Fast generation of ultrastable computer glasses by minimization of an augmented potential energy

We present a model and protocol that enable the generation of extremely stable computer glasses at minimal computational cost. The protocol consists of an instantaneous quench in an augmented potential energy landscape, with particle radii as additional degrees of freedom. We demonstrate how our glasses' mechanical stability, which is readily tunable in our approach, is reflected both in microscopic and macroscopic observables. Our observations indicate that the stability of our computer glasses is at least comparable to that of computer glasses generated by the celebrated Swap Monte Carlo algorithm. Strikingly, some key properties support even qualitatively enhanced stability in our scheme: the density of quasilocalized excitations displays a gap in our most stable computer glasses, whose magnitude scales with the polydispersity of the particles. We explain this observation, which is consistent with the lack of plasticity we observe at small stress. It also suggests that these glasses are depleted from two-level systems, similarly to experimental vapor-deposited ultrastable glasses.Comment: 11 pages, 10 figure

Nonlinear quasilocalized excitations in glasses. I. True representatives of soft spots

Structural glasses formed by quenching a melt possess a population of soft quasilocalized excitations --- often called `soft spots' --- that are believed to play a key role in various thermodynamic, transport and mechanical phenomena. Under a narrow set of circumstances, quasilocalized excitations assume the form of vibrational (normal) modes, that are readily obtained by a harmonic analysis of the multi-dimensional potential energy. In general, however, direct access to the population of quasilocalized modes via harmonic analysis is hindered by hybridizations with other low-energy excitations, e.g.~phonons. In this series of papers we re-introduce and investigate the statistical-mechanical properties of a class of low-energy quasilocalized modes --- coined here \emph{nonlinear quasilocalized excitations} (NQEs) --- that are defined via an anharmonic (nonlinear) analysis of the potential energy landscape of a glass, and do not hybridize with other low-energy excitations. In this first paper, we review the theoretical framework that embeds a micromechanical definition of NQEs. We demonstrate how harmonic quasilocalized modes hybridize with other soft excitations, whereas NQEs properly represent soft spots without hybridization. We show that NQEs' energies converge to the energies of the softest, non-hybridized harmonic quasilocalized modes, cementing their status as true representatives of soft spots in structural glasses. Finally, we perform a statistical analysis of the mechanical properties of NQEs, which results in a prediction for the distribution of potential energy barriers that surround typical inherent states of structural glasses, as well as a prediction for the distribution of local strain thresholds to plastic instability.Comment: 15 pages, 9 figures, accepted manuscrip

Wave attenuation in glasses: Rayleigh and generalized-Rayleigh scattering scaling

The attenuation of long-wavelength phonons (waves) by glassy disorder plays a central role in various glass anomalies, yet it is neither fully characterized, nor fully understood. Of particular importance is the scaling of the attenuation rate $\Gamma(k)$ with small wavenumbers $k\!\to\!0$ in the thermodynamic limit of macroscopic glasses. Here we use a combination of theory and extensive computer simulations to show that the macroscopic low-frequency behavior emerges at intermediate frequencies in finite-size glasses, above a recently identified crossover wavenumber $k_\dagger$, where phonons are no longer quantized into bands. For $k\!<\!k_\dagger$, finite-size effects dominate $\Gamma(k)$, which is quantitatively described by a theory of disordered phonon bands. For $k\!>\!k_\dagger$, we find that $\Gamma(k)$ is affected by the number of quasilocalized nonphononic excitations, a generic signature of glasses that feature a universal density of states. In particular, we show that in a frequency range in which this number is small, $\Gamma(k)$ follows a Rayleigh scattering scaling $\sim\!k^{d+1}$ ($d$ is the spatial dimension), and that in a frequency range in which this number is sufficiently large, the recently observed generalized-Rayleigh scaling of the form $\sim\!k^{d+1}\log\!{(k_0/k)}$ emerges ($k_0\!>k_\dagger$ is a characteristic wavenumber). Our results suggest that macroscopic glasses --- and, in particular, glasses generated by conventional laboratory quenches that are known to strongly suppress quasilocalized nonphononic excitations --- exhibit Rayleigh scaling at the lowest wavenumbers $k$ and a crossover to generalized-Rayleigh scaling at higher $k$. Some supporting experimental evidence from recent literature is presented.Comment: 15 pages, 10 figures (including appendices). v2 includes a new appendix with 2 figures (Fig.7 & Fig.8

Finite correlation length scaling with infinite projected entangled-pair states

We show how to accurately study 2D quantum critical phenomena using infinite projected entangled-pair states (iPEPS). We identify the presence of a finite correlation length in the optimal iPEPS approximation to Lorentz-invariant critical states which we use to perform a finite correlation-length scaling (FCLS) analysis to determine critical exponents. This is analogous to the one-dimensional (1D) finite entanglement scaling with infinite matrix product states. We provide arguments why this approach is also valid in 2D by identifying a class of states that despite obeying the area law of entanglement seems hard to describe with iPEPS. We apply these ideas to interacting spinless fermions on a honeycomb lattice and obtain critical exponents which are in agreement with Quantum Monte Carlo results. Furthermore, we introduce a new scheme to locate the critical point without the need of computing higher order moments of the order parameter. Finally, we also show how to obtain an improved estimate of the order parameter in gapless systems, with the 2D Heisenberg model as an example

Does mesoscopic elasticity control viscous slowing down in glassforming liquids?

The dramatic slowing down of relaxation dynamics of liquids approaching the glass transition remains a highly debated problem, where the crux of the puzzle resides in the elusive increase of the activation barrier $\Delta E(T)$ with decreasing temperature $T$. A class of theoretical frameworks -- known as elastic models -- attribute this temperature dependence to the variations of the liquid's macroscopic elasticity, quantified by the high-frequency shear modulus $G_\infty(T)$. While elastic models find some support in a number of experimental studies, these models do not take into account the spatial structures, length scales, and heterogeneity associated with structural relaxation in supercooled liquids. Here, we propose that viscous slowing down is controlled by a mesoscopic elastic stiffness $\kappa(T)$, defined as the characteristic stiffness of response fields to local dipole forces in the liquid's underlying inherent states. First, we show that $\kappa(T)$ -- which is intimately related to the energy and length scales characterizing quasilocalized, nonphononic excitations in glasses -- increases more strongly with decreasing $T$ than the macroscopic inherent state shear modulus $G(T)$ in several computer liquids. Second, we show that the simple relation $\Delta E(T)\propto\kappa(T)$ holds remarkably well for some computer liquids, implying a direct connection between the liquid's underlying mesoscopic elasticity and enthalpic energy barriers. On the other hand, we show that for other computer liquids, the above relation fails. Finally, we provide strong evidence that what distinguishes computer liquids in which the $\Delta E(T) \propto \kappa(T)$ relation holds, from those in which it does not, is that the latter feature highly granular potential energy landscapes, where many sub-basins separated by low activation barriers exist. [Rest of abstract abridged]Comment: 15 pages, 12 figure