Publications

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• Mean-field model of interacting quasilocalized excitations in glasses

  Corrado Rainone, Pierfrancesco Urbani, Francesco Zamponi, Edan Lerner, and Eran Bouchbinder

  SciPost Phys. Core 4, 008 (2021) · published 16 April 2021 | Toggle abstract · pdf

  Structural glasses feature quasilocalized excitations whose frequencies $\omega$ follow a universal density of states ${\cal D}(\omega)\!\sim\!\omega^4$. Yet, the underlying physics behind this universality is not yet fully understood. Here we study a mean-field model of quasilocalized excitations in glasses, viewed as groups of particles embedded inside an elastic medium and described collectively as anharmonic oscillators. The oscillators, whose harmonic stiffness is taken from a rather featureless probability distribution (of upper cutoff $\kappa_0$) in the absence of interactions, interact among themselves through random couplings (characterized by strength $J$) and with the surrounding elastic medium (an interaction characterized by a constant force $h$). We first show that the model gives rise to a gapless density of states ${\cal D}(\omega)\!=\!A_{\rm g}\,\omega^4$ for a broad range of model parameters, expressed in terms of the strength of stabilizing anharmonicity, which plays a decisive role in the model. Then --- using scaling theory and numerical simulations --- we provide a complete understanding of the non-universal prefactor $A_{\rm g}(h,J,\kappa_0)$, of the oscillators' interaction-induced mean square displacement and of an emerging characteristic frequency, all in terms of properly identified dimensionless quantities. In particular, we show that $A_{\rm g}(h,J,\kappa_0)$ is a non-monotonic function of $J$ for a fixed $h$, varying predominantly exponentially with $-(\kappa_0 h^{2/3}\!/J^2)$ in the weak interactions (small $J$) regime --- reminiscent of recent observations in computer glasses --- and predominantly decays as a power-law for larger $J$, in a regime where $h$ plays no role. We discuss the physical interpretation of the model and its possible relations to available observations in structural glasses, along with delineating some future research directions.

  20 citations

• A non-Abelian parton state for the $ν=2+3/8$ fractional quantum Hall effect

  Ajit Coimbatore Balram

  SciPost Phys. 10, 083 (2021) · published 15 April 2021 | Toggle abstract · pdf

  Fascinating structures have arisen from the study of the fractional quantum Hall effect (FQHE) at the even denominator fraction of $5/2$. We consider the FQHE at another even denominator fraction, namely $\nu=2+3/8$, where a well-developed and quantized Hall plateau has been observed in experiments. We examine the non-Abelian state described by the "$\bar{3}\bar{2}^{2}1^{4}$" parton wave function and numerically demonstrate it to be a feasible candidate for the ground state at $\nu=2+3/8$. We make predictions for experimentally measurable properties of the $\bar{3}\bar{2}^{2}1^{4}$ state that can reveal its underlying topological structure.

  17 citations

• Simulating Floquet topological phases in static systems

  Selma Franca, Fabian Hassler, Ion Cosma Fulga

  SciPost Phys. Core 4, 007 (2021) · published 15 April 2021 | Toggle abstract · pdf

  We show that scattering from the boundary of static, higher-order topological insulators (HOTIs) can be used to simulate the behavior of (time-periodic) Floquet topological insulators. We consider D-dimensional HOTIs with gapless corner states which are weakly probed by external waves in a scattering setup. We find that the unitary reflection matrix describing back-scattering from the boundary of the HOTI is topologically equivalent to a (D-1)-dimensional nontrivial Floquet operator. To characterize the topology of the reflection matrix, we introduce the concept of `nested' scattering matrices. Our results provide a route to engineer topological Floquet systems in the lab without the need for external driving. As benefit, the topological system does not to suffer from decoherence and heating.

  7 citations

• Impurities in systems of noninteracting trapped fermions

  David S. Dean, Pierre Le Doussal, Satya N. Majumdar, Gregory Schehr

  SciPost Phys. 10, 082 (2021) · published 14 April 2021 | Toggle abstract · pdf

  We study the properties of spin-less non-interacting fermions trapped in a confining potential in one dimension but in the presence of one or more impurities which are modelled by delta function potentials. We use a method based on the single particle Green's function. For a single impurity placed in the bulk, we compute the density of the Fermi gas near the impurity. Our results, in addition to recovering the Friedel oscillations at large distance from the impurity, allow the exact computation of the density at short distances. We also show how the density of the Fermi gas is modified when the impurity is placed near the edge of the trap in the region where the unperturbed system is described by the Airy gas. Our method also allows us to compute the effective potential felt by the impurity both in the bulk and at the edge. In the bulk this effective potential is shown to be a universal function only of the local Fermi wave vector, or equivalently of the local fermion density. When the impurity is placed near the edge of the Fermi gas, the effective potential can be expressed in terms of Airy functions. For an attractive impurity placed far outside the support of the fermion density, we show that an interesting transition occurs where a single fermion is pulled out of the Fermi sea and forms a bound state with the impurity. This is a quantum analogue of the well-known Baik-Ben Arous-P\'ech\'e (BBP) transition, known in the theory of spiked random matrices. The density at the location of the impurity plays the role of an order parameter. We also consider the case of two impurities in the bulk and compute exactly the effective force between them mediated by the background Fermi gas.

  7 citations

• Conformal partial waves in momentum space

  Marc Gillioz

  SciPost Phys. 10, 081 (2021) · published 13 April 2021 | Toggle abstract · pdf

  The decomposition of 4-point correlation functions into conformal partial waves is a central tool in the study of conformal field theory. We compute these partial waves for scalar operators in Minkowski momentum space, and find a closed-form result valid in arbitrary space-time dimension $d \geq 3$ (including non-integer $d$). Each conformal partial wave is expressed as a sum over ordinary spin partial waves, and the coefficients of this sum factorize into a product of vertex functions that only depend on the conformal data of the incoming, respectively outgoing operators. As a simple example, we apply this conformal partial wave decomposition to the scalar box integral in $d = 4$ dimensions.

  9 citations

• Probabilistic theories and reconstructions of quantum theory

  Markus P. Müller

  SciPost Phys. Lect. Notes 28 (2021) · published 31 March 2021 | Toggle abstract · pdf

  These lecture notes provide a basic introduction to the framework of generalized probabilistic theories (GPTs) and a sketch of a reconstruction of quantum theory (QT) from simple operational principles. To build some intuition for how physics could be even more general than quantum, I present two conceivable phenomena beyond QT: superstrong nonlocality and higher-order interference. Then I introduce the framework of GPTs, generalizing both quantum and classical probability theory. Finally, I summarize a reconstruction of QT from the principles of Tomographic Locality, Continuous Reversibility, and the Subspace Axiom. In particular, I show why a quantum bit is described by a Bloch ball, why it is three-dimensional, and how one obtains the complex numbers and operators of the usual representation of QT.

  22 citations

• Schur sector of Argyres-Douglas theory and $W$-algebra

  Dan Xie, Wenbin Yan

  SciPost Phys. 10, 080 (2021) · published 30 March 2021 | Toggle abstract · pdf

  We study the Schur index, the Zhu's $C_2$ algebra, and the Macdonald index of a four dimensional $\mathcal{N}=2$ Argyres-Douglas (AD) theories from the structure of the associated two dimensional $W$-algebra. The Schur index is derived from the vacuum character of the corresponding $W$-algebra and can be rewritten in a very simple form, which can be easily used to verify properties like level-rank dualities, collapsing levels, and S-duality conjectures. The Zhu's $C_2$ algebra can be regarded as a ring associated with the Schur sector, and a surprising connection between certain Zhu's $C_2$ algebra and the Jacobi algebra of a hypersurface singularity is discovered. Finally, the Macdonald index is computed from the Kazhdan filtration of the $W$-algebra.

  9 citations

• QGOpt: Riemannian optimization for quantum technologies

  Ilia A. Luchnikov, Alexander Ryzhov, Sergey N. Filippov, Henni Ouerdane

  SciPost Phys. 10, 079 (2021) · published 30 March 2021 | Toggle abstract · pdf

  Many theoretical problems in quantum technology can be formulated and addressed as constrained optimization problems. The most common quantum mechanical constraints such as, e.g., orthogonality of isometric and unitary matrices, CPTP property of quantum channels, and conditions on density matrices, can be seen as quotient or embedded Riemannian manifolds. This allows to use Riemannian optimization techniques for solving quantum-mechanical constrained optimization problems. In the present work, we introduce QGOpt, the library for constrained optimization in quantum technology. QGOpt relies on the underlying Riemannian structure of quantum-mechanical constraints and permits application of standard gradient based optimization methods while preserving quantum mechanical constraints. Moreover, QGOpt is written on top of TensorFlow, which enables automatic differentiation to calculate necessary gradients for optimization. We show two application examples: quantum gate decomposition and quantum tomography.

  12 citations

• Chiral magnetism: a geometric perspective

  Daniel Hill, Valeriy Slastikov, Oleg Tchernyshyov

  SciPost Phys. 10, 078 (2021) · published 29 March 2021 | Toggle abstract · pdf

  We discuss a geometric perspective on chiral ferromagnetism. Much like gravity becomes the effect of spacetime curvature in theory of relativity, the Dzyaloshinski-Moriya interaction arises in a Heisenberg model with nontrivial spin parallel transport. The Dzyaloshinskii-Moriya vectors serve as a background SO(3) gauge field. In 2 spatial dimensions, the model is partly solvable when an applied magnetic field matches the gauge curvature. At this special point, solutions to the Bogomolny equation are exact excited states of the model. We construct a variational ground state in the form of a skyrmion crystal and confirm its viability by Monte Carlo simulations. The geometric perspective offers insights into important problems in magnetism, e.g., conservation of spin current in the presence of chiral interactions.

  13 citations

• QMetrology from QCosmology: Study with entangled two qubit open quantum system in De Sitter space

  Sayantan Choudhury, Satyaki Chowdhury, Nitin Gupta, Abinash Swain

  SciPost Phys. Core 4, 006 (2021) · published 29 March 2021 | Toggle abstract · pdf

  In this paper, our prime objective is to apply the techniques of parameter estimation theory and the concept of Quantum Metrology in the form of Fisher Information to investigate the role of certain physical quantities in the open quantum dynamics of a two entangled qubit system under the Markovian approximation. There exist various physical parameters which characterize such system, but can not be treated as any quantum mechanical observable. It becomes imperative to do a detailed parameter estimation analysis to determine the physically consistent parameter space of such quantities. We apply both Classical Fisher Information (CFI) and Quantum Fisher Information (QFI) to correctly estimate these parameters, which play significant role to describe the out-of-equilibrium and the long range quantum entanglement phenomena of open quantum system. Quantum Metrology, compared to classical parameter estimation theory, plays a two-fold superior role, improving the precision and accuracy of parameter estimation. Additionally, in this paper we present a new avenue in terms of Quantum Metrology, which beats the classical parameter estimation. We also present an interesting result of revival of out-of-equilibrium feature at the late time scales, arising due to the long range quantum entanglement at early time scale and provide a physical interpretation for the same in terms of Bell's Inequality Violation in early time scale giving rise to non-locality.

  3 citations