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We study a $\mathbb{Z}_3$ Kitaev model on the honeycomb lattice with nearest neighbor interactions. Based on matrix product state simulations and symmetry considerations, we find evidence that, with ferromagnetic isotropic couplings, the model realizes a chiral spin liquid, characterized by a possible $\mathrm{U}(1)_{12}$ chiral topological order. This is supported by simulations on both cylinder and strip geometries. On infinitely long cylinders with various widths, scaling analysis of entanglement entropy and maximal correlation length suggests that the model has a gapped 2D bulk. The topological entanglement entropy is extracted and found to be in agreement with the $\mathrm{U}(1)_{12}$ topological order. On infinitely long strips with moderate widths, we find the model is critical with a central charge consistent with the chiral edge theory of the $\mathrm{U}(1)_{12}$ topological phase. We conclude by discussing several open questions., Comment: v2: title changed, results significantly revised. v3: published version

Recent experiments have shown that the out-of-plane dielectric constant of water confined in nanoslits of graphite and hexagonal boron nitride (hBN) is vanishingly small. Despite extensive effort based mainly on classical force-field molecular dynamics (FFMD) approaches, the origin of this phenomenon is under debate. Here we used ab initio molecular dynamics simulations (AIMD) and AIMD-trained machine learning potentials to explore the structure and electronic properties of water confined inside graphene and hBN slits. We found that the reduced dielectric constant arises mainly from the anti-parallel alignment of the water dipoles in the perpendicular direction to the surface in the first two water layers near the solid interface. Although the water molecules retain liquid-like mobility, the interfacial layers exhibit a net ferroelectric ordering and constrained hydrogen-bonding orientations which lead to much reduced polarization fluctuations in the out-of-plane direction at room temperature. Importantly, we show that this effect is independent of the distance between the two confining surfaces of the slit, and it originates in the spontaneous polarization of interfacial water. Our calculations also show no significant variations in the structure and polarization of water near graphene and hBN, despite their different electronic structures. These results are important as they offer new insight into a property of water that plays a critical role in the long-range interactions between surfaces, the electric double-layer formation, ion solvation and transport, as well as biomolecular functioning.

Phonons are the primary heat carriers in non-metallic solids. In compositionally heterogeneous materials, the thermal properties are believed to be mainly governed by the disrupted phonon transport due to mass disorder and strain fluctuations, while the effects of compositional fluctuation induced local phonon states are usually ignored. Here, by scanning transmission electron microscopy electron energy loss spectroscopy and sophisticated calculations, we identify the vibrational properties of ingredient-dependent interface phonon modes in AlxGa1-xN and quantify their various contributions to the local interface thermal conductance. We demonstrate that atomic-scale compositional fluctuation has significant influence on the vibrational thermodynamic properties, highly affecting the mode ratio and vibrational amplitude of interface phonon modes and subsequently redistributing their modal contribution to the ITC. Our work provides fundamental insights into understanding of local phonon-boundary interactions in nanoscale inhomogeneities, which reveal new opportunities for optimization of thermal properties via engineering ingredient distribution.

Quantum Monte Carlo approaches based on the stochastic sampling of the determinant space have evolved to be powerful methods to compute the electronic states of molecules. These methods not only calculate the correlation energy at an unprecedented accuracy but also provides insightful information on the electronic structure of computed states, e.g. the population, connection, and clustering of determinants, which have not been fully explored. In this work, we devise a configuration graph for visualizing the determinant space, revealing the nature of the molecule's electronic structure. In addition, we propose two analytical descriptors to quantify the extent of configuration clustering of multi-determinant wave functions. The graph and descriptors provide us with a fresh perspective of the electronic structure of molecules and can assist the further development of configuration interaction based electronic structure methods.

Natural materials usually consist of isotopic mixtures, for which different isotopic ratios can lead to distinct material properties such as thermal conductivity and nucleation process. However, the knowledge of isotopic interface remains largely unexplored mainly due to the challenges in isotopic identification and property measurement at an atomic scale. Here, by using monochromated electron energy-loss spectroscopy in a scanning transmission electron microscope, we reveal momentum-transfer-dependent lattice vibration behavior at an artificial h-10BN/h-11BN heterostructure with sub-unit-cell resolution. We find the vibrational energy changes across the isotopic interface gradually, featuring a wide transition regime, which suggests strong delocalization of the out-of-plane optical phonons at the interface. In addition, we identify phonons near the Brillouin zone center have a transition regime ~3.34 nm (10 atomic layers), whereas phonons at the Brillouin zone boundary transition in ~1.66 nm (5 atomic layers). We propose that the isotope-induced charge effect at the interface accounts for the distinct delocalization behavior. Moreover, intra-atomic layer variation of vibration energy is also sensitive to the momentum transfer, thus at the interface it depends on both of momentum transfer and mass change. The revealed lattice vibration behavior at an isotopic interface provides new insights to understand the isotopic effects on properties in natural materials.

The infinite projected entangled simplex state (iPESS), a type of tensor network (TN) state, has been used successfully for simulating and characterizing {\it non-chiral} spin liquids on the kagome lattice. Here, we demonstrate that iPESS also provides a faithful representation of a {\it chiral} spin liquid (CSL) on the same lattice, namely the ground state of the spin-$1/2$ kagome Heisenberg antiferromagnet with a scalar chirality. By classifying local tensors according to SU$(2)$ and point group symmetries, we construct a chiral ansatz breaking reflection $P$ and time reversal $T$ symmetries while preserving $PT$. The variational TN states are shown to host, for bond dimension $D\ge 8$, a chiral gapless entanglement spectrum following SU$(2)_1$ conformal field theory. The correlation function shows a small weight long-range tail complying with the prediction of the TN bulk-edge correspondence. %{\color{red}With more constraints included, the chiral ansatz is reduced to a non-chiral one which preserves full point group symmetries due to an emergent {\it tensor conservation law} and is of relevance to the ground state at the Heisenberg point. Lastly, by simulations in the complete ansatz family we discuss the transition from the non-chiral spin liquid to the CSL induced by the scalar chirality term.} We identify a non-chiral manifold spanned by only a subset of symmetric tensors where a new emergent {\it tensor conservation law} is realized. This allows us to both probe the stability of the non-chiral spin liquid and discuss its transition to CSL induced by a scalar chirality term.

Accurate ab initio calculations are of fundamental importance in physics, chemistry, biology, and materials science, which have witnessed rapid development in the last couple of years with the help of machine learning computational techniques such as neural networks. Most of the recent efforts applying neural networks to ab initio calculation have been focusing on the energy of the system. In this study, we take a step forward and look at the interatomic force obtained with neural network wavefunction methods by implementing and testing several commonly used force estimators in variational quantum Monte Carlo (VMC). Our results show that neural network ansatz can improve the calculation of interatomic force upon traditional VMC. The relation between the force error and the quality of neural network, the contribution of different force terms, and the computational cost of each term are also discussed to provide guidelines for future applications. Our work demonstrates that it is promising to apply neural network wavefunction methods in simulating structures/dynamics of molecules/materials and provide training data for developing accurate force fields.

The nanoscale lattice imperfections, such as dislocations, have a significant impact on the thermal transport properties in non-metallic materials. Understanding such effects requires the knowledge of defect phonon modes, which however is largely unexplored in experiments due to the challenge in characterization of phonons for the atomic-sized defects. Here, at the atomic scale we directly measure the localized phonon modes of dislocations at a Si/Ge interface using scanning transmission electron microscopy electron energy loss spectroscopy. We find that the dislocation induces new phonon modes localized within ~2-unit cells of the core, which experience a redshift of several milli-electron-volts compared to the dislocation-free case. The observed spectral features agree well with simulations. These localized modes are expected to reduce the phonon transmission channels across the defect and thus the local thermal conductivity. The revealed phonon modes localized at dislocations may help us to improve the thermal properties in thermoelectric generators and thermal management systems with proper defect engineering.

Diffusion Monte Carlo (DMC) based on fixed-node approximation has enjoyed significant developments in the past decades and become one of the go-to methods when accurate ground state energy of molecules and materials is needed. The remaining bottleneck is the limitations of the inaccurate nodal structure, prohibiting more challenging electron correlation problems to be tackled with DMC. In this work, we apply the neural-network based trial wavefunction in fixed-node DMC, which allows accurate calculation of a broad range of atomic and molecular systems of different electronic characteristics. Our method is superior in both accuracy and efficiency compared to state-of-the-art neural network methods using variational Monte Carlo. Overall, this computational framework provides a new benchmark for accurate solution of correlated electronic wavefunction and also shed light on the chemical understanding of molecules.

Full configuration interaction quantum Monte Carlo (FCIQMC) is a state-of-the-art stochastic electronic structure method, providing a methodology to compute FCI-level state energies of molecular systems within a quantum chemical basis. However, especially to probe {\em dynamics} at the FCIQMC level, it is necessary to devise more efficient schemes to produce nuclear forces and potential energy surfaces (PES) from FCIQMC. In this work, we derive the general formula for nuclear force from FCIQMC, and clarify different contributions of the total force. This method to obtain FCIQMC forces eliminates previous restrictions, and can be used with frozen core approximation and free selection of orbitals, making it promising for more efficient nuclear force calculations. After numerical check of this procedure on the binding curve of N$_2$ molecule, we use the FCIQMC energy and force to obtain the full-dimensional ground state PES of water molecule via Gaussian processes regression. The new water FCIQMC PES can be used as the basis for H$_2$O ground state nuclear dynamics, structure optimization, and rotation-vibrational spectrum calculation.

Previous electroencephalogram (EEG) emotion recognition relies on single-task learning, which may lead to overfitting and learned emotion features lacking generalization. In this paper, a graph-based multi-task self-supervised learning model (GMSS) for EEG emotion recognition is proposed. GMSS has the ability to learn more general representations by integrating multiple self-supervised tasks, including spatial and frequency jigsaw puzzle tasks, and contrastive learning tasks. By learning from multiple tasks simultaneously, GMSS can find a representation that captures all of the tasks thereby decreasing the chance of overfitting on the original task, i.e., emotion recognition task. In particular, the spatial jigsaw puzzle task aims to capture the intrinsic spatial relationships of different brain regions. Considering the importance of frequency information in EEG emotional signals, the goal of the frequency jigsaw puzzle task is to explore the crucial frequency bands for EEG emotion recognition. To further regularize the learned features and encourage the network to learn inherent representations, contrastive learning task is adopted in this work by mapping the transformed data into a common feature space. The performance of the proposed GMSS is compared with several popular unsupervised and supervised methods. Experiments on SEED, SEED-IV, and MPED datasets show that the proposed model has remarkable advantages in learning more discriminative and general features for EEG emotional signals.

It is commonly believed that it is unfavourable for adsorbed H atoms on carbonaceous surfaces to form H$_2$ without the help of incident H atoms. Using ring-polymer instanton theory to describe multidimensional tunnelling effects, combined with ab initio electronic structure calculations, we find that these quantum-mechanical simulations reveal a qualitatively different picture. Recombination of adsorbed H atoms, which was believed to be irrelevant at low temperature due to high barriers, is enabled by deep tunnelling, with reaction rates enhanced by tens of orders of magnitude. Furthermore, we identify a new path for H recombination that proceeds via multidimensional tunnelling, but would have been predicted to be unfeasible by a simple one-dimensional description of the reaction. The results suggest that hydrogen molecule formation at low temperatures are rather fast processes that should not be ignored in experimental settings and natural environments with graphene, graphite and other planar carbon segments.

Neural networks have been applied to tackle many-body electron correlations for small molecules and physical models in recent years. Here we propose a new architecture that extends molecular neural networks with the inclusion of periodic boundary conditions to enable ab initio calculation of real solids. The accuracy of our approach is demonstrated in four different types of systems, namely the one-dimensional periodic hydrogen chain, the two-dimensional graphene, the three-dimensional lithium hydride crystal, and the homogeneous electron gas, where the obtained results, e.g. total energies, dissociation curves, and cohesive energies, outperform many traditional ab initio methods and reach the level of the most accurate approaches. Moreover, electron densities of typical systems are also calculated to provide physical intuition of various solids. Our method of extending a molecular neural network to periodic systems can be easily integrated into other neural network structures, highlighting a promising future of ab initio solution of more complex solid systems using neural network ansatz, and more generally endorsing the application of machine learning in materials simulation and condensed matter physics.