Kinks and nanofriction: Structural phases in few-atom chains

We theoretically analyse the equation of topological solitons in a chain of particles interacting via a repulsive power-law potential and confined by a periodic lattice. Starting from the discrete model, we perform a gradient expansion and obtain the kink equation in the continuum limit for a power-law exponent n ≥ 1 . The power-law interaction modifies the sine-Gordon equation, giving rise to a rescaling of the coefficient multiplying the second derivative (the kink width) and to an additional integral term. We argue that the integral term does not affect the local properties of the kink, but it governs the behaviour at the asymptotics. The kink behaviour at the center is dominated by a sine-Gordon equation and its width tends to increase with the power law exponent. When the interaction is the Coulomb repulsion, in particular, the kink width depends logarithmically on the chain size. We define an appropriate thermodynamic limit and compare our results with existing studies performed for infinite chains. Our formalism allows one to systematically take into account the finite-size effects and also slowly varying external potentials, such as for instance the curvature in an ion trap.

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“…These effects modify the kink's width and form. Moreover, they significantly modify the dynamical properties [42,43].…”

Section: Discussionmentioning

confidence: 99%

Static Kinks in Chains of Interacting Atoms

2020

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“…Long-range interactions between spins of atomic ions can be generated by means of optical dipole forces, where the resulting system can be described by a sine-Gordon model with long-range interactions [11]. When superimposing an additional periodic corrugation potential onto the ion crystal, the resulting system can be used as a quantum simulator for friction on the nano scale [59][60][61]. Recently, quantum effects in the associated Aubry transition have been investigated [62].…”

Section: B Example 2: Nonlinear Coulomb Forces In Ion Chainsmentioning

confidence: 99%

Exact Continuum Representation of Long-range Interacting Systems and Emerging Exotic Phases in Unconventional Superconductors

Buchheit¹,

Keßler²,

Schuhmacher³

et al. 2022

Preprint

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Continuum limits are a powerful tool in the study of many-body systems, yet their validity is often unclear when long-range interactions are present. In this work, we rigorously address this issue and put forth an exact representation of long-range interacting lattices that separates the model into a term describing its continuous analogue, the integral contribution, and a term that fully resolves the microstructure, the lattice contribution. For any system dimension, any lattice, any power-law interaction and for linear, nonlinear, and multi-atomic lattices, we show that the lattice contribution can be described by a differential operator based on the multidimensional generalization of the Riemann zeta function, namely the Epstein zeta function. We determine the conditions under which this contribution becomes particularly relevant, demonstrating the existence of quasi scale-invariant lattice contributions in a wide range of fundamental physical phenomena. Our representation provides a broad set of tools for studying the analytical properties of the system and it yields an efficient numerical method for the evaluation of the arising lattice sums. We benchmark its performance by computing classical forces and energies in three important physical examples, in which the standard continuum approximation fails: Skyrmions in a two-dimensional long-range interacting spin lattice, defects in ion chains, and spin waves in a three-dimensional pyrochlore lattice with dipolar interactions. We demonstrate that our method exhibits the accuracy of exact summation at the numerical cost of an integral approximation, allowing for precise simulations of long-range interacting systems even at macroscopic scales. Finally, we apply our analytical tool set to the study of quantum spin lattices and derive anomalous quantum spin wave dispersion relations due to long-range interactions in arbitrary dimensions.

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“…It is in contrast to the meaning of ref. [33] where the authors claim that kinks are an indicator for incommensurate lattices.…”

Section: Introductionmentioning

confidence: 99%

The movement of a one-dimensional Wigner solid explained by a modified Frenkel-Kontorova model

2020

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We propose a Frenkel-Kontorova model for a 1D chain of electrons forming a Wigner solid over 4 He. It is a highly idealized picture, but with the model at hand we can study the movement of the chain. We find out that the energetically most preferable movement is the successive sliding of a kink or an antikink through the chain. Then the force for a movement does not depend on the length of the chain. The force uniformly applied to all electrons must be larger than a force exciting only a kink or an antikink. We calculate two cases, one with stiff 'springs' between the electrons and one with weak 'springs'. The side potential of the 'dimples' is additionally damped at the periphery. We study the cases with 33, 66, and 101 particles.

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Kinks and nanofriction: Structural phases in few-atom chains

Cited by 15 publications

References 44 publications

Static Kinks in Chains of Interacting Atoms

Static Kinks in Chains of Interacting Atoms

Exact Continuum Representation of Long-range Interacting Systems and Emerging Exotic Phases in Unconventional Superconductors

The movement of a one-dimensional Wigner solid explained by a modified Frenkel-Kontorova model

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