Publications

Order by: publication date number of citations

• Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape

  Marin Bukov, Markus Schmitt, Maxime Dupont

  SciPost Phys. 10, 147 (2021) · published 17 June 2021 | Toggle abstract · pdf

  Strongly interacting quantum systems described by non-stoquastic Hamiltonians exhibit rich low-temperature physics. Yet, their study poses a formidable challenge, even for state-of-the-art numerical techniques. Here, we investigate systematically the performance of a class of universal variational wave-functions based on artificial neural networks, by considering the frustrated spin-$1/2$ $J_1-J_2$ Heisenberg model on the square lattice. Focusing on neural network architectures without physics-informed input, we argue in favor of using an ansatz consisting of two decoupled real-valued networks, one for the amplitude and the other for the phase of the variational wavefunction. By introducing concrete mitigation strategies against inherent numerical instabilities in the stochastic reconfiguration algorithm we obtain a variational energy comparable to that reported recently with neural networks that incorporate knowledge about the physical system. Through a detailed analysis of the individual components of the algorithm, we conclude that the rugged nature of the energy landscape constitutes the major obstacle in finding a satisfactory approximation to the ground state wavefunction, and prevents learning the correct sign structure. In particular, we show that in the present setup the neural network expressivity and Monte Carlo sampling are not primary limiting factors.

  38 citations

• Rank $Q$ E-string on a torus with flux

  Sara Pasquetti, Shlomo S. Razamat, Matteo Sacchi, Gabi Zafrir

  SciPost Phys. 8, 014 (2020) · published 29 January 2020 | Toggle abstract · pdf

  We discuss compactifications of rank $Q$ E-string theory on a torus with fluxes for abelian subgroups of the $E_8$ global symmetry of the $6d$ SCFT. We argue that the theories corresponding to such tori are built from a simple model we denote as $E[USp(2Q)]$. This model has a variety of non trivial properties. In particular the global symmetry is $USp(2Q)\times USp(2Q)\times U(1)^2$ with one of the two $USp(2Q)$ symmetries emerging in the IR as an enhancement of an $SU(2)^Q$ symmetry of the UV Lagrangian. The $E[USp(2Q)]$ model after dimensional reduction to $3d$ and a subsequent Coulomb branch flow is closely related to the familiar $3d$ $T[SU(Q)]$ theory, the model residing on an S-duality domain wall of $4d$ $\mathcal{N}=4$ $SU(Q)$ SYM. Gluing the $E[USp(2Q)]$ models by gauging the $USp(2Q)$ symmetries with proper admixtures of chiral superfields gives rise to systematic constructions of many examples of $4d$ theories with emergent IR symmetries. We support our claims by various checks involving computations of anomalies and supersymmetric partition functions. Many of the needed identities satisfied by the supersymmetric indices follow directly from recent mathematical results obtained by E. Rains.

  38 citations

• Mutually attracting spin waves in the square-lattice quantum antiferromagnet

  Michael Powalski, Kai P. Schmidt, Götz S. Uhrig

  SciPost Phys. 4, 001 (2018) · published 17 January 2018 | Toggle abstract · pdf

  The Heisenberg model for S=1/2 describes the interacting spins of electrons localized on lattice sites due to strong repulsion. It is the simplest strong-coupling model in condensed matter physics with wide-spread applications. Its relevance has been boosted further by the discovery of curate high-temperature superconductors. In leading order, their undoped parent compounds realize the Heisenberg model on square-lattices. Much is known about the model, but mostly at small wave vectors, i.e., for long-range processes, where the physics is governed by spin waves (magnons), the Goldstone bosons of the long-range ordered antiferromagnetic phase. Much less, however, is known for short-range processes, i.e., at large wave vectors. Yet these processes are decisive for understanding high-temperature superconductivity. Recent reports suggest that one has to resort to qualitatively different fractional excitations, spinons. By contrast, we present a comprehensive picture in terms of dressed magnons with strong mutual attraction on short length scales. The resulting spectral signatures agree strikingly with experimental data.

  37 citations

• The Infrared Physics of Bad Theories

  Benjamin Assel, Stefano Cremonesi

  SciPost Phys. 3, 024 (2017) · published 28 September 2017 | Toggle abstract · pdf

  We study the complete moduli space of vacua of 3d $\mathcal{N}=4$ $U(N)$ SQCD theories with $N_f$ fundamentals, building on the algebraic description of the Coulomb branch, and deduce the low energy physics in any vacuum from the local geometry of the moduli space. We confirm previous claims for good and ugly SQCD theories, and show that bad theories flow to the same interacting fixed points as good theories with additional free twisted hypermultiplets. A Seiberg-like duality proposed for bad theories with $N \le N_f \le 2N-2$ is ruled out: the spaces of vacua of the putative dual theories are different. However such bad theories have a distinguished vacuum, which preserves all the global symmetries, whose infrared physics is that of the proposed dual. We finally explain previous results on sphere partition functions and elucidate the relation between the UV and IR $R$-symmetry in this symmetric vacuum.

  37 citations

• One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance

  Yannis Brun, Jérôme Dubail

  SciPost Phys. 2, 012 (2017) · published 4 April 2017 | Toggle abstract · pdf

  The one-particle density matrix of the one-dimensional Tonks-Girardeau gas with inhomogeneous density profile is calculated, thanks to a recent observation that relates this system to a two-dimensional conformal field theory in curved space. The result is asymptotically exact in the limit of large particle density and small density variation, and holds for arbitrary trapping potentials. In the particular case of a harmonic trap, we recover a formula obtained by Forrester et al. [Phys. Rev. A 67, 043607 (2003)] from a different method.

  37 citations

• 2-Group symmetries in class S

  Lakshya Bhardwaj

  SciPost Phys. 12, 152 (2022) · published 9 May 2022 | Toggle abstract · pdf

  2-group symmetries are generalized symmetries that arise when 1-form and 0-form symmetries mix with each other. We uncover the existence of a class of 2-group symmetries in general 4d N=2 theories of Class S that can be constructed by compactifying 6d N=(2,0) SCFTs on Riemann surfaces carrying arbitrary regular punctures and outer-automorphism twist lines. The 2-group structure can be captured in terms of equivalence classes of line defects plus flavor Wilson lines, which can be thought of as accounting for screening of line defects while keeping track of flavor charges. We describe a method for computing these equivalence classes for a general Class S theory using the data on the Riemman surface used for compactifying its parent 6d N=(2,0) theory.

  36 citations

• Phase space sampling and inference from weighted events with autoregressive flows

  Bob Stienen, Rob Verheyen

  SciPost Phys. 10, 038 (2021) · published 17 February 2021 | Toggle abstract · pdf

  We explore the use of autoregressive flows, a type of generative model with tractable likelihood, as a means of efficient generation of physical particle collider events. The usual maximum likelihood loss function is supplemented by an event weight, allowing for inference from event samples with variable, and even negative event weights. To illustrate the efficacy of the model, we perform experiments with leading-order top pair production events at an electron collider with importance sampling weights, and with next-to-leading-order top pair production events at the LHC that involve negative weights.

  36 citations

• Dynamical phases in a ``multifractal'' Rosenzweig-Porter model

  Ivan M. Khaymovich, Vladimir E. Kravtsov

  SciPost Phys. 11, 045 (2021) · published 31 August 2021 | Toggle abstract · pdf

  We consider the static and the dynamic phases in a Rosenzweig-Porter (RP) random matrix ensemble with a distribution of off-diagonal matrix elements of the form of the large-deviation ansatz. We present a general theory of survival probability in such a random-matrix model and show that the {\it averaged} survival probability may decay with time as a simple exponent, as a stretch-exponent and as a power-law or slower. Correspondingly, we identify the exponential, the stretch-exponential and the frozen-dynamics phases. As an example, we consider the mapping of the Anderson localization model on Random Regular Graph onto the RP model and find exact values of the stretch-exponent $\kappa$ in the thermodynamic limit. As another example we consider the logarithmically-normal RP random matrix ensemble and find analytically its phase diagram and the exponent $\kappa$. Our theory allows to describe analytically the finite-size multifractality and to compute the critical length with the exponent $\nu_{MF}=1$ associated with it.

  36 citations

• Classification of out-of-time-order correlators

  Felix M. Haehl, R. Loganayagam, Prithvi Narayan, Mukund Rangamani

  SciPost Phys. 6, 001 (2019) · published 7 January 2019 | Toggle abstract · pdf

  The space of n-point correlation functions, for all possible time-orderings of operators, can be computed by a non-trivial path integral contour, which depends on how many time-ordering violations are present in the correlator. These contours, which have come to be known as timefolds, or out-of-time-order (OTO) contours, are a natural generalization of the Schwinger-Keldysh contour (which computes singly out-of-time-ordered correlation functions). We provide a detailed discussion of such higher OTO functional integrals, explaining their general structure, and the myriad ways in which a particular correlation function may be encoded in such contours. Our discussion may be seen as a natural generalization of the Schwinger-Keldysh formalism to higher OTO correlation functions. We provide explicit illustration for low point correlators (n=2,3,4) to exemplify the general statements.

  36 citations

• Fractons in curved space

  Akash Jain, Kristan Jensen

  SciPost Phys. 12, 142 (2022) · published 29 April 2022 | Toggle abstract · pdf

  We consistently couple simple continuum field theories with fracton excitations to curved spacetime backgrounds. We consider homogeneous and isotropic fracton field theories, with a conserved $U(1)$ charge and dipole moment. Coupling to background fields allows us to consistently define a stress-energy tensor for these theories and obtain the respective Ward identities. Along the way, we find evidence for a mixed gauge-gravitational anomaly in the symmetric tensor gauge theory which naturally couples to conserved dipoles. Our results generalise to systems with arbitrarily higher conserved moments, in particular, a conserved quadrupole moment.

  36 citations