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

• A constructive theory of the numerically accessible many-body localized to thermal crossover

  Philip J D Crowley, Anushya Chandran

  SciPost Phys. 12, 201 (2022) · published 24 June 2022 | Toggle abstract · pdf

  The many-body localised (MBL) to thermal crossover observed in exact diagonalisation studies remains poorly understood as the accessible system sizes are too small to be in an asymptotic scaling regime. We develop a model of the crossover in short 1D chains in which the MBL phase is destabilised by the formation of many-body resonances. The model reproduces several properties of the numerically observed crossover, including an apparent correlation length exponent $\nu=1$, exponential growth of the Thouless time with disorder strength, linear drift of the critical disorder strength with system size, scale-free resonances, apparent $1/\omega$ dependence of disorder-averaged spectral functions, and sub-thermal entanglement entropy of small subsystems. In the crossover, resonances induced by a local perturbation are rare at numerically accessible system sizes $L$ which are smaller than a \emph{resonance length} $\lambda$. For $L \gg \sqrt{\lambda}$ (in lattice units), resonances typically overlap, and this model does not describe the asymptotic transition. The model further reproduces controversial numerical observations which Refs. [Suntajs et al 2019, Sels & Polkovnikov 2020] claimed to be inconsistent with MBL. We thus argue that the numerics to date is consistent with a MBL phase in the thermodynamic limit.

  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

• 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

• Dynamics of Majorana-based qubits operated with an array of tunable gates

  Bela Bauer, Torsten Karzig, Ryan V. Mishmash, Andrey E. Antipov, Jason Alicea

  SciPost Phys. 5, 004 (2018) · published 19 July 2018 | Toggle abstract · pdf

  We study the dynamics of Majorana zero modes that are shuttled via local tuning of the electrochemical potential in a superconducting wire. By performing time-dependent simulations of microscopic lattice models, we show that diabatic corrections associated with the moving Majorana modes are quantitatively captured by a simple Landau-Zener description. We further simulate a Rabi-oscillation protocol in a specific qubit design with four Majorana zero modes in a single wire and quantify constraints on the timescales for performing qubit operations in this setup. Our simulations utilize a Majorana representation of the system, which greatly simplifies simulations of superconductors at the mean-field level.

  36 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

• Self-consistent theory of many-body localisation in a quantum spin chain with long-range interactions

  Sthitadhi Roy, David E. Logan

  SciPost Phys. 7, 042 (2019) · published 3 October 2019 | Toggle abstract · pdf

  Many-body localisation is studied in a disordered quantum spin-1/2 chain with long-ranged power-law interactions, and distinct power-law exponents for interactions between longitudinal and transverse spin components. Using a self-consistent mean-field theory centring on the local propagator in Fock space and its associated self-energy, a localisation phase diagram is obtained as a function of the power-law exponents and the disorder strength of the random fields acting on longitudinal spin-components. Analytical results are corroborated using the well-studied and complementary numerical diagnostics of level statistics, entanglement entropy, and participation entropy, obtained via exact diagonalisation. We find that increasing the range of interactions between transverse spin components hinders localisation and enhances the critical disorder strength. In marked contrast, increasing the interaction range between longitudinal spin components is found to enhance localisation and lower the critical disorder.

  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