Aubry transition studied by direct evaluation of the modulation functions of infinite incommensurate systems

Incommensurate structures can be described by the Frenkel Kontorova model. Aubry has shown that, at a critical value K_c of the coupling of the harmonic chain to an incommensurate periodic potential, the system displays the analyticity breaking transition between a sliding and pinned state. The ground state equations coincide with the standard map in non-linear dynamics, with smooth or chaotic orbits below and above K_c respectively. For the standard map, Greene and MacKay have calculated the value K_c=.971635. Conversely, evaluations based on the analyticity breaking of the modulation function have been performed for high commensurate approximants. Here we show how the modulation function of the infinite system can be calculated without using approximants but by Taylor expansions of increasing order. This approach leads to a value K_c'=.97978, implying the existence of a golden invariant circle up to K_c' > K_c.Comment: 7 pages, 5 figures, file 'epl.cls' necessary for compilation provided; Revised version, accepted for publication in Europhysics Letter

Ground state wavefunction of the quantum Frenkel-Kontorova model

The wavefunction of an incommensurate ground state for a one-dimensional discrete sine-Gordon model -- the Frenkel-Kontorova (FK) model -- at zero temperature is calculated by the quantum Monte Carlo method. It is found that the ground state wavefunction crosses over from an extended state to a localized state when the coupling constant exceeds a certain critical value. So, although the quantum fluctuation has smeared out the breaking of analyticity transition as observed in the classical case, the remnant of this transition is still discernible in the quantum regime.Comment: 5 Europhys pages, 3 EPS figures, accepted for publication in Europhys. Letter

Localization in momentum space of ultracold atoms in incommensurate lattices

We characterize the disorder induced localization in momentum space for ultracold atoms in one-dimensional incommensurate lattices, according to the dual Aubry-Andr\'e model. For low disorder the system is localized in momentum space, and the momentum distribution exhibits time-periodic oscillations of the relative intensity of its components. The behavior of these oscillations is explained by means of a simple three-mode approximation. We predict their frequency and visibility by using typical parameters of feasible experiments. Above the transition the system diffuses in momentum space, and the oscillations vanish when averaged over different realizations, offering a clear signature of the transition

Fidelity, fidelity susceptibility and von Neumann entropy to characterize the phase diagram of an extended Harper model

For an extended Harper model, the fidelity for two lowest band edge states corresponding to different model parameters, the fidelity susceptibility and the von Neumann entropy of the lowest band edge states, and the spectrum-averaged von Neumann entropy are studied numerically, respectively. The fidelity is near one when parameters are in the same phase or same phase boundary; otherwise it is close to zero. There are drastic changes in fidelity when one parameter is at phase boundaries. For fidelity susceptibility the finite scaling analysis performed, the critical exponents $\alpha$, $\beta$, and $\nu$ depend on system sizes for the metal-metal phase transition, while not for the metal-insulator phase transition. For both phase transitions $\nu/\alpha\approx2$. The von Neumann entropy is near one for the metallic phase, while small for the insulating phase. There are sharp changes in von Neumann entropy at phase boundaries. According to the variation of the fidelity, fidelity susceptibility, and von Neumann entropy with model parameters, the phase diagram, which including two metallic phases and one insulating phase separated by three critical lines with one bicritical point, can be completely characterized, respectively. These numerical results indicate that the three quantities are suited for revealing all the critical phenomena in the model.Comment: 9 pages, 12 figure

An analytical law for size effects on thermal conductivity of nanostructures

The thermal conductivity of a nanostructure is sensitive to its dimensions. A simple analytical scaling law that predicts how conductivity changes with the dimensions of the structure, however, has not been developed. The lack of such a law is a hurdle in "phonon engineering" of many important applications. Here, we report an analytical scaling law for thermal conductivity of nanostructures as a function of their dimensions. We have verified the law using very large molecular dynamics simulations