Publications

Order by: publication date number of citations

• Many-body localization in the Fock space of natural orbitals

  Wouter Buijsman, Vladimir Gritsev, Vadim Cheianov

  SciPost Phys. 4, 038 (2018) · published 25 June 2018 | Toggle abstract · pdf

  We study the eigenstates of a paradigmatic model of many-body localization in the Fock basis constructed out of the natural orbitals. By numerically studying the participation ratio, we identify a sharp crossover between different phases at a disorder strength close to the disorder strength at which subdiffusive behaviour sets in, significantly below the many-body localization transition. We repeat the analysis in the conventionally used computational basis, and show that many-body localized eigenstates are much stronger localized in the Fock basis constructed out of the natural orbitals than in the computational basis.

  10 citations

• The Inhomogeneous Gaussian Free Field, with application to ground state correlations of trapped 1d Bose gases

  Yannis Brun, Jérôme Dubail

  SciPost Phys. 4, 037 (2018) · published 25 June 2018 | Toggle abstract · pdf

  Motivated by the calculation of correlation functions in inhomogeneous one-dimensional (1d) quantum systems, the 2d Inhomogeneous Gaussian Free Field (IGFF) is studied and solved. The IGFF is defined in a domain $\Omega \subset \mathbb{R}^2$ equipped with a conformal class of metrics $[{\rm g}]$ and with a real positive coupling constant $K: \Omega \rightarrow \mathbb{R}_{>0}$ by the action $\mathcal{S}[h] = \frac{1}{8\pi } \int_\Omega \frac{\sqrt{{\rm g}} d^2 {\rm x}}{K({\rm x})} \, {\rm g}^{i j} (\partial_i h)(\partial_j h)$. All correlations functions of the IGFF are expressible in terms of the Green's functions of generalized Poisson operators that are familiar from 2d electrostatics in media with spatially varying dielectric constants. This formalism is then applied to the study of ground state correlations of the Lieb-Liniger gas trapped in an external potential $V(x)$. Relations with previous works on inhomogeneous Luttinger liquids are discussed. The main innovation here is in the identification of local observables $\hat{O} (x)$ in the microscopic model with their field theory counterparts $\partial_x h, e^{i h(x)}, e^{-i h(x)}$, etc., which involve non-universal coefficients that themselves depend on position --- a fact that, to the best of our knowledge, was overlooked in previous works on correlation functions of inhomogeneous Luttinger liquids ---, and that can be calculated thanks to Bethe Ansatz form factors formulae available for the homogeneous Lieb-Liniger model. Combining those position-dependent coefficients with the correlation functions of the IGFF, ground state correlation functions of the trapped gas are obtained. Numerical checks from DMRG are provided for density-density correlations and for the one-particle density matrix, showing excellent agreement.

  40 citations

• Current-induced magnetization hysteresis defines atom trapping in a superconducting atomchip

  Fritz Diorico, Stefan Minniberger, Thomas Weigner, Benedikt Gerstenecker, Naz Shokrani, Zaneta Kurpias, Jorg Schmiedmayer

  SciPost Phys. 4, 036 (2018) · published 22 June 2018 | Toggle abstract · pdf

  The physics of superconducting films, and especially the role of remnant magnetization has a defining influence on the magnetic fields used to hold and manipulate atoms on superconducting atomchips. We magnetically trap ultracold ^{87}Rb atoms on a 200{\mu}m wide and 500nm thick cryogenically cooled niobium Z wire structure. By measuring the distance of the atomcloud to the trapping wire for different transport currents and bias fields, we probe the trapping characteristics of the niobium superconducting structure. At distances closer than the trapping wire width, we observe a different behaviour than that of normal conducting wire traps. Furthermore, we measure a stable magnetic trap at zero transport current. These observations point to the presence of a remnant magnetization in our niobium film which is induced by a transport current. This current-induced magnetization defines the trap close to the chip surface. Our measurements agree very well with an analytic prediction based on the critical state model (CSM). Our results provide a new tool to control atom trapping on superconducting atomchips by designing the current distribution through its current history.

  4 citations

• Tagging Jets in Invisible Higgs Searches

  Anke Biekoetter, Fabian Keilbach, Rhea Moutafis, Tilman Plehn, Jennifer M. Thompson

  SciPost Phys. 4, 035 (2018) · published 22 June 2018 | Toggle abstract · pdf

  Searches for invisible Higgs decays in weak boson fusion are a well-known laboratory for jets and QCD studies. We present a series of results on tagging jets and central jet activity. First, precision analyses of the central jet activity require full control of single top production in some analyses. Second, the rate dependence on the size of the tagging jets is not limited to weak boson fusion. For the first time, we show how subjet information on the tagging jets and on the additional jet activity can be used to extract the Higgs signal. The additional observables relieve some of the pressure on other, critical observables. Finally, we compare the performance of weak boson fusion and associated Higgs production.

  9 citations

• Two-point boundary correlation functions of dense loop models

  Alexi Morin-Duchesne, Jesper Lykke Jacobsen

  SciPost Phys. 4, 034 (2018) · published 19 June 2018 | Toggle abstract · pdf

  We investigate six types of two-point boundary correlation functions in the dense loop model. These are defined as ratios $Z/Z^0$ of partition functions on the $m\times n$ square lattice, with the boundary condition for $Z$ depending on two points $x$ and $y$. We consider: the insertion of an isolated defect (a) and a pair of defects (b) in a Dirichlet boundary condition, the transition (c) between Dirichlet and Neumann boundary conditions, and the connectivity of clusters (d), loops (e) and boundary segments (f) in a Neumann boundary condition. For the model of critical dense polymers, corresponding to a vanishing loop weight ($\beta = 0$), we find determinant and pfaffian expressions for these correlators. We extract the conformal weights of the underlying conformal fields and find $\Delta = -\frac18$, $0$, $-\frac3{32}$, $\frac38$, $1$, $\tfrac \theta \pi (1+\tfrac{2\theta}\pi)$, where $\theta$ encodes the weight of one class of loops for the correlator of type f. These results are obtained by analysing the asymptotics of the exact expressions, and by using the Cardy-Peschel formula in the case where $x$ and $y$ are set to the corners. For type b, we find a $\log|x-y|$ dependence from the asymptotics, and a $\ln (\ln n)$ term in the corner free energy. This is consistent with the interpretation of the boundary condition of type b as the insertion of a logarithmic field belonging to a rank two Jordan cell. For the other values of $\beta = 2 \cos \lambda$, we use the hypothesis of conformal invariance to predict the conformal weights and find $\Delta = \Delta_{1,2}$, $\Delta_{1,3}$, $\Delta_{0,\frac12}$, $\Delta_{1,0}$, $\Delta_{1,-1}$ and $\Delta_{\frac{2\theta}\lambda+1,\frac{2\theta}\lambda+1}$, extending the results of critical dense polymers. With the results for type f, we reproduce a Coulomb gas prediction for the valence bond entanglement entropy of Jacobsen and Saleur.

  3 citations

• Puzzles and pitfalls involving Haar-typicality in holography

  Ning Bao, Aidan Chatwin-Davies

  SciPost Phys. 4, 033 (2018) · published 19 June 2018 | Toggle abstract · pdf

  Holographic states that have a well-defined geometric dual in AdS/CFT are not faithfully represented by Haar-typical states in finite-dimensional models. As such, trying to apply principles and lessons from Haar-random ensembles of states to holographic states can lead to apparent puzzles and contradictions. We point out a handful of these pitfalls.

  1 citation

• Deconstructing S-Duality

  Kyle Aitken, Andreas Karch, Brandon Robinson

  SciPost Phys. 4, 032 (2018) · published 19 June 2018 | Toggle abstract · pdf

  We use the technique of deconstruction to lift dualities from 2+1 to 3+1 dimensions. In this work we demonstrate the basic idea by deriving S-duality of maximally supersymmetric electromagnetism in 3+1 dimensions from mirror symmetry in 2+1. We also study the deconstruction of a non-supersymmetric duality in 3+1 dimensions using Abelian bosonization in 2+1 dimensions.

  8 citations

• Entanglement entropies of minimal models from null-vectors

  Thomas Dupic, Benoit Estienne, Yacine Ikhlef

  SciPost Phys. 4, 031 (2018) · published 18 June 2018 | Toggle abstract · pdf

  We present a new method to compute R\'enyi entropies in one-dimensional critical systems. The null-vector conditions on the twist fields in the cyclic orbifold allow us to derive a differential equation for their correlation functions. The latter are then determined by standard bootstrap techniques. We apply this method to the calculation of various R\'enyi entropies in the non-unitary Yang-Lee model.

  33 citations

• Ground state solutions of inhomogeneous Bethe equations

  S. Belliard, A. Faribault

  SciPost Phys. 4, 030 (2018) · published 15 June 2018 | Toggle abstract · pdf

  The distribution of Bethe roots, solution of the inhomogeneous Bethe equations, which characterize the ground state of the periodic XXX Heisenberg spin-$\frac{1}{2}$ chain is investigated. Numerical calculations show that, for this state, the new inhomogeneous term does not contribute to the Baxter T-Q equation in the thermodynamic limit. Different families of Bethe roots are identified and their large N behaviour are conjectured and validated.

  2 citations

• Exact results for a fractional derivative of elementary functions

  Gavriil Shchedrin, Nathanael C. Smith, Anastasia Gladkina, Lincoln D. Carr

  SciPost Phys. 4, 029 (2018) · published 15 June 2018 | Toggle abstract · pdf

  We present exact analytical results for the Caputo fractional derivative of a wide class of elementary functions, including trigonometric and inverse trigonometric, hyperbolic and inverse hyperbolic, Gaussian, quartic Gaussian, and Lorentzian functions. These results are especially important for multi-scale physical systems, such as porous materials, disordered media, and turbulent fluids, in which transport is described by fractional partial differential equations. The exact results for the Caputo fractional derivative are obtained from a single generalized Euler's integral transform of the generalized hyper-geometric function with a power-law argument. We present a proof of the generalized Euler's integral transform and directly apply it to the exact evaluation of the Caputo fractional derivative of a broad spectrum of functions, provided that these functions can be expressed in terms of a generalized hyper-geometric function with a power-law argument. We determine that the Caputo fractional derivative of elementary functions is given by the generalized hyper-geometric function. Moreover, we show that in the most general case the final result cannot be reduced to elementary functions, in contrast to both the Liouville-Caputo and Fourier fractional derivatives. However, we establish that in the infinite limit of the argument of elementary functions, all three definitions of a fractional derivative - the Caputo, Liouville-Caputo, and Fourier- converge to the same result given by the elementary functions. Finally, we prove the equivalence between Liouville-Caputo and Fourier fractional derivatives.

  5 citations