arXiv subjects

O. Cépas

Publications and source records attributed to O. Cépas.

7 recordsLinked to original sources

arXiv2025

Denjoy's anachronistic topological viewpoint on Aubry transition

The Aubry transition is a phase transition between two types of incommensurate states, originally described as a transition by ``breaking of analyticity''. Here we present Denjoy's (anachronistic) viewpoint, who almost hundred years ago described certain mathematical properties of circle homeomorphisms with irrational rotation numbers. The connection between the two lies in the existence of a change of variables from the incommensurate ground state variables to new simple phase variables that rotate by a constant irrational angle. This confers a cyclic order, an essential property of models with the Aubry transition. Denjoy's description indicates that there are two types of cyclic order, distinguished by the regular or singular nature of the change of variables or, in mathematical terms, by the distinction between topological conjugacy versus semiconjugacy. This allows rephrasing the breaking of analyticity as a breaking of topological conjugacy. We illustrate this description with numerical calculations on the Frenkel-Kontorova model.

cond-mat.other↗

arXiv2024

Aubry transition with small distortions

We show that when the Aubry transition occurs in incommensurately distorted structures, the amplitude of the distortions is not necessarily large as suggested by the standard Frenkel-Kontorova mechanical model. By modifying the shape of the potential in such a way that the mechanical force is locally stronger (i.e. increasing the nonlinearities), the transition may occur at a small amplitude of the potential with small distortions. A "phason" gap then opens, while the phonon spectrum resembles a standard undistorted spectrum at higher energies. This may explain the existence of pinned phases with small distortions as experimentally observed in charge-density waves.

cond-mat.other↗

arXiv2022

On the intrinsic pinning and shape of charge-density waves in 1D Peierls systems

Within the standard perturbative approach of Peierls, a charge-density wave is usually assumed to have a cosine shape of weak amplitude. In nonlinear physics, we know that waves can be deformed. What are the effects of the nonlinearities of the electron-lattice models in the physical properties of Peierls systems? We study in details a nonlinear discrete model, introduced by Brazovskii, Dzyaloshinskii and Krichever. First, we recall its exact analytical solution at integrable points. It is a cnoidal wave, with a continuous envelope, which may slide over the lattice potential at no energy cost, following Fröhlich's argument. Second, we show numerically that integrability-breaking terms modify some important physical properties. The envelope function may become discontinuous: electrons form stronger chemical bonds which are local dimers or oligomers. We show that an Aubry transition from the sliding phase to an insulating pinned phase occurs when the model is no longer integrable.

cond-mat.str-el↗

arXiv2021

Topological interpretation of color exchange invariants: hexagonal lattice on a torus

We explain a correspondence between some invariants in the dynamics of color exchange in a 2d coloring problem, which are polynomials of winding numbers, and linking numbers in 3d. One invariant is visualized as linking of lines on a special surface with Arf-Kervaire invariant one, and is interpreted as resulting from an obstruction to transform the surface into its chiral image with special continuous deformations. We also consider additional constraints on the dynamics and see how the surface is modified.

math.GT↗

arXiv2019

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

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.

cond-mat.stat-mech↗

arXiv2014

High-field spectroscopy of singlet-triplet transitions in the spin-dimer systems Sr3Cr2O8 and Ba3Cr2O8

Magnetic excitations in the isostructural spin-dimer systems Sr3Cr2O8 and Ba3Cr2O8 are probed by means of high-field electron spin resonance at sub-terahertz frequencies. Three types of magnetic modes were observed. One mode is gapless and corresponds to transitions within excited states, while two other sets of modes are gapped and correspond to transitions from the ground to the first excited states. The selection rules of the gapped modes are analyzed in terms of a dynamical Dzyaloshinskii-Moriya interaction, suggesting the presence of phonon-assisted effects in the low-temperature spin dynamics of Sr3Cr2O8 and Ba3Cr2O8

cond-mat.str-el↗

arXiv2013

Microscopic properties of the "pinwheel" kagome compound Rb_2Cu_3SnF_{12}

Using $^{63,65}$Cu nuclear magnetic resonance (NMR) in magnetic fields up to 30 T we study the microscopic properties of the 12-site valence-bond-solid ground state in the "pinwheel" kagome compound Rb$_2$Cu$_3$SnF$_{12}$. We find that the ground state is characterized by a strong transverse staggered spin polarization whose temperature and field dependence points to a mixing of the singlet and triplet states. This is further corroborated by the field dependence of the gap $Δ(H)$, which has a level anticrossing with a large minimum gap value of $\approx Δ(0)/2$, with no evidence of a phase transition down to 1.5\,K. By the exact diagonalization of small clusters, we show that the observed anticrossing is mainly due to staggered tilts of the $g$-tensors defined by the crystal structure, and reveal symmetry properties of the low-energy excitation spectrum compatible with the absence of level crossing.

cond-mat.str-el↗