Publications

Order by: publication date number of citations

• Fusion and monodromy in the Temperley-Lieb category

  Jonathan Belletête, Yvan Saint-Aubin

  SciPost Phys. 5, 041 (2018) · published 31 October 2018 | Toggle abstract · pdf

  Graham and Lehrer (1998) introduced a Temperley-Lieb category $\mathsf{\widetilde{TL}}$ whose objects are the non-negative integers and the morphisms in $\mathsf{Hom}(n,m)$ are the link diagrams from $n$ to $m$ nodes. The Temperley-Lieb algebra $\mathsf{TL}_{n}$ is identified with $\mathsf{Hom}(n,n)$. The category $\mathsf{\widetilde{TL}}$ is shown to be monoidal. We show that it is also a braided category by constructing explicitly a commutor. A twist is also defined on $\mathsf{\widetilde{TL}}$. We introduce a module category ${\text{ Mod}_{\mathsf{\widetilde{TL}}}}$ whose objects are functors from $\mathsf{\widetilde{TL}}$ to $\mathsf{Vect}_{\mathbb C}$ and define on it a fusion bifunctor extending the one introduced by Read and Saleur (2007). We use the natural morphisms constructed for $\mathsf{\widetilde{TL}}$ to induce the structure of a ribbon category on ${\text{ Mod}_{\mathsf{\widetilde{TL}}}}(\beta=-q-q^{-1})$, when $q$ is not a root of unity. We discuss how the braiding on $\mathsf{\widetilde{TL}}$ and integrability of statistical models are related. The extension of these structures to the family of dilute Temperley-Lieb algebras is also discussed.

  1 citation

• Quantum gravity, renormalizability and diffeomorphism invariance

  Tim R. Morris

  SciPost Phys. 5, 040 (2018) · published 30 October 2018 | Toggle abstract · pdf

  We show that the Wilsonian renormalization group (RG) provides a natural regularisation of the Quantum Master Equation such that to first order the BRST algebra closes on local functionals spanned by the eigenoperators with constant couplings. We then apply this to quantum gravity. Around the Gaussian fixed point, RG properties of the conformal factor of the metric allow the construction of a Hilbert space $\mathfrak{L}$ of renormalizable interactions, non-perturbative in $\hbar$, and involving arbitrarily high powers of the gravitational fluctuations. We show that diffeomorphism invariance is violated for interactions that lie inside $\mathfrak{L}$, in the sense that only a trivial quantum BRST cohomology exists for interactions at first order in the couplings. However by taking a limit to the boundary of $\mathfrak{L}$, the couplings can be constrained to recover Newton's constant, and standard realisations of diffeomorphism invariance, whilst retaining renormalizability. The limits are sufficiently flexible to allow this also at higher orders. This leaves open a number of questions that should find their answer at second order. We develop much of the framework that will allow these calculations to be performed.

  17 citations

• Nested Algebraic Bethe Ansatz in integrable models: recent results

  Stanislav Pakuliak, Eric Ragoucy, Nikita Slavnov

  SciPost Phys. Lect. Notes 6 (2018) · published 29 October 2018 | Toggle abstract · pdf

  This short note summarizes the works done in collaboration between S. Belliard (CEA, Saclay), L. Frappat (LAPTh, Annecy), S. Pakuliak (JINR, Dubna), E. Ragoucy (LAPTh, Annecy), N. Slavnov (Steklov Math. Inst., Moscow) and more recently A. Hutsalyuk (Wuppertal / Moscow) and A. Liashyk (Kiev / Moscow). It presents the construction of Bethe vectors, their scalar products and the form factors of local operator for integrable models based on the (super)algebras $gl_n$, $gl_{m|p}$ or their quantum deformations. It corresponds to two talks given by E.R. and N.S. at \textsl{Correlation functions of quantum integrable systems and beyond}, in honor of Jean-Michel Maillet for his 60's (ENS Lyon, October 2017).

  6 citations

• Effective field theory of a vortex lattice in a bosonic superfluid

  Sergej Moroz, Carlos Hoyos, Claudio Benzoni, Dam Thanh Son

  SciPost Phys. 5, 039 (2018) · published 26 October 2018 | Toggle abstract · pdf

  Using boson-vortex duality, we formulate a low-energy effective theory of a two-dimensional vortex lattice in a bosonic Galilean-invariant compressible superfluid. The excitation spectrum contains a gapped Kohn mode and an elliptically polarized Tkachenko mode that has quadratic dispersion relation at low momenta. External rotation breaks parity and time-reversal symmetries and gives rise to Hall responses. We extract the particle number current and stress tensor linear responses and investigate the relations between them that follow from Galilean symmetry. We argue that elementary particles and vortices do not couple to the spin connection which suggests that the Hall viscosity at zero frequency and momentum vanishes in a vortex lattice.

  23 citations

• Flux-closure domains in high aspect ratio electroless-deposited CoNiB nanotubes

  Michal Staňo, Sandra Schaefer, Alexis Wartelle, Maxime Rioult, Rachid Belkhou, Alessandro Sala, Tevfik Onur Menteş, Andrea Locatelli, Laurent Cagnon, Beatrix Trapp, Sebastian Bochmann, Sylvain Martin, Eric Gautier, Jean-Christophe Toussaint, Wolfgang Ensinger, Olivier Fruchart

  SciPost Phys. 5, 038 (2018) · published 25 October 2018 | Toggle abstract · pdf

  We report the imaging of magnetic domains in ferromagnetic CoNiB nanotubes with very long aspect ratio, fabricated by electroless plating. While axial magnetization is expected for long tubes made of soft magnetic materials, we evidence series of azimuthal domains. We tentatively explain these by the interplay of anisotropic strain and/or grain size, with magneto-elasticity and/or anisotropic interfacial magnetic anisotropy. This material could be interesting for dense data storage, as well as curvature-induced magnetic phenomena such as the non-reciprocity of spin-wave propagation.

  17 citations

• Monitoring continuous spectrum observables: the strong measurement limit

  Michel Bauer, Denis Bernard, Tony Jin

  SciPost Phys. 5, 037 (2018) · published 24 October 2018 | Toggle abstract · pdf

  We revisit aspects of monitoring observables with continuous spectrum in a quantum system subject to dissipative (Lindbladian) or conservative (Hamiltonian) evolutions. After recalling some of the salient features of the case of pure monitoring, we deal with the case when monitoring is in competition with a Lindbladian evolution. We show that the strong measurement limit leads to a diffusion on the spectrum of the observable. For the case with competition between observation and Hamiltonian dynamics, we exhibit a scaling limit in which the crossover between the classical regime and a diffusive regime can be analyzed in details.

  3 citations

• Dark matter in anomaly-free gauge extensions

  Martin Bauer, Sascha Diefenbacher, Tilman Plehn, Michael Russell, Daniel A. Camargo

  SciPost Phys. 5, 036 (2018) · published 19 October 2018 | Toggle abstract · pdf

  A consistent model for vector mediators to dark matter needs to be anomaly-free and include a scalar mode from mass generation. For the leading U(1) extensions we review the structure and constraints, including kinetic mixing at loop level. The thermal relic density suggests that the vector and scalar masses are similar. For the LHC we combine a $Z'$ shape analysis with mono-jets. For the latter, we find that a shape analysis offers significant improvement over existing cut-and-count approaches. Direct detection limits strongly constrain the kinetic mixing angle and we propose a $\ell^+\ell^- E_T$ search strategy based on the scalar mediator.

  21 citations

• Solution of Baxter equation for the $q$-Toda and Toda$_2$ chains by NLIE

  Olivier Babelon, Karol K. Kozlowski, Vincent Pasquier

  SciPost Phys. 5, 035 (2018) · published 18 October 2018 | Toggle abstract · pdf

  We construct a basis of solutions of the scalar $\boldsymbol{ \texttt{t} }- \boldsymbol{ \texttt{Q} }$ equation describing the spectrum of the $q$-Toda and Toda$_2$ chains by using auxiliary non-linear integral equations. Our construction allows us to provide quantisation conditions for the spectra of these models in the form of thermodynamic Bethe Ansatz-like equations.

  3 citations

• Actual Physics behind Mono-X

  Elias Bernreuther, Jan Horak, Tilman Plehn, Anja Butter

  SciPost Phys. 5, 034 (2018) · published 17 October 2018 | Toggle abstract · pdf

  Mono-X searches are standard dark matter search strategies at the LHC. First, we show how in the case of initial state radiation they essentially collapse to mono-jet searches. Second, we systematically study mono-X signatures from decays of heavier dark matter states. Direct detection constraints strongly limit our MSSM expectations, but largely vanish for mono-Z and mono-Higgs signals once we include light NMSSM mediators. Finally, the decay topology motivates mono-W-pair and mono-Higgs-pair searches, strengthening and complementing their mono-X counterparts.

  12 citations

• Spreading of entanglement and correlations after a quench with intertwined quasiparticles

  Alvise Bastianello, Pasquale Calabrese

  SciPost Phys. 5, 033 (2018) · published 15 October 2018 | Toggle abstract · pdf

  We extend the semiclassical picture for the spreading of entanglement and correlations to quantum quenches with several species of quasiparticles that have non-trivial pair correlations in momentum space. These pair correlations are, for example, relevant in inhomogeneous lattice models with a periodically-modulated Hamiltonian parameter. We provide explicit predictions for the spreading of the entanglement entropy in the space-time scaling limit. We also predict the time evolution of one- and two-point functions of the order parameter for quenches within the ordered phase. We test all our predictions against exact numerical results for quenches in the Ising chain with a modulated transverse field and we find perfect agreement.

  45 citations