformally invariant boundary conditions, is related to the dimensions of boundary operators by Cardy, the actual spectra of lattice models are affected by both bulk and boundary perturbations and contain non-universal boundary energies. We obtain a general expression of the finite-size energy levels in the presence of bulk and boundary perturbations. In particular, a generic boundary perturbation related to the energy-momentum tensor gives rise to a renormalization of the effective system size. We verify our field-theory formulation by comparing the results with the exact solution of the critical transverse-field Ising chain and with accurate numerical results on the critical three-state Potts chain obtained by Density-Matrix Renormalization Group.

  3 citations

• Modulation induced transport signatures in correlated electron waveguides

  Gal Shavit, Yuval Oreg

  SciPost Phys. 9, 051 (2020) · published 14 October 2020 | Toggle abstract · pdf

  Recent transport experiments in spatially modulated quasi-1D structures created on top of LaAlO$_3$/SrTiO$_3$ interfaces have revealed some interesting features, including phenomena conspicuously absent without the modulation. In this work, we focus on two of these remarkable features and provide theoretical analysis allowing their interpretation. The first one is the appearance of two-terminal conductance plateaus at rational fractions of $e^2/h$. We explain how this phenomenon, previously believed to be possible only in systems with strong repulsive interactions, can be stabilized in a system with attraction in the presence of the modulation. Using our theoretical framework we find the plateau amplitude and shape, and characterize the correlated phase which develops in the system due to the partial gap, namely a Luttinger liquid of electronic trions. The second observation is a sharp conductance dip below a conductance of $1\times e^2/h$, which changes its value over a wide range when tuning the system. We theorize that it is due to resonant backscattering caused by a periodic spin-orbit field. The behavior of this dip can be reliably accounted for by considering the finite length of the electronic waveguides, as well as the interactions therein. The phenomena discussed in this work exemplify the intricate interplay of strong interactions and spatial modulations, and reveal the potential for novel strongly correlated phases of matter in systems which prominently feature both.

  3 citations

• Quantum phases of hardcore bosons with repulsive dipolar density-density interactions on two-dimensional lattices

  J. A. Koziol, G. Morigi, K. P. Schmidt

  SciPost Phys. 17, 111 (2024) · published 10 October 2024 | Toggle abstract · pdf

  We analyse the ground-state quantum phase diagram of hardcore Bosons interacting with repulsive dipolar potentials. The bosons dynamics is described by the extended-Bose-Hubbard Hamiltonian on a two-dimensional lattice. The ground state results from the interplay between the lattice geometry and the long-range interactions, which we account for by means of a classical spin mean-field approach limited by the size of the considered unit cells. This extended classical spin mean-field theory accounts for the long-range density-density interaction without truncation. We consider three different lattice geometries: square, honeycomb, and triangular. In the limit of zero hopping the ground state is always a devil's staircase of solid (gapped) phases. Such crystalline phases with broken translational symmetry are robust with respect to finite hopping amplitudes. At intermediate hopping amplitudes, these gapped phases melt, giving rise to various lattice supersolid phases, which can have exotic features with multiple sublattice densities. At sufficiently large hoppings the ground state is a superfluid. The stability of phases predicted by our approach is gauged by comparison to the known quantum phase diagrams of the Bose-Hubbard model with nearest-neighbour interactions as well as quantum Monte Carlo simulations for the dipolar case on the square and triangular lattice. Our results are of immediate relevance for experimental realisations of self-organised crystalline ordering patterns in analogue quantum simulators, e.g., with ultracold dipolar atoms in an optical lattice.

  3 citations

• Quantum collider probes of the fermionic Higgs portal

  Ulrich Haisch, Maximilian Ruhdorfer, Konstantin Schmid, Andreas Weiler

  SciPost Phys. 16, 112 (2024) · published 25 April 2024 | Toggle abstract · pdf

  We explore the sensitivity of future hadron colliders to constrain the fermionic Higgs portal, with a focus on scenarios where the new fermions cannot be directly observed in exotic Higgs decays. This portal emerges in various models including twin-Higgs scenarios and dark matter models, posing significant challenges for collider tests. Working in an effective field theory (EFT), we determine the reach of the high-luminosity option of the Large Hadron Collider (HL-LHC), the high-energy upgrade of the LHC (HE-LHC) and a proposed Future Circular Collider (FCC) in probing the fermionic Higgs portal through off-shell and double-Higgs production. Notably, we find that quantum-enhanced indirect probes offer a better sensitivity than other direct Higgs measurements. We argue that this finding is valid in a wide class of ultraviolet realisations of the EFT. Our study presents a roadmap of a multifaceted search strategy for exploring the fermionic Higgs portal at forthcoming hadron machines.

  3 citations

• Constraints on beta functions in field theories

  Han Ma, Sung-Sik Lee

  SciPost Phys. 12, 046 (2022) · published 1 February 2022 | Toggle abstract · pdf

  The $\beta$-functions describe how couplings run under the renormalization group flow in field theories. In general, all couplings that respect the symmetry and locality are generated under the renormalization group flow, and the exact renormalization group flow is characterized by the $\beta$-functions defined in the infinite dimensional space of couplings. In this paper, we show that the renormalization group flow is highly constrained so that the $\beta$-functions defined in a measure zero subspace of couplings completely determine the $\beta$-functions in the entire space of couplings. We provide a quantum renormalization group-based algorithm for reconstructing the full $\beta$-functions from the $\beta$-functions defined in the subspace. As examples, we derive the full $\beta$-functions for the $O(N)$ vector model and the $O_L(N) \times O_R(N)$ matrix model entirely from the $\beta$-functions defined in the subspace of single-trace couplings.

  3 citations

• Generalized hydrodynamics of integrable quantum circuits

  Friedrich Hübner, Eric Vernier, Lorenzo Piroli

  SciPost Phys. 18, 135 (2025) · published 24 April 2025 | Toggle abstract · pdf

  Quantum circuits make it possible to simulate the continuous-time dynamics of a many-body Hamiltonian by implementing discrete Trotter steps of duration $\tau$. However, when $\tau$ is sufficiently large, the discrete dynamics exhibit qualitative differences compared to the original evolution, potentially displaying novel features and many-body effects. We study an interesting example of this phenomenon, by considering the integrable Trotterization of a prototypical integrable model, the XXZ Heisenberg spin chain. We focus on the well-known bipartition protocol, where two halves of a large system are prepared in different macrostates and suddenly joined together, yielding non-trivial nonequilibrium dynamics. Building upon recent results and adapting the generalized hydrodynamics (GHD) of integrable models, we develop an exact large-scale description of an explicit one-dimensional quantum-circuit setting, where the input left and right qubits are initialized in two distinct product states. We explore the phenomenology predicted by the GHD equations, which depend on the Trotter step and the gate parameters. In some phases of the parameter space, we show that the quantum-circuit large-scale dynamics is qualitatively different compared to the continuous-time evolution. In particular, we find that a single microscopic defect at the junction, such as the addition of a single qubit, may change the nonequilibrium macrostate appearing at late time.

  3 citations

• Dynamics of hot Bose-Einstein condensates: stochastic Ehrenfest relations for number and energy damping

  Rob G. McDonald, Peter S. Barnett, Fradom Atayee, Ashton S. Bradley

  SciPost Phys. 8, 029 (2020) · published 18 February 2020 | Toggle abstract · pdf

  Describing partially-condensed Bose gases poses a long-standing theoretical challenge. We present exact stochastic Ehrenfest relations for the stochastic projected Gross-Pitaevskii equation, including both number and energy damping mechanisms, and all projector terms that arise from the energy cutoff separating system from reservoir. We test the theory by applying it to the centre of mass fluctuations of a harmonically trapped prolate system, finding close agreement between c-field simulations and analytical results. The formalism lays the foundation to analytically explore experimentally accessible hot Bose-Einstein condensates.

  3 citations