Recent application of neural networks (NNs) to modeling interatomic interactions has shown the learning machines' encouragingly accurate performance for select elemental and multicomponent systems. In this study, we explore the possibility of building a library of NN-based models by introducing a hierarchical NN training. In such a stratified procedure NNs for multicomponent systems are obtained by sequential training from the bottom up: first unaries, then binaries, and so on. Advantages of constructing NN sets with shared parameters include acceleration of the training process and intact description of the constituent systems. We use an automated generation of diverse structure sets for NN training on density functional theory-level reference energies. In the test case of Cu, Pd, Ag, Cu-Pd, Cu-Ag, Pd-Ag, and Cu-Pd-Ag systems, NNs trained in the traditional and stratified fashions are found to have essentially identical accuracy for defect energies, phonon dispersions, formation energies, etc. The models' robustness is further illustrated via unconstrained evolutionary structure searches in which the NN is used for the local optimization of crystal unit cells.

The so-called "non-Fermi liquid" behavior is very common in strongly correlated systems. However, its operational definition in terms of "what it is not" is a major obstacle against theoretical understanding of this fascinating correlated state. Recently there has been much interest in entanglement entropy as a theoretical tool to study non-Fermi liquids. So far explicit calculations have been limited to models without direct experimental realizations. Here we focus on a two dimensional electron fluid under magnetic field and filling fraction ν = 1/2, which is believed to be a non-Fermi liquid state. Using the composite fermion (CF) wave-function which captures the ν = 1/2 state very accurately, we compute the second Rényi entropy using variational Monte-Carlo technique and an efficient parallel algorithm. We find the entanglement entropy scales as L log L with the length of the boundary L as it does for free fermions, albeit with a pre-factor twice that of the free fermion. We contrast the results against theoretical conjectures and discuss the implications of the results.Despite its ubiquity in strongly correlated materials, the metallic 'non-Fermi liquid' behavior has been challenging to characterize theoretically. At the phenomenological level, non-Fermi liquid behavior is defined by a metallic system exhibiting physical properties that are qualitatively inconsistent with Landau's Fermi-liquid theory. Examples of non-Fermi liquid metals include the strange-metal phase of the high T c cuprates[1], systems near a metallic quantum critical point[2-4] and twodimensional electron system subject to a magnetic field at filling ν = 1/2 (often referred to as Fermi-liquid-like state) [5][6][7]. However, there are many ways in which a system can deviate from a normal Fermi-liquid, such as diverging effective mass, vanishing quasiparticle weight, and anomalous transport [3,[8][9][10][11][12] and little is known about how different forms of deviation can be related. Hence the theoretical challenge of addressing a problem without a weakly interacting quasiparticle description has been compounded by the lack of a measure that can be used to define and classify non-Fermi liquids.Here we turn to a quantum information measure that is sensitive to entangled nature of many-body wavefunctions: the bi-partite entanglement entropy. For gapped systems, the entanglement entropy of the reduced density matrix ρ A ≡ Tr B |Ψ Ψ| of a subsystem A with respect to its complement B for a given ground state wave-function |Ψ is widely believed to follow the area law, i.e., asymptotically proportional to the contact area of two subsystems, with rigorous arguments for lattice systems [13,14]. On the other hand, an explicit formula for a multiplicative logarithmic correction to the area law was suggested by Gioev and Klich [15] based on the Widom conjecture [16] and numerically confirmed in Ref. [17] for free fermions at dimensions d > 1. This dramatic violation of the area law for free fermions is in stark contrast to the area law found for crit...

The group-IV tin has been hypothesized to possess intriguing electronic properties in an atom-thick hexagonal form. An attractive pathway of producing sizable 2D crystallites of tin is based on deintercalation of bulk compounds with suitable tin frameworks. Here, we have identified a new synthesizable metal distannide, NaSn2, with a 3D stacking of flat hexagonal layers and examined a known compound, BaSn2, with buckled hexagonal layers. Our ab initio results illustrate that despite being an exception to the 8-electron rule, NaSn2 should form under pressures easily achievable in multi-anvil cells and remain (meta)stable under ambient conditions. Based on calculated Z2 invariants, the predicted NaSn2 may display topologically non-trivial behavior and the known BaSn2 could be a strong topological insulator.

Nematicity in quantum Hall systems has been experimentally well established at excited Landau levels. The mechanism of the symmetry breaking, however, is still unknown. Pomeranchuk instability of Fermi liquid parameter F ≤ −1 in the angular momentum = 2 channel has been argued to be the relevant mechanism, yet there are no definitive theoretical proofs. Here we calculate, using the variational Monte Carlo technique, Fermi liquid parameters F of the composite fermion Fermi liquid with a finite layer width. We consider F in different Landau levels n = 0, 1, 2 as a function of layer width parameter η. We find that unlike the lowest Landau level, which shows no sign of Pomeranchuk instability, higher Landau levels show nematic instability below critical values of η. Furthermore, the critical value η c is higher for the n = 2 Landau level, which is consistent with observation of nematic order in ambient conditions only in the n = 2 Landau levels. The picture emerging from our work is that approaching the true 2D limit brings half-filled higher Landau-level systems to the brink of nematic Pomeranchuk instability.

BaSn2 has been shown to form as layers of buckled stanene intercalated by barium ions 1 . However, despite an apparently straightforward synthesis and significant interest in stanene as a topological material, BaSn2 has been left largely unexplored, and has only recently been recognized as a potential topological insulator. Belonging to neither the lead nor bismuth chalcogenide families, it would represent a unique manifestation of the topological insulating phase. Here we present a detailed investigation of BaSn2, using both ab initio and experimental methods. First-principles calculations demonstrate that this overlooked material is a indeed strong topological insulator with a bulk band gap of 360meV, among the largest observed for topological insulators. We characterize the surface state dependence on termination chemistry, providing guidance for experimental efforts to measure and manipulate its topological properties. Additionally, through ab initio modeling and synthesis experiments we explore the stability and accessibility of this phase, revealing a complicated phase diagram that indicates a challenging path to obtaining single crystals.