Instabilities on graphene's honeycomb lattice with electron-phonon interactions

We study the impact of electron-phonon interactions on the many-body instabilities of electrons on the honeycomb lattice and their interplay with repulsive local and non-local Coulomb interactions at charge neutrality. To that end, we consider in-plane optical phonon modes with wavevectors close to the $\Gamma$ point as well as to the $K, -K$ points and calculate the effective phonon-mediated electron-electron interaction by integrating out the phonon modes. Ordering tendencies are studied by means of a momentum-resolved functional renormalization group approach allowing for an unbiased investigation of the appearing instabilities. In the case of an exclusive and supercritical phonon-mediated interaction, we find a Kekul\'e and a nematic bond ordering tendency being favored over the $s$-wave superconducting state. The competition between the different phonon-induced orderings clearly shows a repulsive interaction between phonons at small and large wavevector transfers. We further discuss the influence of phonon-mediated interactions on electronically-driven instabilities induced by onsite, nearest neighbor and next-to-nearest neighbor density-density interactions. We find an extension of the parameter regime of the spin density wave order going along with an increase of the critical scales where ordering occurs, and a suppression of competing orders.Comment: 9 pages, 5 figure

Fermion-induced quantum criticality in two-dimensional Dirac semimetals: Non-perturbative flow equations, fixed points and critical exponents

We establish a scenario where fluctuations of new degrees of freedom at a quantum phase transition change the nature of a transition beyond the standard Landau-Ginzburg paradigm. To this end we study the quantum phase transition of gapless Dirac fermions coupled to a $\mathbb{Z}_3$ symmetric order parameter within a Gross-Neveu-Yukawa model in 2+1 dimensions, appropriate for the Kekul\'e transition in honeycomb lattice materials. For this model the standard Landau-Ginzburg approach suggests a first order transition due to the symmetry-allowed cubic terms in the action. At zero temperature, however, quantum fluctuations of the massless Dirac fermions have to be included. We show that they reduce the putative first-order character of the transition and can even render it continuous, depending on the number of Dirac fermions $N_f$. A non-perturbative functional renormalization group approach is employed to investigate the phase transition for a wide range of fermion numbers. For the first time we obtain the critical $N_f$, where the nature of the transition changes. Furthermore, it is shown that for large $N_f$ the change from the first to second order of the transition as a function of dimension occurs exactly in the physical 2+1 dimensions. We compute the critical exponents and predict sizable corrections to scaling for $N_f =2$.Comment: 12+5 pages, 5 figure

Ladder-like optical conductivity in the spin-fermion model

In the nested limit of the spin-fermion model for the cuprates, one-dimensional physics in the form of half-filled two-leg ladders emerges. We show that the renormalization group flow of the corresponding ladder is towards the d-Mott phase, a gapped spin-liquid with short-ranged d-wave pairing correlations, and reveals an intermediate SO(5)$\times$SO(3) symmetry. We use the results of the renormalization group in combination with a memory-function approach to calculate the optical conductivity of the spin-fermion model in the high-frequency regime, where processes within the hot spot region dominate the transport. We argue that umklapp processes play a major role. For finite temperatures, we determine the resistivity in the zero-frequency (dc) limit. Our results show an approximate linear temperature dependence of the resistivity and a conductivity that follows a non-universal power law. A comparison to experimental data supports our assumption that the conductivity is dominated by the antinodal contribution above the pseudogap.Comment: 11+2 pages, 8 figure

Low temperature acoustic properties of amorphous silica and the Tunneling Model

Internal friction and speed of sound of a-SiO(2) was measured above 6 mK using a torsional oscillator at 90 kHz, controlling for thermal decoupling, non-linear effects, and clamping losses. Strain amplitudes e(A) = 10^{-8} mark the transition between the linear and non-linear regime. In the linear regime, excellent agreement with the Tunneling Model was observed for both the internal friction and speed of sound, with a cut-off energy of E(min) = 6.6 mK. In the non-linear regime, two different behaviors were observed. Above 10 mK the behavior was typical for non-linear harmonic oscillators, while below 10 mK a different behavior was found. Its origin is not understood.Comment: 1 tex file, 6 figure

Ground state phase diagram of the half-filled bilayer Hubbard model

Employing a combination of functional renormalization group calculations and projective determinantal quantum Monte Carlo simulations, we examine the Hubbard model on the square lattice bilayer at half filling. From this combined analysis, we obtain a comprehensive account on the ground state phase diagram with respect to the extent of the system's metallic and (antiferromagnetically ordered) Mott-insulating as well as band-insulating regions. By means of an unbiased functional renormalization group approach, we exhibit the antiferromagnetic Mott-insulating state as the relevant instability of the free metallic state, induced by any weak finite onsite repulsion. Upon performing a careful analysis of the quantum Monte Carlo data, we resolve the difficulty of identifying this antiferromagnetic ground state for finite interlayer hopping in the weak-coupling regime, where nonmonotonous finite-size corrections are shown to relate to the two-sheeted Fermi surface structure of the metallic phase. On the other hand, quantum Monte Carlo simulations are well suited to identify the transition between the Mott-insulating phase and the band insulator in the intermediate-to-strong coupling regime. Here, we compare our numerical findings to indications for the transition region obtained from the functional renormalization group procedure.Comment: 12 pages, 15 figure

Cavitation of Electrons Bubbles in Liquid Helium Below saturation Pressure

We have used a Hartree-type electron-helium potential together with a density functional description of liquid $^4$He and $^3$He to study the explosion of electron bubbles submitted to a negative pressure. The critical pressure at which bubbles explode has been determined as a function of temperature. It has been found that this critical pressure is very close to the pressure at which liquid helium becomes globally unstable in the presence of electrons. It is shown that at high temperatures the capillary model overestimates the critical pressures. We have checked that a commonly used and rather simple electron-helium interaction yields results very similar to those obtained using the more accurate Hartree-type interaction. We have estimated that the crossover temperature for thermal to quantum nucleation of electron bubbles is very low, of the order of 6 mK for $^4$He.Comment: 22 pages, 9 figure

Feature Nets: behavioural modelling of software product lines

Software product lines (SPL) are diverse systems that are developed using a dual engineering process: (a)family engineering defines the commonality and variability among all members of the SPL, and (b) application engineering derives specific products based on the common foundation combined with a variable selection of features. The number of derivable products in an SPL can thus be exponential in the number of features. This inherent complexity poses two main challenges when it comes to modelling: Firstly, the formalism used for modelling SPLs needs to be modular and scalable. Secondly, it should ensure that all products behave correctly by providing the ability to analyse and verify complex models efficiently. In this paper we propose to integrate an established modelling formalism (Petri nets) with the domain of software product line engineering. To this end we extend Petri nets to Feature Nets. While Petri nets provide a framework for formally modelling and verifying single software systems, Feature Nets offer the same sort of benefits for software product lines. We show how SPLs can be modelled in an incremental, modular fashion using Feature Nets, provide a Feature Nets variant that supports modelling dynamic SPLs, and propose an analysis method for SPL modelled as Feature Nets. By facilitating the construction of a single model that includes the various behaviours exhibited by the products in an SPL, we make a significant step towards efficient and practical quality assurance methods for software product lines