Publications

Order by: publication date number of citations

• The equilibrium landscape of the Heisenberg spin chain

  Enej Ilievski, Eoin Quinn

  SciPost Phys. 7, 033 (2019) · published 13 September 2019 | Toggle abstract · pdf

  We characterise the equilibrium landscape, the entire manifold of local equilibrium states, of an interacting integrable quantum model. Focusing on the isotropic Heisenberg spin chain, we describe in full generality two complementary frameworks for addressing equilibrium ensembles: the functional integral Thermodynamic Bethe Ansatz approach, and the lattice regularisation transfer matrix approach. We demonstrate the equivalence between the two, and in doing so clarify several subtle features of generic equilibrium states. In particular we explain the breakdown of the canonical Y-system, which reflects a hidden structure in the parametrisation of equilibrium ensembles.

  10 citations

• Invariants of winding-numbers and steric obstruction in dynamics of flux lines

  Olivier Cépas, Peter M. Akhmetiev

  SciPost Phys. 7, 032 (2019) · published 12 September 2019 | Toggle abstract · pdf

  We classify the sectors of configurations that result from the dynamics of 2d crossing flux lines, which are the simplest degrees of freedom of the 3-coloring lattice model. We show that the dynamical obstruction is the consequence of two effects: (i) conservation laws described by a set of invariants that are polynomials of the winding numbers of the loop configuration, (ii) steric obstruction that prevents paths between configurations, for lack of free space. We argue that the invariants fully classify the configurations in five, chiral and achiral, sectors and no further obstruction in the limit of low-winding numbers.

  1 citation

• The self-consistent quantum-electrostatic problem in strongly non-linear regime

  Pacome Armagnat, A. Lacerda-Santos, Benoit Rossignol, Christoph Groth, Xavier Waintal

  SciPost Phys. 7, 031 (2019) · published 11 September 2019 | Toggle abstract · pdf

  The self-consistent quantum-electrostatic (also known as Poisson-Schr\"odinger) problem is notoriously difficult in situations where the density of states varies rapidly with energy. At low temperatures, these fluctuations make the problem highly non-linear which renders iterative schemes deeply unstable. We present a stable algorithm that provides a solution to this problem with controlled accuracy. The technique is intrinsically convergent including in highly non-linear regimes. We illustrate our approach with (i) a calculation of the compressible and incompressible stripes in the integer quantum Hall regime and (ii) a calculation of the differential conductance of a quantum point contact geometry. Our technique provides a viable route for the predictive modeling of the transport properties of quantum nanoelectronics devices.

  16 citations

• Gauged sigma models and magnetic Skyrmions

  Bernd J Schroers

  SciPost Phys. 7, 030 (2019) · published 10 September 2019 | Toggle abstract · pdf

  We define a gauged non-linear sigma model for a 2-sphere valued field and a $SU(2)$ connection on an arbitrary Riemann surface whose energy functional reduces to that for critically coupled magnetic skyrmions in the plane, with arbitrary Dzyaloshinskii-Moriya interaction, for a suitably chosen gauge field. We use the interplay of unitary and holomorphic structures to derive a general solution of the first order Bogomol'nyi equation of the model for any given connection. We illustrate this formula with examples, and also point out applications to the study of impurities.

  25 citations

• Anomalous phase ordering of a quenched ferromagnetic superfluid

  Lewis A. Williamson, P. Blair Blakie

  SciPost Phys. 7, 029 (2019) · published 9 September 2019 | Toggle abstract · pdf

  Coarsening dynamics, the canonical theory of phase ordering following a quench across a symmetry breaking phase transition, is thought to be driven by the annihilation of topological defects. Here we show that this understanding is incomplete. We simulate the dynamics of an isolated spin-1 condensate quenched into the easy-plane ferromagnetic phase and find that the mutual annihilation of spin vortices does not take the system to the equilibrium state. A nonequilibrium background of long wavelength spin waves remain at the Berezinskii-Kosterlitz-Thouless temperature, an order of magnitude hotter than the equilibrium temperature. The coarsening continues through a second much slower scale invariant process with a length scale that grows with time as $t^{1/3}$. This second regime of coarsening is associated with spin wave energy transport from low to high wavevectors, bringing about the the eventual equilibrium state. Because the relevant spin waves are noninteracting, the transport occurs through a dynamic coupling to other degrees of freedom of the system. The transport displays features of a spin wave energy cascade, providing a potential profitable connection with the emerging field of spin wave turbulence. Strongly coupling the system to a reservoir destroys the second regime of coarsening, allowing the system to thermalise following the annihilation of vortices.

  5 citations

• Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds

  Guillaume Bossard, Charles Cosnier-Horeau, Boris Pioline

  SciPost Phys. 7, 028 (2019) · published 5 September 2019 | Toggle abstract · pdf

  Motivated by precision counting of BPS black holes, we analyze six-derivative couplings in the low energy effective action of three-dimensional string vacua with 16 supercharges. Based on perturbative computations up to two-loop, supersymmetry and duality arguments, we conjecture that the exact coefficient of the $\nabla^2(\nabla\phi)^4$ effective interaction is given by a genus-two modular integral of a Siegel theta series for the non-perturbative Narain lattice times a specific meromorphic Siegel modular form. The latter is familiar from the Dijkgraaf-Verlinde-Verlinde (DVV) conjecture on exact degeneracies of 1/4-BPS dyons. We show that this Ansatz reproduces the known perturbative corrections at weak heterotic coupling, including tree-level, one- and two-loop corrections, plus non-perturbative effects of order $e^{-1/g_3^2}$. We also examine the weak coupling expansions in type I and type II string duals and find agreement with known perturbative results, as well as new predictions for higher genus perturbative contributions. In the limit where a circle in the internal torus decompactifies, our Ansatz predicts the exact $\nabla^2 F^4$ effective interaction in four-dimensional CHL string vacua, along with infinite series of exponentially suppressed corrections of order $e^{-R}$ from Euclideanized BPS black holes winding around the circle, and further suppressed corrections of order $e^{-R^2}$ from Taub-NUT instantons. We show that instanton corrections from 1/4-BPS black holes are precisely weighted by the BPS index predicted from the DVV formula, including the detailed moduli dependence. We also extract two-instanton corrections from pairs of 1/2-BPS black holes, demonstrating consistency with supersymmetry and wall-crossing, and estimate the size of instanton-anti-instanton contributions.

  9 citations

• Anomalous dimensions of potential top-partners

  Diogo Buarque Franzosi, Gabriele Ferretti

  SciPost Phys. 7, 027 (2019) · published 4 September 2019 | Toggle abstract · pdf

  We discuss anomalous dimensions of top-partner candidates in theories of Partial Compositeness. First, we revisit, confirm and extend the computation by DeGrand and Shamir of anomalous dimensions of fermionic trilinears. We present general results applicable to all matter representations and to composite operators of any allowed spin. We then ask the question of whether it is reasonable to expect some models to have composite operators of sufficiently large anomalous dimension to serve as top-partners. While this question can be answered conclusively only by lattice gauge theory, within perturbation theory we find that such values could well occur for some specific models. In the Appendix we collect a number of practical group theory results for fourth-order invariants of general interest in gauge theories with many irreducible representations of fermions.

  24 citations

• Anisotropic scaling of the two-dimensional Ising model I: the torus

  Hendrik Hobrecht, Alfred Hucht

  SciPost Phys. 7, 026 (2019) · published 2 September 2019 | Toggle abstract · pdf

  We present detailed calculations for the partition function and the free energy of the finite two-dimensional square lattice Ising model with periodic and antiperiodic boundary conditions, variable aspect ratio, and anisotropic couplings, as well as for the corresponding universal free energy finite-size scaling functions. Therefore, we review the dimer mapping, as well as the interplay between its topology and the different types of boundary conditions. As a central result, we show how both the finite system as well as the scaling form decay into contributions for the bulk, a characteristic finite-size part, and - if present - the surface tension, which emerges due to at least one antiperiodic boundary in the system. For the scaling limit we extend the proper finite-size scaling theory to the anisotropic case and show how this anisotropy can be absorbed into suitable scaling variables.

  9 citations

• Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point

  Grégoire Misguich, Nicolas Pavloff, Vincent Pasquier

  SciPost Phys. 7, 025 (2019) · published 29 August 2019 | Toggle abstract · pdf

  We study the dynamics of a spin-1/2 XXZ chain which is initially prepared in a domain-wall state. We compare the results of time-dependent Density Matrix Renormalization Group simulations with those of an effective description in terms of a classical anisotropic Landau-Lifshitz (LL) equation. Numerous quantities are analyzed: magnetization (x, y and z components), energy density, energy current, but also some spin-spin correlation functions or entanglement entropy in the quantum chain. Without any adjustable parameter a quantitative agreement is observed between the quantum and the LL problems in the long time limit, when the models are close to the isotropic point. This is explained as a consequence of energy conservation. At the isotropic point the mapping between the LL equation and the nonlinear Schr\"odinger equation is used to construct a variational solution capturing several aspects of the problem.

  31 citations

• Entanglement in a fermion chain under continuous monitoring

  Xiangyu Cao, Antoine Tilloy, Andrea De Luca

  SciPost Phys. 7, 024 (2019) · published 23 August 2019 | Toggle abstract · pdf

  We study the entanglement entropy of the quantum trajectories of a free fermion chain under continuous monitoring of local occupation numbers. We propose a simple theory for entanglement entropy evolution from disentangled and highly excited initial states. It is based on generalized hydrodynamics and the quasi-particle pair approach to entanglement in integrable systems. We test several quantitative predictions of the theory against extensive numerics and find good agreement. In particular, the volume law entanglement is destroyed by the presence of arbitrarily weak measurement.

  189 citations