Dual topological nonlinear sigma models of QED\text{QED} theory by dimensional reduction and monopole operators

Nonlinear $\sigma$ models (NLSM) with topological terms, i.e., Wess-Zumino-Witten (WZW) terms, or topological NLSM, are potent descriptions of many critical points and phases beyond the Landau paradigm. These critical systems include the deconfined quantum critical points (DQCP) between the Neel order and valance bond solid, and the Dirac spin liquid, in which the topological NLSMs are dual descriptions of the corresponding fermionic models or $\text{QED}$ theory. In this paper, we propose a dimensional reduction scheme to derive the $\text{U}(1)$ gauged topological NLSM in $n$-dimensional spacetime on a general target space represented by a Hermitian matrix from the dual QED theory. Compared with the famous Abanov-Wiegmann (AW) mechanism, which generally requires the fermions to be Dirac fermions in the infrared (IR), our method is also applicable to non-relativistic fermions in IR, which can have quadratic dispersion or even a Fermi surface. As concrete examples, we construct several two dimensional lattice models, whose IR theories are all the $N_f=4$ $\text{QED}_3$ with fermions of quadratic dispersion and show that its topological NLSM dual description has level-2 WZW terms on the Grassmannian manifold $\frac{\text{U(4)}}{\text{U(2)}\times \text{U(2)}}$ coupled with a dynamical $\text{U(1)}$ gauge field. We also study 't Hooft anomaly matching and the same effect of defects in both theories, such as interface, gauge monopoles and skyrmions, which further support our duality. Finally, we discuss how the macroscopic symmetries act on the $\text{U(1)}$ monopole operators and the corresponding quantum number.Comment: 27 pages, 3 figures; Minor improvements of the presentatio

Generalized Kramers-Wanier Duality from Bilinear Phase Map

We present the Bilinear Phase Map (BPM), a concept that extends the Kramers-Wannier (KW) transformation to investigate unconventional gapped phases, their dualities, and phase transitions. Defined by a matrix of $\mathbb{Z}_2$ elements, the BPM not only encapsulates the essence of KW duality but also enables exploration of a broader spectrum of generalized quantum phases and dualities. By analyzing the BPM's linear algebraic properties, we elucidate the loss of unitarity in duality transformations and derive general non-invertible fusion rules. Applying this framework to (1+1)D systems yields the discovery of new dualities, shedding light on the interplay between various Symmetry Protected Topological (SPT) and Spontaneous Symmetry Breaking (SSB) phases. Additionally, we construct a duality web that interconnects these phases and their transitions, offering valuable insights into relations between different quantum phases.Comment: 5 pages, 2 figures, and appendi

Oxide Ion Conduction in A-site Bi-containing Perovskite-type Ceramics

Oxide ion conductors have drawn significant attention due to their important technical applications in electrochemical devices. This project is based on a new oxide ion conductor Na0.5Bi0.5TiO3 (NBT) which indicates (undoped) conducting NBT is a potential electrolyte material that possesses a high level of nearly pure oxide ion conduction. Na non-stoichiometry in the starting composition (Na-series), acceptor doping (Mg2+ → Ti4+, Na0.5Bi0.5Ti1-xMgxO3-x) and donor doping (Nb5+ → Ti4+, Na0.5Bi0.5Ti1-xNbxO3+x/2) in NBT have been investigated. It has been shown that similar to a previously reported Bi non-stoichiometric series (Bi-series), the electrical properties of NBT are highly sensitive to low levels of Na non-stoichiometry. However, the defect mechanisms for Na and Bi non-stoichiometry are different and leads to a contrasting influence on the properties of NBT ceramics. Na-rich samples from the Na-series behave like Bi-deficient samples from the Bi-series whereas Na-deficient samples from the Na-series behave like Bi-rich samples from the Bi-series. Generally speaking, the bulk conductivity (oxide ion conduction) of NBT is dependent on the Na/Bi ratio in the nominal starting composition. Samples with a Na/Bi ratio ≥ 1 exhibit high, nearly pure oxygen ion conduction with a low activation energy (< 0.9 eV) for bulk conduction whereas samples with a Na/Bi ratio < 1 are electronic insulators with a high activation energy (~ 1.6 eV) for bulk conduction. Mg B-site acceptor doping, (Na,Bi)Ti1-xMgxO3-x, can further enhance the bulk conductivity and produces oxide ion transport numbers, tion, close to unity. This doping also stabilises NBT ceramics to reducing atmospheres (eg 5%H2/95%N2 at 500 oC) to demonstrate their potential as an electrolyte material for Intermediate Temperature Solid Oxide Fuel Cells. In contrast, Nb donor doping, (Na,Bi)Ti1-xNbxO3+x/2, systematically suppresses the oxide-ion conductivity; very low levels of Nb doping (0.002 ~ 0.003) leads to a mixed oxide ion and n-type conduction and an intermediate tion (~ 0.5). A further increase of Nb doping level (≥ 0.005) suppresses the oxide ion conduction and results in dielectric materials with predominant n-type electronic bulk conduction with tion ≤ 0.07 at elevated temperature (eg > 600 oC). It is worth noting that, extremely Bi-rich (undoped) NBT (Bi ≥ 0.52) also induces mixed ionic/electronic behaviour by reintroducing higher oxide-ion conductivity with tion ~ 0.4–0.6. The ferroelectric Aurivillius phase Bi4Ti3O12 (BiT) has also been determined to exhibit high levels of oxide ion conduction. Un-doped BiT shows mixed p-type and oxide ion conduction at low temperature; however, tion approaches near unity close to the Curie Temperature, TC ~ 675 oC. As BiT contains both extrinsic and intrinsic defects, the Bi nonstoichiometry has limited influence on its electrical properties. Isovalent doping (La3+ → Bi3+; Bi4-xLaxTi3O12) acceptor doping (Sr2+ → Bi3+; Bi4-xSrxTi3O12-x/2) and donor doping (Nb5+ → Ti4+; Bi4Ti3-xNbxO12+x/2) are all investigated. La-doping (x ≤ 2) can shift TC to lower temperature and makes BiT a potentially good oxygen ion conductor at ~ 600 oC, but the bulk conductivity gradually reduces with increasing x. Sr-doping has a rather limited solid solution limit (x ≤ 0.12) compared to La doping but can maintain the bulk conductivity while lowering the TC. Nb donor doping on Ti-site can compensate oxygen vacancies and suppress the oxide ion conduction. K0.5Bi0.5TiO3 (KBT) has been determined to be a mixed conductor where the ionic contribution can be oxide ions and/or protons. The proton conduction in KBT is controlled by the K/Bi ratio in the nominal starting composition. Samples with a starting K/Bi ratio > 1 exhibit substantial proton conductivity whereas samples with a starting K/Bi ratio ≤ 1 exhibit lower proton conduction. Compared to NBT, the oxide ion conduction in KBT is significantly lower and relatively independent of the starting A-site non-stoichiometry

Intrinsically/Purely Gapless-SPT from Non-Invertible Duality Transformations

The Kennedy-Tasaki (KT) transformation was used to construct the gapped symmetry protected topological (SPT) phase from the symmetry breaking phase with open boundary condition, and was generalized in our proceeding work [L. Li et al. arXiv:2301.07899] on a ring by sacrificing the unitarity, and should be understood as a non-invertible duality transformation. In this work, we further apply the KT transformation to systematically construct gapless symmetry protected topological phases. This construction reproduces the known examples of (intrinsically) gapless SPT where the non-trivial topological features come from the gapped sectors by means of decorated defect constructions. We also construct new (intrinsically) purely gapless SPTs where there are no gapped sectors, hence are beyond the decorated defect construction. This construction elucidates the field theory description of the various gapless SPTs, and can also be applied to analytically study the stability of various gapless SPT models on the lattice under certain symmetric perturbations

Reasoning on Graphs: Faithful and Interpretable Large Language Model Reasoning

Large language models (LLMs) have demonstrated impressive reasoning abilities in complex tasks. However, they lack up-to-date knowledge and experience hallucinations during reasoning, which can lead to incorrect reasoning processes and diminish their performance and trustworthiness. Knowledge graphs (KGs), which capture vast amounts of facts in a structured format, offer a reliable source of knowledge for reasoning. Nevertheless, existing KG-based LLM reasoning methods only treat KGs as factual knowledge bases and overlook the importance of their structural information for reasoning. In this paper, we propose a novel method called reasoning on graphs (RoG) that synergizes LLMs with KGs to enable faithful and interpretable reasoning. Specifically, we present a planning-retrieval-reasoning framework, where RoG first generates relation paths grounded by KGs as faithful plans. These plans are then used to retrieve valid reasoning paths from the KGs for LLMs to conduct faithful reasoning. Furthermore, RoG not only distills knowledge from KGs to improve the reasoning ability of LLMs through training but also allows seamless integration with any arbitrary LLMs during inference. Extensive experiments on two benchmark KGQA datasets demonstrate that RoG achieves state-of-the-art performance on KG reasoning tasks and generates faithful and interpretable reasoning results.Comment: Accepted by ICLR 202

Longitudinal beam dynamics design fpr Super Tau-Charm Facility

The project of Super Tau-Charm Facility (STCF) proposed in China, as a new-generation high-luminosity $e^+e^-$ collider in the low-energy region with the center-of-mass energy of 2-7 GeV, is well underway. The luminosity is targeted at $1.0\times10^{35} cm^{-2}s^{-1}$ at the optimized beam energy of 2 GeV. Longitudinal beam dynamics becomes of great importance for the STCF due to the constraints from the novel beam-beam effect called coherent X-Z instability and severe beam collective effects. In this paper, we will develop an iterative optimization model for the STCF longitudinal beam dynamics design, which takes into account the influence of transverse dynamics, coherent X-Z instability, and collective effects

The influence of excess K2O on the electrical properties of (K,Na)1/2Bi1/2TiO3 ceramics

The solid solution (KxNa0.50-x)Bi0.50TiO3 (KNBT) between Na1/2Bi1/2TiO3 (NBT) and K1/2Bi1/2TiO3 (KBT) has been extensively researched as a candidate lead-free piezoelectric material because of its relatively high Curie temperature and good piezoelectric properties, especially near the morphotropic phase boundary (MPB) at x ~ 0.10 (20 mol% KBT). Here we show low levels of excess K2O in the starting compositions, i.e. (Ky+0.03Na0.50-y)Bi0.50TiO3.015 (y-series), can significantly change the conduction mechanism and electrical properties compared to a nominally stoichiometric KNBT series (KxNa0.50-x)Bi0.50TiO3 (x-series). Impedance Spectroscopy measurements reveal significantly higher bulk conductivity (σb) values for y ≥ 0.10 samples (activation energy, Ea, ≤ 0.95 eV) compared to the corresponding x-series samples which possess band-gap type electronic conduction (Ea ~ 1.26 to 1.85 eV). The largest difference in electrical properties occurs close to the MPB composition (20 mol% KBT) where y = 0.10 ceramics possess b (at 300 oC) that is 4 orders of magnitude higher than x = 0.10 and the oxide-ion transport number in the former is ~ 0.70 – 0.75 compared to < 0.05 in the latter (between 600 and 800 oC). The effect of excess K2O can be rationalised on the basis of the (K + Na):Bi ratio in the starting composition prior to ceramic processing. This demonstrates the electrical properties of KNBT to be sensitive to low levels of A-site nonstoichiometry and indicates excess K2O in KNBT starting compositions to compensate for volatilisation can lead to undesirable high dielectric loss and leakage currents at elevated temperatures

Dynamic Anchor Learning for Arbitrary-Oriented Object Detection

Arbitrary-oriented objects widely appear in natural scenes, aerial photographs, remote sensing images, etc., thus arbitrary-oriented object detection has received considerable attention. Many current rotation detectors use plenty of anchors with different orientations to achieve spatial alignment with ground truth boxes, then Intersection-over-Union (IoU) is applied to sample the positive and negative candidates for training. However, we observe that the selected positive anchors cannot always ensure accurate detections after regression, while some negative samples can achieve accurate localization. It indicates that the quality assessment of anchors through IoU is not appropriate, and this further lead to inconsistency between classification confidence and localization accuracy. In this paper, we propose a dynamic anchor learning (DAL) method, which utilizes the newly defined matching degree to comprehensively evaluate the localization potential of the anchors and carry out a more efficient label assignment process. In this way, the detector can dynamically select high-quality anchors to achieve accurate object detection, and the divergence between classification and regression will be alleviated. With the newly introduced DAL, we achieve superior detection performance for arbitrary-oriented objects with only a few horizontal preset anchors. Experimental results on three remote sensing datasets HRSC2016, DOTA, UCAS-AOD as well as a scene text dataset ICDAR 2015 show that our method achieves substantial improvement compared with the baseline model. Besides, our approach is also universal for object detection using horizontal bound box. The code and models are available at https://github.com/ming71/DAL.Comment: Accepted to AAAI 2021. The code and models are available at https://github.com/ming71/DA

ChatRule: Mining Logical Rules with Large Language Models for Knowledge Graph Reasoning

Logical rules are essential for uncovering the logical connections between relations, which could improve the reasoning performance and provide interpretable results on knowledge graphs (KGs). Although there have been many efforts to mine meaningful logical rules over KGs, existing methods suffer from the computationally intensive searches over the rule space and a lack of scalability for large-scale KGs. Besides, they often ignore the semantics of relations which is crucial for uncovering logical connections. Recently, large language models (LLMs) have shown impressive performance in the field of natural language processing and various applications, owing to their emergent ability and generalizability. In this paper, we propose a novel framework, ChatRule, unleashing the power of large language models for mining logical rules over knowledge graphs. Specifically, the framework is initiated with an LLM-based rule generator, leveraging both the semantic and structural information of KGs to prompt LLMs to generate logical rules. To refine the generated rules, a rule ranking module estimates the rule quality by incorporating facts from existing KGs. Last, a rule validator harnesses the reasoning ability of LLMs to validate the logical correctness of ranked rules through chain-of-thought reasoning. ChatRule is evaluated on four large-scale KGs, w.r.t. different rule quality metrics and downstream tasks, showing the effectiveness and scalability of our method.Comment: 11 pages, 4 figure