Publications

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• From complex to simple : hierarchical free-energy landscape renormalized in deep neural networks

  Hajime Yoshino

  SciPost Phys. Core 2, 005 (2020) · published 15 April 2020 | Toggle abstract · pdf

  We develop a statistical mechanical approach based on the replica method to study the design space of deep and wide neural networks constrained to meet a large number of training data. Specifically, we analyze the configuration space of the synaptic weights and neurons in the hidden layers in a simple feed-forward perceptron network for two scenarios: a setting with random inputs/outputs and a teacher-student setting. By increasing the strength of constraints,~i.e. increasing the number of training data, successive 2nd order glass transition (random inputs/outputs) or 2nd order crystalline transition (teacher-student setting) take place layer-by-layer starting next to the inputs/outputs boundaries going deeper into the bulk with the thickness of the solid phase growing logarithmically with the data size. This implies the typical storage capacity of the network grows exponentially fast with the depth. In a deep enough network, the central part remains in the liquid phase. We argue that in systems of finite width N, the weak bias field can remain in the center and plays the role of a symmetry-breaking field that connects the opposite sides of the system. The successive glass transitions bring about a hierarchical free-energy landscape with ultrametricity, which evolves in space: it is most complex close to the boundaries but becomes renormalized into progressively simpler ones in deeper layers. These observations provide clues to understand why deep neural networks operate efficiently. Finally, we present some numerical simulations of learning which reveal spatially heterogeneous glassy dynamics truncated by a finite width $N$ effect.

  5 citations

• Electron glass effects in amorphous NbSi films

  Julien Delahaye, Thierry Grenet, Claire A Marrache-Kikuchi, Vincent Humbert, Laurent Bergé, Louis Dumoulin

  SciPost Phys. 8, 056 (2020) · published 9 April 2020 | Toggle abstract · pdf

  We report on non equilibrium field effect in insulating amorphous NbSi thin films having different Nb contents and thicknesses. The hallmark of an electron glass, namely the logarithmic growth of a memory dip in conductance versus gate voltage curves, is observed in all the films after a cooling from room temperature to 4.2 K. A very rich phenomenology is demonstrated. While the memory dip width is found to strongly vary with the film parameters, as was also observed in amorphous indium oxide films, screening lengths and temperature dependence of the dynamics are closer to what is observed in granular Al films. Our results demonstrate that the differentiation between continuous and discontinuous systems is not relevant to understand the discrepancies reported between various systems in the electron glass features. We suggest instead that they are not of fundamental nature and stem from differences in the protocols used and in the electrical inhomogeneity length scales within each material.

  4 citations

• Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics

  Márton Mestyán, Vincenzo Alba

  SciPost Phys. 8, 055 (2020) · published 9 April 2020 | Toggle abstract · pdf

  We consider a molecular dynamics method, the so-called flea gas for computing the evolution of entanglement after inhomogeneous quantum quenches in an integrable quantum system. In such systems the evolution of local observables is described at large space-time scales by the Generalized Hydrodynamics approach, which is based on the presence of stable, ballistically propagating quasiparticles. Recently it was shown that the GHD approach can be joined with the quasiparticle picture of entanglement evolution, providing results for entanglement growth after inhomogeneous quenches. Here we apply the flea gas simulation of GHD to obtain numerical results for entanglement growth. We implement the flea gas dynamics for the gapped anisotropic Heisenberg XXZ spin chain, considering quenches from globally homogeneous and piecewise homogeneous initial states. While the flea gas method applied to the XXZ chain is not exact even in the scaling limit (in contrast to the Lieb--Liniger model), it yields a very good approximation of analytical results for entanglement growth in the cases considered. Furthermore, we obtain the {\it full-time} dynamics of the mutual information after quenches from inhomogeneous settings, for which no analytical results are available.

  15 citations

• $1/8$-BPS couplings and exceptional automorphic functions

  Guillaume Bossard, Axel Kleinschmidt, Boris Pioline

  SciPost Phys. 8, 054 (2020) · published 8 April 2020 | Toggle abstract · pdf

  Unlike the $R^4$ and $\nabla^4 R^4$ couplings, whose coefficients are Langlands--Eisenstein series of the U-duality group, the coefficient $\mathcal{E}^{(d)}_{(0,1)}$ of the $\nabla^6 R^4$ interaction in the low-energy effective action of type II strings compactified on a torus $T^d$ belongs to a more general class of automorphic functions, which satisfy Poisson rather than Laplace-type equations. In earlier work, it was proposed that the exact coefficient is given by a two-loop integral in exceptional field theory, with the full spectrum of mutually 1/2-BPS states running in the loops, up to the addition of a particular Langlands--Eisenstein series. Here we compute the weak coupling and large radius expansions of these automorphic functions for any $d$. We find perfect agreement with perturbative string theory up to genus three, along with non-perturbative corrections which have the expected form for 1/8-BPS instantons and bound states of 1/2-BPS instantons and anti-instantons. The additional Langlands--Eisenstein series arises from a subtle cancellation between the two-loop amplitude with 1/4-BPS states running in the loops, and the three-loop amplitude with mutually 1/2-BPS states in the loops. For $d=4$, the result is shown to coincide with an alternative proposal in terms of a covariantised genus-two string amplitude, due to interesting identities between the Kawazumi--Zhang invariant of genus-two curves and its tropical limit, and between double lattice sums for the particle and string multiplets, which may be of independent mathematical interest.

  8 citations

• Topological thermal Hall effect for topological excitations in spin liquid: Emergent Lorentz force on the spinons

  Yong Hao Gao, Gang Chen

  SciPost Phys. Core 2, 004 (2020) · published 8 April 2020 | Toggle abstract · pdf

  We study the origin of Lorentz force on the spinons in a U(1) spin liquid. We are inspired by the previous observation of gauge field correlation in the pairwise spin correlation using the neutron scattering measurement when the Dzyaloshinskii-Moriya interaction intertwines with the lattice geometry. We extend this observation to the Lorentz force that exerts on the (neutral) spinons. The external magnetic field, that polarizes the spins, effectively generates an internal U(1) gauge flux for the spinons and twists the spinon motion through the Dzyaloshinskii-Moriya interaction. Such a mechanism for the emergent Lorentz force differs fundamentally from the induction of the internal U(1) gauge flux in the weak Mott insulating regime from the charge fluctuations. We apply this understanding to the specific case of spinon metals on the kagome lattice. Our suggestion of emergent Lorentz force generation and the resulting topological thermal Hall effect may apply broadly to other non-centrosymmetric spin liquids with Dzyaloshinskii-Moriya interaction. We discuss the relevance with the thermal Hall transport in kagome materials volborthite and kapellasite.

  14 citations

• Zero temperature momentum distribution of an impurity in a polaron state of one-dimensional Fermi and Tonks-Girardeau gases

  Oleksandr Gamayun, Oleg Lychkovskiy, Mikhail B. Zvonarev

  SciPost Phys. 8, 053 (2020) · published 7 April 2020 | Toggle abstract · pdf

  We investigate the momentum distribution function of a single distinguishable impurity particle which formed a polaron state in a gas of either free fermions or Tonks-Girardeau bosons in one spatial dimension. We obtain a Fredholm determinant representation of the distribution function for the Bethe ansatz solvable model of an impurity-gas δ-function interaction potential at zero temperature, in both repulsive and attractive regimes. We deduce from this representation the fourth power decay at a large momentum, and a weakly divergent (quasi-condensate) peak at a finite momentum. We also demonstrate that the momentum distribution function in the limiting case of infinitely strong interaction can be expressed through a correlation function of the one-dimensional impenetrable anyons.

  16 citations

• A non-abelian analogue of DBI from $T \overline{T}$

  T. Daniel Brennan, Christian Ferko, Savdeep Sethi

  SciPost Phys. 8, 052 (2020) · published 7 April 2020 | Toggle abstract · pdf

  The Dirac action describes the physics of the Nambu-Goldstone scalars found on branes. The Born-Infeld action defines a non-linear theory of electrodynamics. The combined Dirac-Born-Infeld (DBI) action describes the leading interactions supported on a single D-brane in string theory. We define a non-abelian analogue of DBI using the $T \overline{T}$ deformation in two dimensions. The resulting quantum theory is compatible with maximal supersymmetry and such theories are quite rare.

  23 citations

• The Fröhlich-Morchio-Strocchi mechanism and quantum gravity

  Axel Maas

  SciPost Phys. 8, 051 (2020) · published 6 April 2020 | Toggle abstract · pdf

  Taking manifest invariance under both gauge symmetry and diffeomorphisms as a guiding principle physical objects are constructed for Yang-Mills-Higgs theory coupled to quantum gravity. These objects are entirely classified by quantum numbers defined in the tangent space. Applying the Fr\"ohlich-Morchio-Strocchi mechanism to these objects reveals that they coincide with ordinary correlation functions in quantum-field theory, if quantum fluctuations of gravity and curvature become small. Taking these descriptions literally exhibits how quantum gravity fields need to dress quantum fields to create physical objects, i.e. giving a graviton component to ordinary observed particles. The same mechanism provides access to the physical spectrum of pure gravitational degrees of freedom.

  8 citations

• Field theories with a vector global symmetry

  Nathan Seiberg

  SciPost Phys. 8, 050 (2020) · published 3 April 2020 | Toggle abstract · pdf

  Motivated by recent discussions of fractons, we explore nonrelativistic field theories with a continuous global symmetry, whose charge is a spatial vector. We present several such symmetries and demonstrate them in concrete examples. They differ by the equations their Noether currents satisfy. Simple cases, other than the translation symmetry, are an ordinary (relativistic) one-form global symmetry and its nonrelativistic generalization. In the latter case the conserved charge is associated with a codimension-one spatial manifold, but it is not topological. More general examples involve charges that are integrated over the entire space. We also discuss the coupling of these systems to gauge fields for these symmetries. We relate our examples to known continuum and lattice constructions.

  97 citations

• Quasi-free limit in the deuteron-deuteron three-body break-up process

  R. Ramazani-Sharifabadi, H. R. Amir-Ahmadi, M. T. Bayat, I. Ciepał, M. Eslami-Kalantari, N. Kalantar-Nayestanaki, St. Kistryn, A. Kozela, M. Mahjour-Shafiei, H. Mardanpour, J. G. Messchendorp, M. Mohammadi-Dadkan, A. Ramazani-Moghaddam-Arani, E. Stephan, and H. Tavakoli-Zaniani

  SciPost Phys. Proc. 3, 057 (2020) · published 1 April 2020 | Toggle abstract · pdf

  Detailed measurements of vector and tensor analyzing powers of the 2H(d, dp)n breakup process are presented. The data were obtained using a polarized deuteron-beam with an energy of 65 MeV/nucleon impinging on a liquid-deuterium target. The experiment was conducted at the AGOR facility at KVI using the BINA 4Pi-detection system. The focus of this contribution is to analyze data of the dd scattering process in the regime at which the neutron acts as a spectator, which we refer to as the quasi-free (QF) limit. To achieve this, events for which the final-state deuteron and proton are coplanar have been analyzed and the data have been sorted for various reconstructed momenta of the missing neutron. In the limit of vanishing neutron momentum and at small deuteron-proton momentum transfer, the data match very well with measured and predicted spin observables of the elastic deuteron-proton scattering process. The agreement deteriorates rapidly with increasing neutron momentum and deuteron-proton momentum transfer. The results of coplanar configurations in four-body phase space are compared with the results of recent available theoretical calculations based on the Single-Scattering Approximation.