arXiv subjects

J. Vidal

Publications and source records attributed to J. Vidal.

At least 19 recordsLinked to original sources

arXiv2023

Density of states of tight-binding models in the hyperbolic plane

We study the energy spectrum of tight-binding Hamiltonian for regular hyperbolic tilings. More specifically, we compute the density of states using the continued-fraction expansion of the Green function on finite-size systems with more than $10^9$ sites and open boundary conditions. The coefficients of this expansion are found to quickly converge so that the thermodynamical limit can be inferred quite accurately. This density of states is in stark contrast with the prediction stemming from the recently proposed hyperbolic band theory. Thus, we conclude that the fraction of the energy spectrum described by the hyperbolic Bloch-like wave eigenfunctions vanishes in the thermodynamical limit.

cond-mat.str-el↗

arXiv2023

Precession-driven flows in stress-free ellipsoids

Motivated by modelling rotating turbulence in planetary fluid layers, we investigate precession-driven flows in ellipsoids subject to stress-free boundary conditions (SF-BC). The SF-BC could indeed unlock numerical constraints associated with the no-slip boundary conditions (NS-BC), but are also relevant for some astrophysical applications. Although SF-BC have been employed in the pioneering work of Lorenzani & Tilgner (J. Fluid Mech., 2003, 492, pp. 363--379), they have scarcely been used due to the discovery of some specific mathematical issues associated with angular momentum conservation. We revisit the problem using asymptotic analysis in the low-viscosity regime, which is validated with numerical simulations. First, we extend the reduced model of uniform-vorticity flows in ellipsoids to account for SF-BC. We show that the long-term evolution of angular momentum is affected by viscosity in triaxial geometries, but also in axisymmetric ellipsoids when the mean rotation axis of the fluid is not the symmetry axis. In a regime relevant to planets, we analytically obtain the primary forced flow in triaxial geometries, which exhibits a second inviscid resonance. Then, we investigate the bulk instabilities existing in precessing ellipsoids. We show that using SF-BC would be useful to explore the non-viscous instabilities (e.g. Kerswell, Geophys. Astrophys. Fluid Dyn., 1993, 72, pp. 107-144), which are presumably relevant for planetary applications but are often hampered in experiments or simulations with NS-BC.

physics.flu-dyn↗

arXiv2022

Aharonov-Bohm cages, flat bands, and gap labeling in hyperbolic tilings

Aharonov-Bohm caging is a localization mechanism stemming from the competition between the geometry and the magnetic field. Originally described for a tight-binding model in the dice lattice, this destructive interference phenomenon prevents any wavepacket spreading away from a strictly confined region. Accordingly, for the peculiar values of the field responsible for this effect, the energy spectrum consists of a discrete set of highly degenerate flat bands. In the present work, we show that Aharonov-Bohm cages are also found in an infinite set of hyperbolic dice tilings defined on a negatively curved hyperbolic plane. We detail the construction of these tilings and compute their Hofstadter butterflies by considering periodic boundary conditions on high-genus surfaces. As recently observed for some regular hyperbolic tilings, these butterflies do not manifest the self-similar structure of their Euclidean counterparts but still contain some gaps. We also consider the energy spectrum of hyperbolic kagome tilings (which are the dual of hyperbolic dice tilings), which displays interesting features, such as highly degenerate states arising for some particular values of the magnetic field. For these two families of hyperbolic tilings, we compute the Chern number in the main gaps of the Hofstadter butterfly and propose a gap labeling inspired by the Euclidean case. Finally, we also study the triangular Husimi cactus, which is a limiting case in the family of hyperbolic kagome tilings, and we derive an exact expression for its spectrum versus magnetic flux.

cond-mat.mes-hall↗

arXiv2021

Partition function of the Levin-Wen model

Using a description of the Levin-Wen model excitations in terms of Wilson lines, we compute the degeneracy of the energy levels for any input anyon theory and for any trivalent graph embedded on any (orientable) compact surface. This result allows one to obtain the finite-size and finite-temperature partition function and to show that there are no thermal phase transitions.

cond-mat.str-el↗

arXiv2021

Competing topological orders in three dimensions: X-cube versus toric code

We study the competition between two different topological orders in three dimensions by considering the X-cube model and the three-dimensional toric code. The corresponding Hamiltonian can be decomposed into two commuting parts, one of which displays a self-dual spectrum. To determine the phase diagram, we compute the high-order series expansions of the ground-state energy in all limiting cases. Apart from the topological order related to the toric code and the fractonic order related to the X-cube model, we found two new phases which are adiabatically connected to classical limits with nontrivial sub-extensive degeneracies. All phase transitions are found to be first order.

cond-mat.str-el↗

arXiv2020

Wegner-Wilson loops in string nets

We study the Wegner-Wilson loops in the string-net model of Levin and Wen in the presence of a string tension. The latter is responsible for a phase transition from a topological deconfined phase (weak tension) to a trivial confined phase (strong tension). We analyze the behavior of all Wegner-Wilson loops in both limiting cases for an arbitrary input theory of the string-net model. Using a fluxon picture, we compute perturbatively the first contributions to a perimeter law in the topological phase as a function of the quantum dimensions. In the trivial phase, we find that Wegner-Wilson loops obey a modified area law, in agreement with a recent mean-field approach.

cond-mat.str-el↗

arXiv2020

Solute-point defect interactions, coupled diffusion, and radiation induced segregation in fcc nickel

Radiation-induced segregation (RIS) of solutes in materials exposed to irradiation is a well-known problem. It affects the life-time of nuclear reactor core components by favouring radiation-induced degradation phenomena such as hardening and embrittlement. In this work, RIS tendencies in face-centered cubic (fcc) Ni-X (X = Cr, Fe, Ti, Mn, Si, P) dilute binary alloys are examined. The goal is to investigate the driving forces and kinetic mechanisms behind the experimentally observed segregation. By means of ab initio calculations, point-defect stabilities and interactions with solutes are determined, together with migration energies and attempt frequencies. Transport and diffusion coefficients are then calculated in a mean-field framework, to get a full picture of solute-defect kinetic coupling in the alloys. Results show that all solutes considered, with the exception of Cr, prefer vacancy-mediated over interstitial-mediated diffusion during both thermal and radiation-induced migration. Cr, on the other hand, preferentially migrates in a mixed-dumbbell configuration. P and Si are here shown to be enriched, and Fe and Mn to be depleted at sinks during irradiation of the material. Ti and Cr, on the other hand, display a crossover between enrichment at lower temperatures, and depletion in the higher temperature range. Results in this work are compared with previous studies in body-centered cubic (bcc) Fe, and discussed in the context of RIS in austenitic alloys.

cond-mat.mtrl-sci↗

arXiv2020

Parity of Chern numbers in the Kitaev honeycomb model and the sixteenfold way

In two dimensions, topological phases of free Majorana fermions coupled to a $\mathbb{Z}_2$ gauge field are known to be classified according to the Chern number $\nu \in \mathbb{Z}$. Its value mod 16 specifies the type of anyonic excitations. In this paper, we investigate triangular vortex configurations (and their dual) in the Kitaev honeycomb model and show that fourteen of these sixteen phases can be obtained by adding a time-reversal symmetry-breaking term. Missing phases are $\nu=\pm 7$. More generally, we prove that any periodic vortex configuration with an odd number of vortices per geometric unit cell can only host even Chern numbers whereas odd Chern numbers can be found in other cases.

cond-mat.str-el↗

arXiv2020

Pressure torque of torsional Alfv\'en modes acting on an ellipsoidal mantle

We investigate the pressure torque between the fluid core and the solid mantle arising from magnetohydrodynamic modes in a rapidly rotating planetary core. A two-dimensional reduced model of the core fluid dynamics is developed to account for the non-spherical core-mantle boundary. The simplification of such a quasi-geostrophic model rests on the assumption of invariance of the equatorial components of the fluid velocity along the rotation axis. We use this model to investigate and quantify the axial torques of linear modes, focusing on the torsional Alfv\'en modes (TM) in an ellipsoid. We verify that the periods of these modes do not depend on the rotation frequency. Furthermore, they possess angular momentum resulting in a net pressure torque acting on the mantle. This torque scales linearly with the equatorial ellipticity. We estimate that for the TM calculated here topographic coupling to the mantle is too weak to account for the variations in the Earth's length-of-day.

physics.geo-ph↗

arXiv2019

Landau level broadening, hyperuniformity, and discrete scale invariance

We study the energy spectrum of a two-dimensional electron in the presence of both a perpendicular magnetic field and a potential. In the limit where the potential is small compared to the Landau level spacing, we show that the broadening of Landau levels is simply expressed in terms of the structure factor of the potential. For potentials that are either periodic or random, we recover known results. Interestingly, for potentials with a dense Fourier spectrum made of Bragg peaks (as found, e.g., in quasicrystals), we find an algebraic broadening with the magnetic field characterized by the hyperuniformity exponent of the potential. Furthermore, if the potential is self-similar such that its structure factor has a discrete scale invariance, the broadening displays log-periodic oscillations together with an algebraic envelope.

cond-mat.other↗

arXiv2018

Ising versus $SU(2)_2$ string-net ladder

We consider the string-net model obtained from $SU(2)_2$ fusion rules. These fusion rules are shared by two different sets of anyon theories. In this work, we study the competition between the two corresponding non-Abelian quantum phases in the ladder geometry. A detailed symmetry analysis shows that the nontrivial low-energy sector corresponds to the transverse-field cluster model that displays a critical point described by the $so(2)_1$ conformal field theory. Other sectors are obtained by freezing spins in this model.

cond-mat.str-el↗

arXiv2017

Subcritical thermal convection of liquid metals in a rapidly rotating sphere

Planetary cores consist of liquid metals (low Prandtl number $Pr$) that convect as the core cools. Here we study nonlinear convection in a rotating (low Ekman number $Ek$) planetary core using a fully 3D direct numerical simulation. Near the critical thermal forcing (Rayleigh number $Ra$), convection onsets as thermal Rossby waves, but as the $Ra$ increases, this state is superceded by one dominated by advection. At moderate rotation, these states (here called the weak branch and strong branch, respectively) are smoothly connected. As the planetary core rotates faster, the smooth transition is replaced by hysteresis cycles and subcriticality until the weak branch disappears entirely and the strong branch onsets in a turbulent state at $Ek < 10^{-6}$. Here the strong branch persists even as the thermal forcing drops well below the linear onset of convection ($Ra=0.7Ra_{crit}$ in this study). We highlight the importance of the Reynolds stress, which is required for convection to subsist below the linear onset. In addition, the Péclet number is consistently above 10 in the strong branch. We further note the presence of a strong zonal flow that is nonetheless unimportant to the convective state. Our study suggests that, in the asymptotic regime of rapid rotation relevant for planetary interiors, thermal convection of liquid metals in a sphere onsets through a subcritical bifurcation.

physics.geo-ph↗

arXiv2016

Self-energies in itinerant magnets: A focus on Fe and Ni

We present a detailed study of local and non-local correlations in the electronic structure of elemental transition metals carried out by means of the Quasiparticle Self-consistent GW (QSGW ) and Dynamical Mean Field Theory (DMFT). Recent high resolution ARPES and Haas-van Alphen data of two typical transition metal systems (Fe and Ni) are used as case study. (i) We find that the properties of Fe are very well described by QSGW. Agreement with cyclotron and very clean ARPES measurements is excellent, provided that final-state scattering is taken into account. This establishes the exceptional reliability of QSGW also in metallic systems. (ii) Nonetheless QSGW alone is not able to provide an adequate description of the Ni ARPES data due to strong local spin fluctuations. We surmount this deficiency by combining nonlocal charge fluctuations in QSGW with local spin fluctuations in DMFT (QSGW + 'Magnetic DMFT'). (iii) Finally we show that the dynamics of the local fluctuations are actually not crucial. The addition of an external static field can lead to similarly good results if non-local correlations are included through QSGW.

cond-mat.str-el↗

arXiv2016

Efficient use of paired spectrum bands through TDD small cell deployments

Traditionally, wireless cellular systems have been designed to operate in Frequency Division Duplexing (FDD) paired bands that allocates the same amount of spectrum for both downlink (DL) and uplink (UL) communication. Such design is very convenient under symmetric DL/UL traffic conditions, as it used to be the case when the voice transmission was the predominant service. However, with the overwhelming advent of data services, bringing along large asymmetries between DL and UL, the conventional FDD solution becomes inefficient. In this regard, flexible duplexing concepts aim to derive procedures for improving the spectrum utilization, by adjusting resources to the actual traffic demand. In this work we review these concepts and propose the use of unpaired Time Division Duplexing (TDD) spectrum on the unused resources for small eNBs (SeNB), so that user equipment (UEs) associated to those SeNB could be served either in DL or UL. This proposal alleviates the saturated DL in FDD-based system through user offloading towards the TDD-based system. The flexible duplexing concept is analyzed from three points of view: a) regulation, b) Long Term Evolution (LTE)standardization, and c) technical solutions.

cs.IT↗

arXiv2016

Hofstadter butterfly of a quasicrystal

The energy spectrum of a tight-binding Hamiltonian is studied for the two-dimensional quasiperiodic Rauzy tiling in a perpendicular magnetic field. This spectrum known as a Hofstadter butterfly displays a very rich pattern of bulk gaps that are labeled by four integers, instead of two for periodic systems. The role of phason-flip disorder is also investigated in order to extract genuinely quasiperiodic properties. This geometric disorder is found to only preserve main quantum Hall gaps.

cond-mat.mes-hall↗

arXiv2016

Bound states in string nets

We discuss the emergence of bound states in the low-energy spectrum of the string-net Hamiltonian in the presence of a string tension. In the ladder geometry, we show that a single bound state arises either for a finite tension or in the zero-tension limit depending on the theory considered. In the latter case, we perturbatively compute the binding energy as a function of the total quantum dimension. We also address this issue in the honeycomb lattice where the number of bound states in the topological phase depends on the total quantum dimension. Finally, the internal structure of these bound states is analyzed in the zero-tension limit.

cond-mat.str-el↗

arXiv2016

Mean-field ansatz for topological phases with string tension

We propose a simple mean-field ansatz to study phase transitions from a topological phase to a trivial phase. We probe the efficiency of this approach by considering the string-net model in the presence of a string tension for any anyon theory. Such a perturbation is known to be responsible for a deconfinement-confinement phase transition which is well described by the present variational setup. We argue that mean-field results become exact in the limit of large total quantum dimension.

cond-mat.str-el↗

arXiv2015

Phase diagram of an extended quantum dimer model on the hexagonal lattice

We introduce a quantum dimer model on the hexagonal lattice that, in addition to the standard three-dimer kinetic and potential terms, includes a competing potential part counting dimer-free hexagons. The zero-temperature phase diagram is studied by means of quantum Monte Carlo simulations, supplemented by variational arguments. It reveals some new crystalline phases and a cascade of transitions with rapidly changing flux (tilt in the height language). We analyze perturbatively the vicinity of the Rokhsar-Kivelson point, showing that this model has the microscopic ingredients needed for the "devil's staircase" scenario [E. Fradkin et al., Phys. Rev. B 69, 224415 (2004)], and is therefore expected to produce fractal variations of the ground-state flux.

cond-mat.str-el↗