UTe2 is a promising candidate for spin-triplet superconductor, yet its exact superconducting order parameter remains highly debated. Here, via scanning tunneling microscopy/spectroscopy, we observe a novel type of magnetic vortex with distinct dark-bright contrast in local density of states on UTe2 (011) surface under a perpendicular magnetic field, resembling the conjugate structure of Yin-Yang diagram in Taoism. Each Yin-Yang vortex contains a quantized magnetic flux, and the boundary between the Yin and Yang parts aligns with the crystallographic a-axis of UTe2. The vortex states exhibit intriguing behaviors -- a sharp zero-energy conductance peak exists at the Yang part, while a superconducting gap with pronounced coherence peaks exists at the Yin part, which is even sharper than those measured far from the vortex core or in the absence of magnetic field. By theoretical modeling, we show that the Yin-Yang vortices on UTe2 (011) surface can be explained by the asymmetric vortex-derived local distortion of the zero-energy surface states associated with spin-triplet pairing with appropriate d-vectors. Therefore, the observation of Yin-Yang vortex confirms the spin-triplet pairing in UTe2 and imposes constraints on the candidate d-vector for the spin-triplet pairing.

Angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM) have become indispensable tools in the study of correlated quantum materials. Both probe complementary aspects of the single-particle excitation spectrum. Taken together, ARPES and STM have the potential to explore properties of the electronic Green's function, a central object of many-body theory. This review explicates this potential with a focus on heavy-electron quantum criticality, especially the role of Kondo destruction. A discussion on how to probe the Kondo destruction effect across the quantum-critical point using ARPES and STM measurements is presented. Particular emphasis is placed on the question of how to distinguish between the signatures of the initial onset of hybridization-gap formation, which is the "high-energy" physics to be expected in all heavy-electron systems, and those of Kondo destruction, which characterizes the low-energy physics and, hence, the nature of quantum criticality. Recent progress and possible challenges in the experimental investigations are surveyed, the STM and ARPES spectra for several quantum-critical heavy-electron compounds are compared, and the prospects for further advances are outlined.

Bismuthates were the first family of oxide high-temperature superconductors, exhibiting superconducting transition temperatures (Tc) up to 32K, but the superconducting mechanism remains under debate despite more than 30 years of extensive research. Our angle-resolved photoemission spectroscopy studies on Ba$_{0.51}$K$_{0.49}$BiO$_3$ reveal an unexpectedly 34% larger bandwidth than in conventional density functional theory calculations. This can be reproduced by calculations that fully account for long-range Coulomb interactions --- the first direct demonstration of bandwidth expansion due to the Fock exchange term, a long-accepted and yet uncorroborated fundamental effect in many body physics. Furthermore, we observe an isotropic superconducting gap with 2\Delta$_0$/k$_B$ T$_c$ = 3.51 $\pm$ 0.05, and strong electron-phonon interactions with a coupling constant \lambda$\sim$ 1.3 $\pm$ 0.2. These findings solve a long-standing mystery --- Ba$_{0.51}$K$_{0.49}$BiO$_3$ is an extraordinary Bardeen-Cooper-Schrieffer (BCS) superconductor, where long-range Coulomb interactions expand the bandwidth, enhance electron-phonon coupling, and generate the high Tc. Such effects will also be critical for finding new superconductors.

Recommender systems play an essential role in the modern business world. They recommend favorable items like books, movies, and search queries to users based on their past preferences. Applying similar ideas and techniques to Monte Carlo simulations of physical systems boosts their efficiency without sacrificing accuracy. Exploiting the quantum to classical mapping inherent in the continuous-time quantum Monte Carlo methods, we construct a classical molecular gas model to reproduce the quantum distributions. We then utilize powerful molecular simulation techniques to propose efficient quantum Monte Carlo updates. The recommender engine approach provides a general way to speed up the quantum impurity solvers.

In heavy-fermion compounds, the dual character of $f$ electrons underlies their rich and often exotic properties like fragile heavy quasipartilces, variety of magnetic orders and unconventional superconductivity. 5$f$-electron actinide materials provide a rich setting to elucidate the larger and outstanding issue of the competition between magnetic order and Kondo entanglement and, more generally, the interplay among different channels of interactions in correlated electron systems. Here, by using angle-resolved photoemission spectroscopy, we present detailed electronic structure of USb$_2$ and observed two different kinds of nearly flat bands in the antiferromagnetic state of USb$_2$. Polarization-dependent measurements show that these electronic states are derived from 5$f$ orbitals with different characters; in addition, further temperature-dependent measurements reveal that one of them is driven by the Kondo correlations between the 5$f$ electrons and conduction electrons, while the other reflects the dominant role of the magnetic order. Our results on the low-energy electronic excitations of USb$_2$ implicate orbital selectivity as an important new ingredient for the competition between Kondo correlations and magnetic order and, by extension, in the rich landscape of quantum phases for strongly correlated $f$ electron systems.

To unravel the interplay between the strong electronic correlation and itinerant-localized dual nature in atypical f electron systems, we employed the density functional theory in combination with the single-site dynamical mean-field theory to systematically investigate the electronic structures of CeSb and USb. We find that the 4f states in CeSb are mostly localized which show a weak quasi-particle resonance peak near the Fermi level. Conversely, the 5f electrons in USb display partially itinerant feature, accompanied by mixed-valence behavior and prominent valence state fluctuations. Particularly, the 4f electronic correlations in CeSb are distinctly orbital-selective with strikingly renormalized 4f5/2 states, according to the low-energy behaviors of 4f self-energy functions. It is believed that the strong electronic correlation and fantastic bonding of f states contribute to elucidate the fascinating magnetism.

Directly manipulating the atomic structure to achieve a specific property is a long pursuit in the field of materials. However, hindered by the disordered, non-prototypical glass structure and the complex interplay between structure and property, such inverse design is dauntingly hard for glasses. Here, combining two cutting-edge techniques, graph neural networks and swap Monte Carlo, we develop a data-driven, property-oriented inverse design route that managed to improve the plastic resistance of Cu-Zr metallic glasses in a controllable way. Swap Monte Carlo, as "sampler", effectively explores the glass landscape, and graph neural networks, with high regression accuracy in predicting the plastic resistance, serves as "decider" to guide the search in configuration space. Via an unconventional strengthening mechanism, a geometrically ultra-stable yet energetically meta-stable state is unraveled, contrary to the common belief that the higher the energy, the lower the plastic resistance. This demonstrates a vast configuration space that can be easily overlooked by conventional atomistic simulations. The data-driven techniques, structural search methods and optimization algorithms consolidate to form a toolbox, paving a new way to the design of glassy materials.

The recent discovery of superconductivity in heavy Fermion compound UTe2, a candidate topological and triplet-paired superconductor, has aroused widespread interest. However, to date, there is no consensus on whether the stoichiometric sample of UTe2 is superconducting or not due to lack of reliable evidence to distinguish the difference between the nominal and real compositions of samples. Here, we are the first to clarify that the stoichiometric UT2 is non-superconducting at ambient pressure and under hydrostatic pressure up to 6 GPa, however we find that it can be compressed into superconductivity by application of quasi-uniaxial pressure. Measurements of resistivity, magnetoresistance and susceptibility reveal that the quasi-uniaxial pressure results in a suppression of the Kondo coherent state seen at ambient pressure, and then leads to a superconductivity initially emerged on the ab-plane at 1.5 GPa. At 4.8 GPa, the superconductivity is developed in three crystallographic directions. The superconducting state coexists with an exotic magnetic ordered state that develops just below the onset temperature of the superconducting transition. The discovery of the quasi-uniaxial-pressure-induced superconductivity with exotic magnetic state in the stoichiometric UTe2 not only provide new understandings on this compound, but also highlight the vital role of Te deficiency in developing the superconductivity at ambient pressures.

Non-Hermiticity enriches the 10-fold Altland-Zirnbauer symmetry class into the 38-fold symmetry class, where critical behavior of the Anderson transitions (ATs) has been extensively studied recently. Here, we propose a correspondence of the universality classes of the ATs between Hermitian and non-Hermitian systems. We illustrate that the critical exponents of the length scale in non-Hermitian systems coincide with the critical exponents in the corresponding Hermitian systems with additional chiral symmetry. A remarkable consequence of the correspondence is superuniversality, i.e., the ATs in some different symmetry classes of non-Hermitian systems are characterized by the same critical exponent. In addition to the comparisons between the known critical exponents for non-Hermitian systems and their Hermitian counterparts, we obtain the critical exponents in symmetry classes AI, AII, AII$^{\dagger}$, CII$^{\dagger}$, and DIII in two and three dimensions. Estimated critical exponents are consistent with the proposed correspondence. According to the correspondence, some of the exponents also give useful information of the unknown critical exponents in Hermitian systems, paving a way to study the ATs of Hermitian systems by the corresponding non-Hermitian systems.

Symmetries associated with complex conjugation and Hermitian conjugation, such as time-reversal symmetry and pseudo-Hermiticity, have great impact on eigenvalue spectra of non-Hermitian random matrices. Here, we show that time-reversal symmetry and pseudo-Hermiticity lead to universal level statistics of non-Hermitian random matrices on and around the real axis. From the extensive numerical calculations of large random matrices, we obtain the five universal level-spacing and level-spacing-ratio distributions of real eigenvalues, each of which is unique to the symmetry class. Furthermore, we analyse spacings of real eigenvalues in physical models, such as bosonic many-body systems and free fermionic systems with disorder and dissipation. We clarify that the level spacings in ergodic (metallic) phases are described by the universal distributions of non-Hermitian random matrices in the same symmetry classes, while the level spacings in many-body localized and Anderson localized phases show the Poisson statistics. We also find that the number of real eigenvalues shows distinct scalings in the ergodic and localized phases in these symmetry classes. These results serve as effective tools for detecting quantum chaos, many-body localization, and real-complex transitions in non-Hermitian systems with symmetries.

We study quantum phase transitions of three-dimensional disordered systems in the chiral classes (AIII and BDI) with and without weak topological indices. We show that the systems with a nontrivial weak topological index universally exhibit an emergent thermodynamic phase where wave functions are delocalized along one spatial direction but exponentially localized in the other two spatial directions, which we call the quasi-localized phase. Our extensive numerical study clarifies that the critical exponent of the Anderson transition between the metallic and quasi-localized phases, as well as that between the quasi-localized and localized phases, are different from that with no weak topological index, signaling the new universality classes induced by topology. The quasi-localized phase and concomitant topological Anderson transition manifest themselves in the anisotropic transport phenomena of disordered weak topological insulators and nodal-line semimetals, which exhibit the metallic behavior in one direction but the insulating behavior in the other directions.

In two-dimensional system with Rashba spin-orbit coupling, it is well-known that superconductivity can have mixed spin-singlet and -triplet parity, and the $\boldsymbol{d}$-vector of spin-triplet pairing is parallel to $\boldsymbol{g}$-vector of Rashba spin-orbit coupling. Here, we propose a model to describe a two-dimensional system with unconventional Rashba bands and study its superconductivity. We show that the $\boldsymbol{d}$-vector of spin-triplet pairing can be either parallel or perpendicular to $\boldsymbol{g}$-vector of Rashba spin-orbit coupling depending on the different pairing interaction. We also propose a junction to generate tunneling current depending on the direction of $\boldsymbol{d}$-vector. It provides a detectable evidence to distinguish these two different but very similar pairing channels. Furthermore, we find this model can give arise to a subleading spin-singlet chiral $p$-wave topological superconducting state. More significantly, we find that such unconventional Rashba bands and unconventional superconudcting pairings can be realized on surface of some superconducting topological materials, such as trigonal layered PtBi$_{2}$.

CeRh$_6$Ge$_4$ stands out as the first stoichiometric metallic compound with a ferromagnetic quantum critical point, thereby garnering significant attention. Ferromagnetic Kondo lattice compounds ReRh$_6$Ge$_4$ (Re=Ce, Ho, Er, Tm) have been systematically investigated with density functional theory incorporating Coulomb interaction U and spin-orbital coupling. We determined the magnetic easy axis of CeRh$_6$Ge$_4$ is within the ab plane, which is in agreement with previous magnetization measurements conducted under external magnetic field and muSR experiments. We also predicted the magnetic easy axes for the other three compounds. For TmRh$_6$Ge$_4$, the magnetic easy axis aligns along the c axis, thus preserving the $C_3$ rotational symmetry of the c axis. Especially, there are triply degenerate nodal points along the $\Gamma-A$ direction in the band structure including spin-orbital coupling. A possible localized to itinerant crossover is revealed as $4f$ electrons increase from CeRh$_6$Ge$_4$ to TmRh$_6$Ge$_4$. Specifically, the $4f$ electrons of TmRh$_6$Ge$_4$ contribute to the formation of a large Fermi surface, indicating their participation in the conduction process. Conversely, the $4f$ electrons in HoRh$_6$Ge$_4$, ErRh$_6$Ge$_4$ and CeRh$_6$Ge$_4$ remain localized, which result in smaller Fermi surfaces for these compounds. These theoretical investigations on electronic structure and magnetic properties shed deep insight into the unique nature of $4f$ electrons, providing critical predictions for subsequent experimental studies.

In this study, we introduce a novel implementation of density functional theory integrated with single-site dynamical mean-field theory to investigate the complex properties of strongly correlated materials. This comprehensive first-principles many-body computational toolkit, termed $\texttt{Zen}$, utilizes the Vienna $\textit{ab initio}$ simulation package and the $\texttt{Quantum ESPRESSO}$ code to perform density functional theory calculations and generate band structures for realistic materials. The challenges associated with correlated electron systems are addressed through two distinct yet complementary quantum impurity solvers: the natural orbitals renormalization group solver for zero temperature and the hybridization expansion continuous-time quantum Monte Carlo solver for finite temperature. Additionally, this newly developed toolkit incorporates several valuable post-processing tools, such as $\texttt{ACFlow}$, which employs the maximum entropy method and the stochastic pole expansion method for the analytic continuation of Matsubara Green's functions and self-energy functions. To validate the performance of this toolkit, we examine three representative cases: the correlated metal SrVO$_{3}$, the nickel-based unconventional superconductor La$_{3}$Ni$_{2}$O$_{7}$, and the wide-gap Mott insulator MnO. The results obtained demonstrate strong agreement with experimental findings and previously available theoretical results. Notably, we successfully elucidate the quasiparticle peak and band renormalization in SrVO$_{3}$, the dominance of Hund correlation in La$_{3}$Ni$_{2}$O$_{7}$, and the pressure-driven insulator-metal transition as well as the high-spin to low-spin transition in MnO. These findings suggest that $\texttt{Zen}$ is proficient in accurately describing the electronic structures of $d$-electron correlated materials.

The Gardner transition in structural glasses is characterized by full-replica symmetry breaking of the free-energy landscape and the onset of anomalous aging dynamics due to marginal stability. Here we show that this transition also has a structural signature in finite-dimensional glasses consisting of hard spheres and disks. By analyzing the distribution of inter-particle gaps in the simulated static configurations at different pressures, we find that the Gardner transition coincides with the emergence of two well-known jamming scalings in the gap distribution, which enables the extraction of a structural order parameter. The jamming scalings reflect a compressible effective force network formed by contact and quasi-contact gaps, while non-contact gaps that do not participate in the effective force network are incompressible. Our results suggest that the Gardner transition in hard-particle glasses is a precursor of the jamming transition. The proposed structural signature and order parameter provide a convenient approach to detecting the Gardner transition in future granular experiments.

PuCoGa5 has attracted significant attention due to its record-breaking superconducting transition temperature Tc=18.5 K among known f-electron superconductors. Here we systematically investigated the evolution of correlated electronic states in the plutonium-based unconventional superconductor PuCoGa5 upon temperature using the embedded dynamical mean-field theory merged with density functional theory. The mixed-valence nature of PuCoGa5 leads to intriguing quasiparticle dynamics and hybridization dynamics. Our findings reveal the presence of Dirac fermions and a temperature-driven localized-itinerant crossover of 5f states. As the temperature decreases, the low-energy quasiparticle resonances develop gradually, while the high-energy quasiparticle resonances exhibit quite different behaviors with an initial increase and subsequent decrease. Furthermore, we identified a characteristic temperature of approximately 290 K for the onset of hybridization gaps, which is much lower than the coherence temperature 580 K for 5f electrons. These results provide valuable insight on the the electronic structures, quasiparticle dynamics, and hybridization processes in 5f correlated electron systems.

ACTest is an open-source toolkit developed in the Julia language. Its central goal is to automatically establish analytic continuation testing datasets, which include a large number of spectral functions and the corresponding Green's functions. These datasets can be used to benchmark various analytic continuation methods and codes. In ACTest, the spectral functions are constructed by a superposition of randomly generated Gaussian, Lorentzian, $\delta$-like, rectangular, and Rise-And-Decay peaks. The spectra can be positive definite or non-positive definite. The corresponding energy grids can be linear or non-linear. ACTest supports both fermionic and bosonic Green's functions on either imaginary time or Matsubara frequency axes. Artificial noise can be superimposed on the synthetic Green's functions to simulate realistic Green's functions obtained by quantum Monte Carlo calculations. ACTest includes a standard testing dataset, namely ACT100. This built-in dataset contains 100 testing cases that cover representative analytic continuation scenarios. Now ACTest is fully integrated with the ACFlow toolkit. It can directly invoke the analytic continuation methods as implemented in the ACFlow toolkit for calculations, analyze calculated results, and evaluate computational efficiency and accuracy. ACTest comprises many examples and detailed documentation. The purpose of this paper is to introduce the major features and usages of the ACTest toolkit. The benchmark results on the ACT100 dataset for the maximum entropy method, which is probably the most popular analytic continuation method, are also presented.

Despite their exceptional flexibility and popularity, the Monte Carlo methods often suffer from slow mixing times for challenging statistical physics problems. We present a general strategy to overcome this difficulty by adopting ideas and techniques from the machine learning community. We fit the unnormalized probability of the physical model to a feedforward neural network and reinterpret the architecture as a restricted Boltzmann machine. Then, exploiting its feature detection ability, we utilize the restricted Boltzmann machine for efficient Monte Carlo updates and to speed up the simulation of the original physical system. We implement these ideas for the Falicov-Kimball model and demonstrate improved acceptance ratio and autocorrelation time near the phase transition point.

We derive an effective classical model to describe the Mott transition of the half-filled one-band Hubbard model in the framework of the dynamical mean-field theory with hybridization expansion of the continuous time quantum Monte Carlo. We find a simple two-body interaction of exponential form and reveal a classical correspondence of the Mott transition driven by a logarithmically divergent interaction length. Our work provides an alternative angle to view the Mott physics and suggests a renewed possibility to extend the application of the quantum-to-classical mapping in understanding condensed matter physics

Analytic continuation is a critical step in quantum many-body computations, connecting imaginary-time or Matsubara Green's functions with real-frequency spectral functions, which can be directly compared to experimental results. However, due to the ill-posed nature of the analytic continuation problems, they have not been completely solved so far. In this paper, we suggest a simple, yet highly efficient method for analytic continuations of Matsubara Green's functions. This method takes advantage of barycentric rational functions to directly interpolate Matsubara Green's functions. At first, the nodes and weights of the barycentric rational functions are determined by the adaptive Antoulas-Anderson algorithm, avoiding reliance on the non-convex optimization. Next, the retarded Green's functions and the relatively spectral functions are evaluated by the resulting interpolants. We systematically explore the performance of this method through a series of toy models and realistic examples, comparing its accuracy and efficiency with other popular methods, such as the maximum entropy method. The benchmark results demonstrate that the new method can accurately reproduce not only continuous but also discrete spectral functions, irrespective of their positive definiteness. It works well even in the presence of intermediate noise, and outperforms traditional analytic continuation methods in computational speed. We believe that this method should stand out for its robustness against noise, broad applicability, high precision, and ultra efficiency, offering a promising alternative to the maximum entropy method.