We study interacting fermions in one dimension subject to random, uncorrelated onsite disorder, a paradigmatic model of many-body localization (MBL). This model realizes an interaction-driven quantum phase transition between an ergodic and a many-body localized phase, with the transition occurring in the many-body eigenstates. We propose a single-particle framework to characterize these phases by the eigenstates (the natural orbitals) and the eigenvalues (the occupation spectrum) of the one-particle density matrix (OPDM) in individual many-body eigenstates. As a main result, we find that the natural orbitals are localized in the MBL phase, but delocalized in the ergodic phase. This qualitative change in these single-particle states is a many-body effect, since without interactions the single-particle energy eigenstates are all localized. The occupation spectrum in the ergodic phase is thermal in agreement with the eigenstate thermalization hypothesis, while in the MBL phase the occupations preserve a discontinuity at an emergent Fermi edge. This suggests that the MBL eigenstates are weakly dressed Slater determinants, with the eigenstates of the underlying Anderson problem as reference states. We discuss the statistical properties of the natural orbitals and of the occupation spectrum in the two phases and as the transition is approached. Our results are consistent with the existing picture of emergent integrability and localized integrals of motion, or quasiparticles, in the MBL phase. We emphasize the close analogy of the MBL phase to a zero-temperature Fermi liquid: in the studied model, the MBL phase is adiabatically connected to the Anderson insulator and the occupation-spectrum discontinuity directly indicates the presence of quasiparticles localized in real space. Finally, we show that the same picture emerges for interacting fermions in the presence of an experimentally-relevant bichromatic lattice and thereby demonstrate that our findings are not limited to a specific model

Understanding nonequilibrium systems and the consequences of irreversibility for the system’s behavior as compared to the equilibrium case, is a fundamental question in statistical physics. Here, we investigate two types of nonequilibrium phase transitions, a second-order and an infinite-order phase transition, in a prototypical q-state vector Potts model which is driven out of equilibrium by coupling the spins to heat baths at two different temperatures. We discuss the behavior of the quantities that are typically considered in the vicinity of (equilibrium) phase transitions, like the specific heat, and moreover investigate the behavior of the entropy production (EP), which directly quantifies the irreversibility of the process. For the second-order phase transition, we show that the universality class remains the same as in equilibrium. Further, the derivative of the EP rate with respect to the temperature diverges with a power-law at the critical point, but displays a non-universal critical exponent, which depends on the temperature difference, i.e., the strength of the driving. For the infinite-order transition, the derivative of the EP exhibits a maximum in the disordered phase, similar to the specific heat. However, in contrast to the specific heat, whose maximum is independent of the strength of the driving, the maximum of the derivative of the EP grows with increasing temperature difference. We also consider entropy fluctuations and find that their skewness increases with the driving strength, in both cases, in the vicinity of the second-order transition, as well as around the infinite-order transition.

Using event-driven kinetic Monte-Carlo simulations we investigate the early stage of nonequilibrium surface growth in a generic model with anisotropic interactions among the adsorbed particles. Specifically, we consider a two-dimensional lattice model of spherical particles where the interaction anisotropy is characterized by a control parameter η measuring the ratio of interaction energy along the two lattice directions. The simplicity of the model allows us to study systematically the effect and interplay between η, the nearest-neighbor interaction energy En, and the flux rate F , on the shapes and the fractal dimension D f of clusters before coalescence. At finite particle flux F we observe the emergence of rod-like and needle-shaped clusters whose aspect ratio R depends on η, En and F . In the regime of strong interaction anisotropy, the cluster aspect ratio shows power-law scaling as function of particle flux, R ∼ F −α . Furthermore, the evolution of the cluster length and width also exhibit power-law scaling with universal growth exponents for all considered values of F . We identify a critical cluster length Lc that marks a transition from one-dimensional to self-similar two-dimensional cluster growth. Moreover, we find that the cluster properties depend markedly on the critical cluster size i * of the isotropically interacting reference system (η = 1).

Kinetic Monte-Carlo (KMC) simulations are a well-established numerical tool to investigate the time-dependent surface morphology in molecular beam epitaxy (MBE) experiments. In parallel, simplified approaches such as limited mobility (LM) models characterized by a fixed diffusion length have been studied. Here, we investigate an extended LM model to gain deeper insight into the role of diffusional processes concerning the growth morphology. Our model is based on the stochastic transition rules of the Das Sarma-Tamborena (DT) model, but differs from the latter via a variable diffusion length. A first guess for this length can be extracted from the saturation value of the meansquared displacement calculated from short KMC simulations. Comparing the resulting surface morphologies in the sub-and multilayer growth regime to those obtained from KMC simulations, we find deviations which can be cured by adding fluctuations to the diffusion length. This mimics the stochastic nature of particle diffusion on a substrate, an aspect which is usually neglected in LM models. We propose to add fluctuations to the diffusion length by choosing this quantity for each adsorbed particle from a Gaussian distribution, where the variance of the distribution serves as a fitting parameter. We show that the diffusional fluctuations have a huge impact on cluster properties during submonolayer growth as well as on the surface profile in the high coverage regime. The analysis of the surface morphologies on one-and two-dimensional substrates during sub-and multilayer growth shows that the LM model can produce structures that are indistinguishable to the ones from KMC simulations at arbitrary growth conditions.

Machine learning is playing an increasing role in the discovery of new materials and may also facilitate the search for optimum growth conditions for crystals and thin films. Here, we perform kinetic Monte-Carlo simulations of sub-monolayer growth. We consider a generic homoepitaxial growth scenario that covers a wide range of conditions with different diffusion barriers (0.4–0.55 eV) and lateral binding energies (0.1–0.4 eV). These simulations are used as a training data set for a convolutional neural network that can predict diffusion barriers and binding energies. Specifically, a single Monte-Carlo image of the morphology is sufficient to determine the energy barriers with an accuracy of approximately 10 meV and the neural network is tolerant to images with noise and lower than atomic-scale resolution. We believe this new machine learning method will be useful for fundamental studies of growth kinetics and growth optimization through better knowledge of microscopic parameters.

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