Tunnelling Two-Level Systems (TLS) dominate the physics of glasses at low temperatures. Yet TLS are extremely rare and it is extremely difficult to directly observe them $\it{in \, silico}$. It is thus crucial to develop simple structural predictors that can provide markers for determining if a TLS is present in a given glass region. It has been speculated that Quasi-Localized vibrational Modes (QLM) are closely related to TLS, and that one can extract information about TLS from QLM. In this work we address this possibility. In particular, we investigate the degree to which a linear or non-linear vibrational mode analysis can predict the location of TLS independently found by energy landscape exploration. We find that even though there is a notable spatial correlation between QLM and TLS, in general TLS are strongly non-linear and their global properties cannot be predicted by a simple normal mode analysis.
The origin of several emergent mechanical and dynamical properties of structural glasses is often attributed to populations of localized structural instabilities, coined quasilocalized modes (QLMs). Under a restricted set of circumstances, glassy QLMs can be revealed by analyzing computer glasses' vibrational spectra in the harmonic approximation. However, this analysis has limitations due to system-size effects and hybridization processes with low energy phononic excitations (plane waves) that are omnipresent in elastic solids. Here we overcome these limitations by exploring the spectrum of a…
Glasses exhibit spatially localized vibrations in the low-frequency regime. These localized modes emerge below the boson peak frequency $ω_\text{BP}$, and their vibrational densities of state follow $g(ω) \propto ω^4$ ($ω$ is frequency). Here, we attempt to address how the localized vibrations behave through the ideal glass transition. To do this, we employ a random pinning method, which enables us to study the thermodynamic glass transition. We find that the localized vibrations survive even in equilibrium glass states. Remarkably, the localized vibrations still maintain the properties of app…
By considering the quantum dynamics of a transverse field Ising spin glass on the Bethe lattice we find the existence of a many body localized region at small transverse field and low temperature. The region is located within the thermodynamic spin glass phase. Accordingly, we conjecture that quantum dynamics inside the glassy region is split in a small MBL and a large delocalized (but not necessarily ergodic) region. This has implications for the analysis of the performance of quantum adiabatic algorithms.
The existence of a constant density of two-level systems (TLS) was proposed as the basis of some intriguing universal aspects of glasses at ultra-low temperatures. Here we ask whether their existence is necessary for explaining the universal density of states quasi-localized modes (QLM) in glasses at ultra-low temperatures. A careful examination of the QLM that exist in a generic atomistic model of a glass former reveals at least two types of them, each exhibiting a different density of states, one depending on the frequency as $ω^3$ and the other as $ω^4$. The properties of the glassy energy …
We numerically study the evolution of the vibrational density of states $D(ω)$ of zero-temperature glasses when their kinetic stability is varied over an extremely broad range, ranging from poorly annealed glasses obtained by instantaneous quenches from above the onset temperature, to ultrastable glasses obtained by quenching systems thermalised below the experimental glass temperature. The low-frequency part of the density of states splits between extended and quasi-localized modes. Extended modes exhibit a boson peak crossing over to Debye behaviour ($D(ω) \sim ω^2$) at low-frequency, with a…
Non-Fermi liquids are metals that cannot be adiabatically deformed into free fermion states. We argue for the existence of "non-Fermi glasses," which are phases of interacting disordered fermions that are fully many-body localized, yet cannot be deformed into an Anderson insulator without an eigenstate phase transition. We explore the properties of such non-Fermi glasses, focusing on a specific solvable example. At high temperature, non-Fermi glasses have qualitatively similar spectral features to Anderson insulators. We identify a diagnostic, based on ratios of correlation functions, that sha…
We study the linear excitations around typical energy minima of a mean-field disordered model with continuous degrees of freedom undergoing a Random First Order Transition (RFOT). Contrary to naive expectations, the spectra of linear excitations are ungapped and we find the presence of a pseudogap corresponding to localized excitations with arbitrary low excitation energy. Moving to deeper minima in the landscape, the excitations appear increasingly localized while their abundance decreases. Beside typical minima, there also exist rare ultra-stable minima, with an energy gap and no localised e…
Effect of glass stability on the low frequency vibrations of vapor deposited glasses
University of Trento（特伦托大学）；European Synchrotron Radiation Facility（欧洲同步辐射装置）；Université libre de Bruxelles (ULB)（布鲁塞尔自由大学）；Universidad Autónoma de Madrid（马德里自治大学）；Universitat Autònoma de Barcelona（巴塞罗那自治大学）；Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST（加泰罗尼亚纳米科学与技术研究所）
In glasses, atomic disorder combined with atomic connectivity makes understanding of the nature of the vibrations much more complex than in crystals or molecules. With a simple model, however, it is possible to show how disorder generates quasi-local modes on optic branches as well as on acoustic branches at low-frequency. The latter modes, possibly hybridizing with low-lying optic modes in real glasses, lead to the excess, low-frequency excitations known as {\it boson-peak modes}, which are lacking in crystals. The spatially quasi-localized vibrations also explain anomalies in thermal conduct…
While soft quasilocalized vibrational modes are known to populate the low-frequency spectrum of glassy solids, their contribution to thermal properties is still not fully elucidated. We numerically show that, despite their spatially localized nature, these modes are as effective heat carriers as the delocalized ones and can contribute non-negligible to the total thermal conductivity in the low-temperature regime, especially for T < 0.05 Tg where Tg is the glass transition temperature. We further prove that the mutual coherence between the low-frequency quasilocalized modes and other modes expl…
Amorphous solids exhibit quasi-universal low-temperature anomalies whose origin has been ascribed to localized tunneling defects. Using an advanced Monte Carlo procedure, we create {\it in silico} glasses spanning from hyperquenched to ultrastable glasses. Using a multidimensional path-finding protocol, we locate tunneling defects with energy splittings smaller than $k_{B}T_Q$, with $T_Q$ the temperature below which quantum effects are relevant ($T_Q \approx 1 \,$K in most experiments). We find that as the stability of a glass increases, its energy landscape as well as the manner in which it i…
The existence of nanoscale ductility during the fracture of silicate glasses remains controversial. Here, based on molecular dynamics simulations coupled with topological constraint theory, we show that nano-ductility arises from the spatial heterogeneity of the atomic network's rigidity. Specifically, we report that localized floppy modes of deformation in under-constrained regions of the glass enable plastic deformations of the network, resulting in permanent change in bond configurations. Ultimately, these heterogeneous plastic events percolate, thereby resulting in a non-brittle mode of fr…
We report an analytical study of the vibrational spectrum of the simplest model of jamming, the soft perceptron. We identify two distinct classes of soft modes. The first kind of modes are related to isostaticity and appear only in the close vicinity of the jamming transition. The second kind of modes instead are present everywhere in the glass phase and are related to the hierarchical structure of the potential energy landscape. Our results highlight the universality of the spectrum of normal modes in disordered systems, and open the way towards a detailed analytical understanding of the vibr…
Further testing the validity of generalized heterogeneous-elasticity theory for low-frequency excitations in structural glasses
Universität Mainz（美因茨大学）；Istituto Italiano di Tecnologia（意大利理工学院）；Universita’ di Roma “La Sapienza”（罗马第一大学）；Univ. of Oxford（牛津大学）；NOMATEN Centre of Excellence, National Center for Nuclear Research（国家核研究中心卓越中心）；Colorado State University（科罗拉多州立大学）
We present results of out--of-equilibrium transport measurements made on strongly-localized Beryllium films and demonstrate that these films exhibit all the earmarks of intrinsic electron-glasses. These include slow (logarithmic) relaxation, memory effects, and more importantly, the observation of a memory dip that has a characteristic width compatible with the carrier-concentration of beryllium. The latter is an empirical signature of the electron-glass. Comparing various non-equilibrium attributes of the beryllium films with other systems that exhibit intrinsic electron-glasses behavior reve…
The low-temperature thermal properties of glasses are anomalous with respect to those of crystals. These thermal anomalies indicate that the low-frequency vibrational properties of glasses differ from those of crystals. Recent studies revealed that, in the simplest model of glasses, i.e., the harmonic potential system, phonon modes coexist with soft localized modes in the low-frequency (continuum) limit. However, the nature of low-frequency vibrational modes of more realistic models is still controversial. In the present work, we study the Lennard-Jones (LJ) system using large-scale molecular-…
Using the concept of tunneling two level systems we explain the reduction of rotational inertia of disordered solid 4He observed in the torsional oscillator experiments. The key point is a peculiar quantum phenomenon of momentum deficit for two level systems in moving solids. We show that an unusual state which is essentially different from both normal and superfluid solid states can be realized in quantum glasses. This state is characterized by reduced rotational inertia in oscillator experiments, by absence of a superflow, and by normal behavior in steady rotation.
The discovery of magnetic and compositional effects in the low temperature properties of multi-component glasses has prompted the need to extend the standard two-level systems (2LSs) tunneling model. A possible extension \cite{Jug2004} assumes that a subset of tunneling quasi-particles is moving in a three-welled potential (TWP) associated with the ubiquitous inhomogeneities of the disordered atomic structure of the glass. We show that within an alternative, cellular description of the intermediate-range atomic structure of glasses the tunneling TWP can be fully justified. We then review how t…
In the three-dimensional Heisenberg spin glass in a random field we study the properties of the inherent structures that are obtained by an instantaneous cooling from infinite temperature. For not too large field the density of states $g(ω)$ develops localized soft {\em plastic} modes and reaches zero as $ω^4$ (for large fiels a gap appears). When we perturb the system adding a force along the softest mode one reaches very similar minima of the energy, separated by small barriers, that appear to be good candidates for classical two-level systems.
It was recently shown that different simple models of glass formers with binary interactions define a universality class in terms of the density of states of their quasi-localized low-frequency modes. Explicitly, once the hybridization with standard Debye (extended) modes is avoided, a number of such models exhibit a universal density of state, depending on the mode frequencies as $D(ω) \sim ω^4$. It is unknown however how wide is this universality class, and whether it also pertains to more realistic models of glass formers. To address this issue we present analysis of the quasi-localized mod…
We use computer simulations to probe the thermodynamic and dynamic properties of a glass-former that undergoes an ideal glass-transition because of the presence of randomly pinned particles. We find that even deep in the equilibrium glass state the system relaxes to some extent because of the presence of localized excitations that allow the system to access different inherent structures, giving thus rise to a non-trivial contribution to the entropy. By calculating with high accuracy the vibrational part of the entropy, we show that also in the equilibrium glass state thermodynamics and dynamic…
The plastic deformation of amorphous solids is mediated by localized shear transformations involving small groups of particles rearranging irreversibly in an elastic background. We introduce and compare three different computational methods to extract the size and orientation of these shear transformations in simulations of a two-dimensional (2D) athermal model glass under simple shear. We find that the shear angles are broadly distributed around the macroscopic shear direction, with a more or less Gaussian distribution with a standard deviation of around 20 $\bullet$ about the direction of ma…
We study the equilibrium statistical properties of the potential energy landscape of several glass models in a temperature regime so far inaccessible to computer simulations. We show that unstable modes of the stationary points undergo a localization transition in real space close to the mode-coupling crossover temperature determined from the dynamics. The concentration of localized unstable modes found at low temperature is a non-universal, finite dimensional feature not captured by mean-field glass theory. Our analysis reconciles, and considerably expands, previous conflicting numerical resu…
We investigate the properties of the low-frequency spectrum in the density of states $D(ω)$ of a three-dimensional model glass former. To magnify the Non-Debye sector of the spectrum, we introduce a random pinning field that freezes a finite particle fraction in order to break the translational invariance and shifts all the vibrational frequencies of the extended modes towards higher frequencies. We show that Non-Debye soft localized modes progressively emerge as the fraction $p$ of pinned particles increases. Moreover, the low-frequency tail of $D(ω)$ goes to zero as a power law $ω^{δ(p)}$, w…
Glasses show vibrational properties that are markedly different to those of crystals which are known as phonons. For example, excess low-frequency modes (the so-called boson peak), vibrational localization, and strong scattering of phonons have been the most discussed topics, and a theoretical understanding of these phenomena is challenging. To address this problem, computational simulations are a powerful tool, which have been employed by many previous works. In this chapter, we describe simulation methods for studying the vibrational properties of glasses (and any solid-state materials). We …
The electron-glass dynamics of Anderson-localized GeSbTe films is dramatically slowed-down following a brief infrared illumination that increases the system carrier-concentration (and thus its conductance). These results demonstrate that the dynamics exhibited by electron-glasses is more sensitive to carrier-concentration than to disorder. In turn, this seems to imply that many-body effects such as the Orthogonality Catastrophe must play a role in the sluggish dynamics observed in the intrinsic electron-glasses.
Motivated by the mean field prediction of a Gardner phase transition between a "normal glass" and a "marginally stable glass", we investigate the off-equilibrium dynamics of three-dimensional polydisperse hard spheres, used as a model for colloidal or granular glasses. Deep inside the glass phase, we find that a sharp crossover pressure $P_{\rm G}$ separates two distinct dynamical regimes. For pressure $P < P_{\rm G}$, the glass behaves as a normal solid, displaying fast dynamics that quickly equilibrates within the glass free energy basin. For $P>P_{\rm G}$, instead, the dynamics becomes stro…
The density of Two-level systems (TLS) controls the low-temperature thermal properties in glasses and has been found to be almost depleted in ultrastable glasses. While this depletion of TLS is thought to have a close relationship with the dramatic decrease of quasi-localized modes (QLMs), it has yet to be clearly formalized. In this work, we argue, based on the \textit{soft-potential} model, that TLS correspond to QLMs with typical frequency $ω_0$. The density $n_0$ of TLS is proportional to both the density of QLMs $D_L(ω_0)$, and the fraction of symmetric double-wells $f(ω_0)$ at $ω_0$, i.e…
Ising spin glasses with bimodal and Gaussian near-neighbor interaction distributions are studied through numerical simulations. The non-self-averaging (normalized inter-sample variance) parameter $U_{22}(T,L)$ for the spin glass susceptibility (and for higher moments $U_{nn}(T,L)$) is reported for dimensions 2, 3, 4, 5 and 7. In each dimension $d$ the non-self-averaging parameters in the paramagnetic regime vary with the sample size L and the correlation length $ξ(T,L)$ as $U_{nn}(β,L) = [K_{d}ξ(T,L)/L]^d$, and so follow a renormalization group law due to Aharony and Harris (1991). Empirically…
We rejuvenate well-aged quasi-2D binary colloidal glasses by thermal cycling, and systematically measure both the statistical responses and particle-level structural evolutions during rejuvenation. While the moduli and boson peak are continuously rejuvenated with increasing number of cycles, the mean square displacement (MSD) fluctuates significantly between different groups of thermal cycles. The decoupling between the thermodynamical and dynamical evolutions suggests different microscopic origins for different bulk properties of glasses. We find that a small fraction of structural rearrangem…
A wide range of glassy and disordered materials exhibit complex, non-exponential, structural relaxation (aging). We propose a simple nonlinear rate equation dδ/dt = a [1-exp (bδ)], where 'δ' is the normalized deviation of a macroscopic variable from its equilibrium value, to describe glassy relaxation. Analysis of extensive experimental data shows that this equation quantitatively captures structural relaxation, where 'a' and 'b' are both temperature-, and more importantly, history-dependent parameters. This analysis explicitly demonstrates that structural relaxation cannot be accurately descr…
Ordinary multi-component silicate glasses belong to a class of amorphous insulators normally displaying no special form of magnetism, save for the Larmor dominant diamagnetism from the constituent atoms' core electrons and the extrinsic Langevin paramagnetism due to the ubiquitous Fe-group dilute paramagnetic impurities. Here we show that the macroscopic magnetisation of three case-study glass types measured in a SQUID-magnetometer cannot be explained solely by means of the Larmor-Langevin contributions. In particular, we reveal a novel {\em intrinsic} contribution to the bulk magnetisation du…
We use a non-equilibrium simulation method to study the spin glass transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity $v$ (temperature change versus time) in Monte Carlo simulations starting at a high temperature. The normally problematic critical slowing-down is not hampering this kind of approach, since the system equilibrates quickly at the initial temperature and the slowing-down is merely reflected in the dynamic scaling of the non-equilibrium order parameter with $v$ and the system size. The equilibrium limit does not have…
The low-temperature quasi-universal behavior of amorphous solids has been attributed to the existence of spatially-localized tunneling defects found in the low-energy regions of the potential energy landscape. Computational models of glasses can be studied to elucidate the microscopic nature of these defects. Recent simulation work has demonstrated the means of generating stable glassy configurations for models that mimic metallic glasses using the swap Monte Carlo algorithm. Building on these studies, we present an extensive exploration of the glassy metabasins of the potential energy landsca…
Under applied shear strain, granular and amorphous materials deform via particle rearrangements, which can be small and localized or organized into system-spanning avalanches. While the statistical properties of avalanches under quasi-static shear are well-studied, the dynamics during avalanches is not. In numerical simulations of sheared soft spheres, we find that avalanches can be decomposed into bursts of localized deformations, which we identify using an extension of persistent homology methods. We also study the linear response of unstable systems during an avalanche, demonstrating that e…
Strongly disordered systems in the many-body localized (MBL) phase can exhibit ground state order in highly excited eigenstates. The interplay between localization, symmetry, and topology has led to the characterization of a broad landscape of MBL phases ranging from spin glasses and time crystals to symmetry protected topological phases. Understanding the nature of phase transitions between these different forms of eigenstate order remains an essential open question. Here, we conjecture that no direct transition between distinct MBL orders can occur; rather, a thermal phase always intervenes.…
The low-temperature properties of glasses present important differences with respect to crystalline matter. In particular, models such as the Debye model of solids, which assume the existence of an underlying regular lattice, predict that the specific heat of solids varies with the cube of temperature at low temperatures. Since the 1970s' at least, it is a well established experimental fact that the specific heat of glasses is instead just linear in $T$ at $T \sim 1K$, and presents a pronounced peak when normalized by $T^{3}$, known as the boson peak. Here we present a new approach which sugge…
Recent numerical studies on glassy systems provide evidences for a population of non-Goldstone modes (NGMs) in the low-frequency spectrum of the vibrational density of states $D(ω)$. Similarly to Goldstone modes (GMs), i. e., phonons in solids, NGMs are soft low-energy excitations. However, differently from GMs, NGMs are localized excitations. Here we first show that the parental temperature $T^*$ modifies the GM/NGM ratio in $D(ω)$. In particular, the phonon attenuation is reflected in a parental temperature dependency of the exponent $s(T^*)$ in the low-frequency power law $D(ω) \sim ω^{s(T^…
To better understand the surprising low-frequency vibrational modes in structural glasses, we study the spectra of a large ensemble of sparse random matrices where disorder is controlled by the distribution of bond weights and network coordination. We find $D(ω)$ has three regimes: a very-low-frequency regime that can be predicted analytically using extremal statistics, an intermediate regime with quasi-localized modes, and a plateau with $D(ω) \sim ω^0$. In the special case of uniform bond weights, the intermediate regime displays $D(ω) \sim ω^4$, independent of network coordination and syste…
The concept of vibrational density of states in glasses has been mirrored in liquids by the instantaneous-normal-mode spectrum. While in glasses instantaneous configurations correspond to minima of the potential-energy hypersurface and all eigenvalues of the associated Hessian matrix are therefore positive, in liquids this is no longer true, and modes corresponding to both positive and negative eigenvalues exist. The instantaneous-normal-mode spectrum has been numerically investigated in the past, and it has been demonstrated to bring important information on the liquid dynamics. A systematic …
