Publications

Order by: publication date number of citations

• Dense Hopfield networks in the teacher-student setting

  Robin Thériault, Daniele Tantari

  SciPost Phys. 17, 040 (2024) · published 8 August 2024 | Toggle abstract · pdf

  Dense Hopfield networks with $p$-body interactions are known for their feature to prototype transition and adversarial robustness. However, theoretical studies have been mostly concerned with their storage capacity. We derive the phase diagram of pattern retrieval in the teacher-student setting of $p$-body networks, finding ferromagnetic phases reminiscent of the prototype and feature learning regimes. On the Nishimori line, we find the critical amount of data necessary for pattern retrieval, and we show that the corresponding ferromagnetic transition coincides with the paramagnetic to spin-glass transition of $p$-body networks with random memories. Outside of the Nishimori line, we find that the student can tolerate extensive noise when it has a larger $p$ than the teacher. We derive a formula for the adversarial robustness of such a student at zero temperature, corroborating the positive correlation between number of parameters and robustness in large neural networks. Our model also clarifies why the prototype phase of $p$-body networks is adversarially robust.

  7 citations

• Free fermions beyond Jordan and Wigner

  Paul Fendley, Balazs Pozsgay

  SciPost Phys. 16, 102 (2024) · published 10 April 2024 | Toggle abstract · pdf

  The Jordan-Wigner transformation is frequently utilised to rewrite quantum spin chains in terms of fermionic operators. When the resulting Hamiltonian is bilinear in these fermions, i.e. the fermions are free, the exact spectrum follows from the eigenvalues of a matrix whose size grows only linearly with the volume of the system. However, several Hamiltonians that do not admit a Jordan-Wigner transformation to fermion bilinears still have the same type of free-fermion spectra. The spectra of such "free fermions in disguise" models can be found exactly by an intricate but explicit construction of the raising and lowering operators. We generalise the methods further to find a family of such spin chains. We compute the exact spectrum, and generalise an elegant graph-theory construction. We also explain how this family admits an N=2 lattice supersymmetry.

  7 citations

• Mobile impurities in integrable models

  Andrew S. Campbell, Dimitri M. Gangardt

  SciPost Phys. 3, 015 (2017) · published 22 August 2017 | Toggle abstract · pdf

  We use a mobile impurity or depleton model to study elementary excitations in one-dimensional integrable systems. For Lieb-Liniger and bosonic Yang-Gaudin models we express two phenomenological parameters characterising renormalised interactions of mobile impurities with superfluid background: the number of depleted particles, $N$ and the superfluid phase drop $\pi J$ in terms of the corresponding Bethe Ansatz solution and demonstrate, in the leading order, the absence of two-phonon scattering resulting in vanishing rates of inelastic processes such as viscosity experienced by the mobile impurities

  7 citations

• Itinerant ferromagnetism in dilute SU(N) Fermi gases

  Jordi Pera, Joaquim Casulleras, Jordi Boronat

  SciPost Phys. 14, 038 (2023) · published 17 March 2023 | Toggle abstract · pdf

  We present exact analytic results for the energy of a SU(N) repulsive Fermi gas as a function of the spin-channel occupation at second order in the gas parameter. This is an extension of previous results that now incorporates the degree of polarization of the system. Therefore, the magnetic properties of the gas can be obtained, free from numerical uncertainties. For spin 1/2 we find that second-order corrections change the itinerant ferromagnetic transition from continuous to first-order. Instead, for spin larger than 1/2 the phase transition is always of first-order type. The transition critical density reduces when the spin increases, making the phase transition more accessible to experiments with ultracold dilute Fermi gases. Estimations for Fermi gases of Yb and Sr with spin 5/2 and 9/2, respectively, are reported.

  7 citations

• Whac-a-constraint with anomaly-free dark matter models

  Sonia El Hedri, Karl Nordström

  SciPost Phys. 6, 020 (2019) · published 7 February 2019 | Toggle abstract · pdf

  Theories where a fermionic dark matter candidate interacts with the Standard Model through a vector mediator are often studied using minimal models, which are not necessarily anomaly-free. In fact, minimal anomaly-free simplified models are usually strongly constrained by either direct detection experiments or collider searches for dilepton resonances. In this paper, we study the phenomenology of models with a fermionic dark matter candidate that couples axially to a leptophobic vector mediator. Canceling anomalies in these models requires considerably enlarging their field content. For an example minimal scenario we show that the additional fields lead to a potentially much richer phenomenology than the one predicted by the original simplified model. In particular collider searches for pair-produced neutralinos and charginos can be more sensitive than traditional monojet searches in thermally motivated parts of the parameter space where the mediator is outside the reach of current searches.

  7 citations

• Spectral representation of Matsubara n-point functions: Exact kernel functions and applications

  Johannes Halbinger, Benedikt Schneider, Björn Sbierski

  SciPost Phys. 15, 183 (2023) · published 1 November 2023 | Toggle abstract · pdf

  In the field of quantum many-body physics, the spectral (or Lehmann) representation simplifies the calculation of Matsubara $n$-point correlation functions if the eigensystem of a Hamiltonian is known. It is expressed via a universal kernel function and a system- and correlator-specific product of matrix elements. Here we provide the kernel functions in full generality, for arbitrary $n$, arbitrary combinations of bosonic or fermionic operators and an arbitrary number of anomalous terms. As an application, we consider bosonic 3- and 4-point correlation functions for the fermionic Hubbard atom and a free spin of length $S$, respectively.

  7 citations

• Determination of the time scale of photoemission from the measurement of spin polarization

  Mauro Fanciulli, J. Hugo Dil

  SciPost Phys. 5, 058 (2018) · published 6 December 2018 | Toggle abstract · pdf

  The Eisenbud-Wigner-Smith (EWS) time delay of photoemission depends on the phase term of the matrix element describing the transition. Because of an interference process between partial channels, the photoelectrons acquire a spin polarization which is also related to the phase term. The analytical model for estimating the time delay by measuring the spin polarization is reviewed in this manuscript. In particular, the distinction between scattering EWS and interfering EWS time delay will be introduced, providing an insight in the chronoscopy of photoemission. The method is applied to the recent experimental data for Cu(111) presented in M. Fanciulli et al., PRL 118, 067402 (2017), allowing to give better upper and lower bounds and estimates for the EWS time delays.

  7 citations

• The one-loop tadpole in the geoSMEFT

  Tyler Corbett

  SciPost Phys. 11, 097 (2021) · published 26 November 2021 | Toggle abstract · pdf

  Making use of the geometric formulation of the Standard Model Effective Field Theory we calculate the one-loop tadpole diagrams to all orders in the Standard Model Effective Field Theory power counting. This work represents the first calculation of a one-loop amplitude beyond leading order in the Standard Model Effective Field Theory, and discusses the potential to extend this methodology to perform similar calculations of observables in the near future.

  7 citations

• Statistics of Green's functions on a disordered Cayley tree and the validity of forward scattering approximation

  Pavel A. Nosov, Ivan M. Khaymovich, Andrey Kudlis, Vladimir E. Kravtsov

  SciPost Phys. 12, 048 (2022) · published 1 February 2022 | Toggle abstract · pdf

  The accuracy of the forward scattering approximation for two-point Green's functions of the Anderson localization model on the Cayley tree is studied. A relationship between the moments of the Green's function and the largest eigenvalue of the linearized transfer-matrix equation is proved in the framework of the supersymmetric functional-integral method. The new large-disorder approximation for this eigenvalue is derived and its accuracy is established. Using this approximation the probability distribution of the two-point Green's function is found and compared with that in the forward scattering approximation (FSA). It is shown that FSA overestimates the role of resonances and thus the probability for the Green's function to be significantly larger than its typical value. The error of FSA increases with increasing the distance between points in a two-point Green's function.

  7 citations

• Ergodic edge modes in the 4D quantum Hall effect

  Benoit Estienne, Blagoje Oblak, Jean-Marie Stéphan

  SciPost Phys. 11, 016 (2021) · published 20 July 2021 | Toggle abstract · pdf

  The gapless modes on the edge of four-dimensional (4D) quantum Hall droplets are known to be anisotropic: they only propagate in one direction, foliating the 3D boundary into independent 1D conduction channels. This foliation is extremely sensitive to the confining potential and generically yields chaotic flows. Here we study the quantum correlations and entanglement of such edge modes in 4D droplets confined by harmonic traps, whose boundary is a squashed three-sphere. Commensurable trapping frequencies lead to periodic trajectories of electronic guiding centers; the corresponding edge modes propagate independently along $S^1$ fibers, forming a bundle of 1D conformal field theories over a 2D base space. By contrast, incommensurable frequencies produce quasi-periodic, ergodic trajectories, each of which covers its invariant torus densely; the corresponding correlation function of edge modes has fractal features. This wealth of behaviors highlights the sharp differences between 4D Hall droplets and their 2D peers; it also exhibits the dependence of 4D edge modes on the choice of trap, suggesting the existence of observable bifurcations due to droplet deformations.

  7 citations