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The recently-discovered high-temperature superconductor La$_3$Ni$_2$O$_7$ under high pressure has stimulated intensive debates. Key controversies concern interlayer versus intralayer pairing scenarios and if the hybridization plays a key role in establishing the superconductivity. But experimental clarification is difficult due to the limitation of employing state-of-the-art techniques under high pressure. Here we propose that quasiparticle tunneling and Andreev reflection on a normal metal-superconductor junction may provide a feasible way to distinguish different pairing scenarios. We predict that an asymmetric Fano line shape may be induced by the hybridization between the $d_{x^2-y^2}$ metallic bands and the strongly renormalized flat $d_{z^2}$ quasiparticle bands. In the superconducting state, we show that the Andreev reflection should be greatly suppressed for interlayer pairing superconductivity with a small interlayer hopping. We propose future experiments to examine these predictions and help clarify the fundamental physics of superconducting La$_3$Ni$_2$O$_7$., Comment: 6 pages, 4 figures

The recent discovery of high-temperature superconductivity in La$_3$Ni$_2$O$_7$ under high pressure has stimulated intensive investigations concerning its paring mechanism and a correct description of its effective low-energy physics. Notable experimental observations include the right-triangle-shaped superconducting dome with the maximum $T_c$ of about 80 K and the strange metal behavior in the normal state above $T_c$. Here we apply the Schwinger boson approach to the bilayer $t$-$V$-$J$ model, which allows us to treat well both the magnetic correlations and the superconducting instability. We obtain a global phase diagram with both metallic and superconducting ground states separated by a quantum phase transition, and predict a minimal interlayer superexchange $J$ and a minimal $d_{z^2}$-hole concentration necessary for the superconductivity, with a highly asymmetric right-triangle-like shape for the $T_c$ curve as well as a maximum $T_c$ comparable with experiments. The normal state is featured with a pseudogap in the $d_{x^2-y^2}$ spectra associated with preformed Cooper pairs and non-Fermi liquid strange metal behavior due to hybridization-induced spinon-holon-electron scattering. Our work clarifies the key difference of the two-component scenario of the superconductivity from other mechanisms, and provides a consistent understanding of the high-temperature superconductivity and strange metallic properties of La$_{3}$Ni$_2$O$_7$ under high pressure., Comment: 9 pages, 5 figures

We prove that multilayer superconductivity with interlayer pairing may naturally decompose into a series of weakly-coupled bilayer and trilayer superconducting blocks in order to minimize its total free energy. Our work is motivated by the recent proposal of interlayer pairing induced by the interlayer superexchange interaction of nearly half-filled $d_{z^2}$ orbitals in the bilayer and trilayer nickelate superconductors. We explore general properties of interlayer pairing superconductivity and perform systematic Ginzburg-Landau analyses of an effective multilayer model. For real materials, our results imply strong superconducting order parameter modulation and short coherence length along the $z$-axis (perpendicular to the layers). This reveals a unique feature of multilayer superconductivity with interlayer pairing and provides a basic framework for future experimental and theoretical investigations., Comment: 8 pages, 3 figures

Tool-augmented large language models (LLMs) leverage tools, often in the form of APIs, to enhance their reasoning capabilities on complex tasks, thus taking on the role of intelligent agents interacting with the real world. The recently introduced ToolLLaMA model by Qin et al. [2024] utilizes the depth-first search-based decision tree (DFSDT) method for reasoning with $16000+$ real-world APIs, which effectively improves the planning and inferencing performance of tool-augmented LLMs compared to traditional chain reasoning approaches. However, their approach only employs successful paths from decision trees (also called inference trees) for supervised fine-tuning (SFT) during training, which does not fully exploit the advantages of the tree of thought. In this study, we propose an inference trajectory optimization framework based on the preference data extracted from decision trees to address this limitation. We first introduce a novel method for constructing preference data from the tree of thought, capitalizing on the failed explorations previously overlooked in the trees. Specifically, we generate an effective step-wise preference dataset, named ToolPreference, for tool use based on the ToolBench dataset. In the subsequent training phase, we first fine-tune the LLM with tool-usage expert trajectories and then use these step-wise preference pairs for direct preference optimization (DPO) to update the policy of the LLM, resulting in our ToolPrefer-LLaMA (TP-LLaMA) model. Our experiments demonstrate that by obtaining insights from errors in inference trees, TP-LLaMA significantly outperforms the baselines across almost all test scenarios by a large margin and exhibits better generalization capabilities with unseen APIs. At the same time, TP-LLaMA has also demonstrated superior reasoning efficiency compared to the baselines, making it more suitable for complex tool-usage reasoning tasks.

The expanding applications call for novel new-generation wide-bandgap semiconductors. Here, we show that a compound only composed of the ordinary elements Na and Cl, namely three-dimensional NaCl2 crystal, is a wide-bandgap semiconductor. This finding benefits from the breaking of conventional stoichiometry frameworks in the theoretical design, leading to the discovery of three-dimensional XY2 (X = Na, Li, K; Y = Cl, F, Br, I) crystals, with covalent bonds of Y pairs inducing the wide bandgap from 2.24 to 4.45 eV. Crucially, such an unexpected NaCl2 crystal was successfully synthesized under ambient conditions. The unconventional stoichiometric strategy with other chemical elements potentially yields more wide-bandgap semiconductors, offering the capability for bandgap tuning. These unconventional stoichiometric materials may also exhibit superconductivity, transparent inorganic electrides, high-energy-density, and beyond.

The recent introduction of prompt tuning based on pre-trained vision-language models has dramatically improved the performance of multi-label image classification. However, some existing strategies that have been explored still have drawbacks, i.e., either exploiting massive labeled visual data at a high cost or using text data only for text prompt tuning and thus failing to learn the diversity of visual knowledge. Hence, the application scenarios of these methods are limited. In this paper, we propose a pseudo-visual prompt~(PVP) module for implicit visual prompt tuning to address this problem. Specifically, we first learn the pseudo-visual prompt for each category, mining diverse visual knowledge by the well-aligned space of pre-trained vision-language models. Then, a co-learning strategy with a dual-adapter module is designed to transfer visual knowledge from pseudo-visual prompt to text prompt, enhancing their visual representation abilities. Experimental results on VOC2007, MS-COCO, and NUSWIDE datasets demonstrate that our method can surpass state-of-the-art~(SOTA) methods across various settings for multi-label image classification tasks. The code is available at https://github.com/njustkmg/PVP., Comment: Accepted for publication at IJCAI 2024; 13 pages; 11 figures

Motivated by the opposite trend of maximum $T_c$ in multilayer nickelate and cuprate superconductors, we propose an interlayer pairing scenario for the superconductivity of the trilayer nickelate La$_4$Ni$_3$O$_{10}$ discovered recently under high pressure. Our theory reveals intrinsic frustration of the spin-singlet pairing formed between two outer layers and the same inner layer, which causes strong superconducting fluctuations between layers and thus explains the reduction of its maximum $T_c$ compared to that of the bilayer La$_3$Ni$_2$O$_{7}$. This supports a fundamental distinction between multilayer nickelate and cuprate superconductors associated with their potentially different (interlayer vs intralayer) pairing mechanisms. Our theory predicts extended $s^\pm$-wave gap structures in La$_4$Ni$_3$O$_{10}$, with varying signs and possible nodes on different Fermi pockets. We also find an intrinsic Josephson coupling with potentially interesting consequences to be examined in future experiments., Comment: 5 figures

The interplay of topological band structures and electronic correlations may lead to novel exotic quantum phenomena with potential applications. First-principles calculations are critical for guiding the experimental discoveries and interpretations, but often fail if electronic correlations cannot be properly treated. Here we show that this issue occurs also in the antiferromagnetic kagome lattice Mn$_3X$ ($X=$ Sn, Ge), which exhibit a large anomalous Hall effect due to topological band structures with Weyl nodes near the Fermi energy. Our systematic investigations reveal a crucial role of the Hund's rule coupling on three key aspects of their magnetic, electronic, and topological properties: (1) the establishment of noncollinear antiferromagnetic orders, (2) the weakly renormalized bands in excellent agreement with ARPES, and (3) a sensitive tuning of the Weyl nodes beyond previous expectations. Our work provides a basis for understanding the topological properties of Mn$_3X$ and challenges previous experimental interpretations based on incorrect band structures.

The identification of new materials with superconducting properties is the pursuit in the realm of superconductivity research. Here, excitedly, we show that the simplest salt daily used can be made a superconductor at normal pressure only by adjusting its stoichiometry of Na and Cl as Na3Cl at normal pressure based on first-principles calculations. This bulk stable abnormal Na-Cl stoichiometric crystal of 3:1, the first 'magic' ratio, includes metallic (Na) atoms in the core as well as hybridization of ionic and metallic bonding, facilitating the electron-phonon-coupling for superconductivity with a critical temperature Tc of 0.13 K. The flat bands and van Hove singularities near the Fermi level produce large densities of states, similar to H3S and LaH10, which is beneficial for the emergence of superconductivity. The crystal composed of with abnormal Na-Cl magic stoichiometry is a precisely tunable, purely sodium and chloride-based, three-dimensional bulk superconductor, which is therefore an ideal material for designing and understanding abnormal stoichiometric crystals. The methodology of constructing this bulk abnormal crystal may be general to almost all elements, which could lead to insights into the physics of other conventional superconductors and even high-critical-temperature superconductors.

Solving quantum impurity problems may advance our understanding of strongly correlated electron physics, but its development in multi-impurity systems has been greatly hindered due to the presence of shared bath. Here, we propose a general operation strategy to disentangle the shared bath into multiple auxiliary baths and relate the problem to a spectral decomposition problem of function matrix for applying the numerical renormalization group (NRG). We prove exactly that such decomposition is possible for models satisfying (block) circulant symmetry, and show how to construct the auxiliary baths for arbitrary impurity configuration by mapping its graph structure to the subgraph of a regular impurity configuration. We further propose an approximate decomposition algorithm to reduce the number of auxiliary baths and save the computational workload. Our work reveals a deep connection between quantum impurity problems and the graph theory, and provides a general scheme to extend the NRG applications for realistic multi-impurity systems.

Competition and cooperation between electron correlation and relativistic spin-orbit coupling give rise to diverse exotic quantum phenomena in solids. An illustrative example is spin-orbit entangled quantum liquids, which exhibit remarkable features such as topological orders and fractional excitations. The Kitaev honeycomb model realizes such interesting states, called the Kitaev spin liquids, but its experimental feasibility is still challenging. Here we theoretically investigate hexagonal heterostructures including a candidate for the Kitaev magnets, MgIrO$_3$, to actively manipulate the electronic and magnetic properties toward realizing the Kitaev spin liquids. For three different structure types of ilmenite bilayers MgIrO$_3$/$A$TiO$_3$ with $A$ = Mn, Fe, Co, and Ni, we obtain the optimized lattice structures, the electronic band structures, the stable magnetic orders, and the effective magnetic couplings. We find that the spin-orbital coupled bands characterized by the pseudospin $j_{\rm eff}=$ 1/2 are retained in the MgIrO$_3$ layer for all the heterostructures, but the magnetic state and the band gap depend on the types of heterostructures as well as the $A$ atoms. In particular, one type becomes metallic irrespective of $A$, while the other two are mostly insulating. We show that the insulating cases provide spin-orbit coupled Mott insulating states with dominant Kitaev-type interactions, accompanied by different combinations of subdominant interactions depending on the heterostructural type and $A$, while the metallic cases realize spin-orbit coupled metals with various doping rates. Our results indicate that these hexagonal heterostructures are a good platform for engineering electronic and magnetic properties of the spin-orbital coupled correlated materials, including the possibility of Majorana Fermi surfaces and topological superconductivity.

Recent observations of contradictory impurity effect in the heavy-fermion superconductor CeCu2Si2 at ambient pressure have hindered the identification of its pairing symmetry. Here we perform theoretical analyses with both intraband and interband impurity scatterings for the nodeless $s^\pm$-wave pairing, and report an anomalous nonmonotonic variation of its $T_c$ suppression with the scattering strength. Our results reproduce the prominent reduction of $T_c$ in good agreement with earlier experiments by atomic substitution and explains as well its robustness against electron irradiation. We ascribe the latter to the screening of the interband impurity potential in the strong scattering or unitary region. This resolves the seeming contradiction in different experimental probes and provides an important support to the nodeless $s^\pm$-wave scenario in CeCu2Si2 at ambient pressure. Our theory may be extended to other narrow band systems such as twisted bilayer graphene and the recently discovered bilayer or trilayer nickelate superconductors, and provide a useful way to distinguish different paring candidates thereof., Comment: 5 pages and 4 figures

Can room temperature superconductivity be achieved in correlated materials under ambient pressure? Our answer to this billion-dollar question is probably no, at least for realistic models within the current theoretical framework. This is shown by our systematic simulations on the pairing instability of some effective models for two-dimensional superconductivity. For a square lattice model with nearest-neighbour pairing, we find a plaquette state formed of weakly-connected $2\times2$ blocks for sufficiently large pairing interaction. The superconductivity is suppressed on both sides away from its melting quantum critical point. Thus, the plaquette state constrains the magnitude of $T_c$ for large pairing interactions and may be viewed as a strong-coupling parent state of $d$-wave superconductivity, in resemblance of other competing orders. We then extend our simulations to a variety of effective models covering nearest-neighbour or onsite pairings, single layer or two-layer structures, intralayer or interlayer pairings, and find an intrinsic maximum of the ratio $T_c/J\approx 0.04-0.07$, where $J$ is the onsite or nearest-neighbour pairing interaction. Comparison with existing experiments supports this constraint in cuprate, iron-based, nickelate, and heavy fermion superconductors, despite that these compounds are so complicated well beyond our simplified models. As a result, the known families of unconventional superconductivity, possibly except the infinite-layer nickelates, seem to almost exhaust their potentials in reaching the maximal $T_c$ allowed by their spin exchange interaction, while achieving room temperature superconductor would require a much larger $J$ beyond 400-700 meV, which seems unrealistic and hence demands novel pairing mechanisms., Comment: 5 figures

Atomic force microscope (AFM) generally works on the basis of manipulating absolute magnitude of van der Waals (vdW) force between the tip and specimen. The force is, however, less sensitive to alternation of atom species than to tip-sample separations, resulting in the difficulty of compositional identification, even under multi-modal strategies and other AFM variations. Here, we report a phenomenon of light enhancement of van der Waals force (LvF), and the enhancement factor is found specific to materials. The force difference prior and after illumination, instead of the tip-specimen force itself, is employed for discriminating heterogeneous phases. The corresponding LvF microscopy (LvFM) demonstrates not only a ultra-high compositional resolution represented by 20 dB enhancement factor and 150 times of the detection limit, but also a sub-10 nm lateral spatial resolution much smaller than the tip size of 20 nm. The simplicity of the opto-thermal mechanism, minuteness of excitation light power and wide availability of boosting lasers at various wavelengths imply broad applications of LvFM on nano-materials characterization, particularly on two-dimensional semiconductors that are promising as new generation of chip materials.

We propose an exactly solvable momentum-space Kondo-BCS model to study heavy fermion superconductivity. The Kondo interaction is local in momentum space, which can be derived from an Anderson lattice with a Hatsugai-Kohmoto interaction between $f$-electrons. By increasing the Kondo interaction, the model exhibits a crossover from a weak-coupling BCS superconductor to a strong-coupling heavy fermion superconductor featured with a large gap ratio and a large specific heat jump anomaly. Accordingly, the normal state evolves from a Fermi liquid above the BCS superconductor to a non-Fermi liquid two-fluid state above the heavy fermion superconductor. The two-fluid normal state also leads to two types of Cooper pairs, one between conduction electrons, the other between composite fermions formed by conduction electrons and $f$-spins, which is responsible for the strong coupling behaviors of heavy fermion superconductivity., Comment: 7 pages, 4 figures

Due to their intrinsic capabilities on parallel signal processing, optical neural networks (ONNs) have attracted extensive interests recently as a potential alternative to electronic artificial neural networks (ANNs) with reduced power consumption and low latency. Preliminary confirmation of the parallelism in optical computing has been widely done by applying the technology of wavelength division multiplexing (WDM) in the linear transformation part of neural networks. However, inter-channel crosstalk has obstructed WDM technologies to be deployed in nonlinear activation in ONNs. Here, we propose a universal WDM structure called multiplexed neuron sets (MNS) which apply WDM technologies to optical neurons and enable ONNs to be further compressed. A corresponding back-propagation (BP) training algorithm is proposed to alleviate or even cancel the influence of inter-channel crosstalk on MNS-based WDM-ONNs. For simplicity, semiconductor optical amplifiers (SOAs) are employed as an example of MNS to construct a WDM-ONN trained with the new algorithm. The result shows that the combination of MNS and the corresponding BP training algorithm significantly downsize the system and improve the energy efficiency to tens of times while giving similar performance to traditional ONNs.

Motivated by the recent discovery of an intermediate quantum critical phase between the antiferromagnetic order and the Fermi liquid in the frustrated Kondo lattice CePdAl, we study here a Kondo-Heisenberg chain with frustrated $J_1$-$J_2$ XXZ interactions among local spins using the density matrix renormalization group method. Our simulations reveal a global phase diagram with rich ground states including the antiferromagnetic order, the valence-bond-solid and bond-order-wave orders, the pair density wave state, the uniform superconducting state, and the Luttinger liquid state. We show that both the pair density wave and uniform superconductivity belong to the family of Luther-Emery liquids and may arise from pair instability of an intermediate quantum critical phase with medium Fermi volume in the presence of strong quantum fluctuations, while the Luttinger liquid has a large Fermi volume. This suggests a deep connection between the pair density wave, the unconventional superconductivity, and the non-Fermi liquid quantum critical phase., Comment: 12 pages, 13 figures

We clarify the pairing mechanism of high-$T_c$ superconductivity in bilayer La$_3$Ni$_2$O$_7$ under high pressure by employing the static auxiliary field Monte Carlo approach to simulate a minimal effective model that contains local $d_{z^2}$ interlayer spin singlets and metallic $d_{x^2-y^2}$ bands. Superconductivity is induced when the local spin singlet pairs are mobilized and attain long-distance phase coherence by hybridization with the metallic bands. When projected onto realistic Fermi surfaces, it yields a nodeless $s$-wave gap on the $\gamma$ Fermi surface, and extended $s$-wave gaps of the same (opposite) sign on the $\alpha$ ($\beta$) Fermi surface due to its bonding (antibonding) character, with nodes or gap minima along the diagonal direction of the two-dimensional Brillouin zone. We find a dual role of the hybridization that not only induces global phase coherence but also competes with the spin singlet formation. This lead to a tentative phase diagram where $T_c$ varies nonmonotonically with the hybridization, in good correspondence with experimental observations. A roughly linear relation is obtained for realistic hopping and hybridization parameters: $T_c\approx 0.04-0.05 J$, where $J$ is the interlayer superexchange interaction. We emphasize the peculiar tunability of the bilayer structure and propose that $T_c$ may be further enhanced by hole doping or applying uniaxial pressure along the $c$ axis on superconducting La$_3$Ni$_2$O$_7$. Our work provides reliable numerical evidence for the pairing mechanism of high-$T_c$ superconductivity in La$_3$Ni$_2$O$_7$ and points out a potential route to achieve even higher $T_c$., Comment: 7 pages,4 figures

The recent discovery of high-$T_{c}$ superconductivity in bilayer nickelate La$_{3}$Ni$_{2}$O$_{7}$ under high pressure has stimulated great interest concerning its pairing mechanism. We argue that the weak coupling model from the almost fully-filled $d_{z^{2}}$ bonding band cannot give rise to its high $T_{c}$, and thus propose a strong coupling model based on local inter-layer spin singlets of Ni-$d_{z^{2}}$ electrons due to their strong on-site Coulomb repulsion. This leads to a minimal effective model that contains local pairing of $d_{z^{2}}$ electrons and a considerable hybridization with near quarter-filled itinerant $d_{x^{2}-y^{2}}$ electrons on nearest-neighbor sites. Their strong coupling provides a unique two-component scenario to achieve high-$T_{c}$ superconductivity. Our theory highlights the importance of the bilayer structure of superconducting La$_{3}$Ni$_{2}$O$_{7}$ and points out a potential route for the exploration of more high-$T_{c}$ superconductors., Comment: 6 pages, 3 figures

The Dark Matter Particle Explorer (DAMPE) is a satellite-borne detector designed to measure high energy cosmic-rays and $\gamma$-rays. As a key sub-detector of DAMPE, the Bismuth Germanium Oxide (BGO) imaging calorimeter is utilized to measure the particle energy with a high resolution. The nonlinear fluorescence response of BGO for large ionization energy deposition, known as the quenching effect, results in an under-estimate of the energy measurement for cosmic-ray nuclei. In this paper, various models are employed to characterize the BGO quenching factors obtained from the experimental data of DAMPE. Applying the proper quenching model in the detector simulation process, we investigate the tuned energy responses for various nuclei and compare the results based on two different simulation softwares, i.e. GEANT4 and FLUKA. The BGO quenching effect results in a decrease of the measured energy by approximately $2.5\%$ ($5.7 \%$) for carbon (iron) at $\sim$10 GeV/n and $<1\%$ above 1 TeV/n, respectively. Accordingly, the correction of the BGO quenching effect leads to an increase of the low-energy flux measurement of cosmic-ray nuclei., Comment: 13 pages, 4 figures, to be published in Nuclear Inst. and Methods in Physics Research, A

We report strongly correlated electronic band structure calculations of the recently discovered double-layer high-temperature superconductor La$_3$Ni$_2$O$_7$ under pressure. Our calculations reveal dual nature of Ni-$d$ electrons with almost localized $d_{z^2}$ orbitals due to onsite Coulomb repulsion and very flat hybridization bands of Ni-$d_{x^2-y^2}$ and Ni-$d_{z^2}$ quasiparticles near the Fermi energy. We find that the quasiparticle effective mass are greatly enhanced by the Hund's rule coupling and their lifetimes are inversely proportional to the temperature, which explains the experimentally observed strange metal behavior in the normal state. We also find strong antiferromagnetic spin correlations of Ni-$d$ electrons, which may provide the pairing force of quasiparticles for the high-temperature superconductivity. These give a potential explanation of two key observations in experiment and connect the superconducting La$_3$Ni$_2$O$_7$ with cuprate high-temperature superconductors. The presence of flat bands and the interplay of orbital-selective Mott, Hund, and Kondo physics make La$_3$Ni$_2$O$_7$ a unique platform for exploring rich emergent quantum many-body phenomena in the future., Comment: 6 pages, 4 figures

Low-dimensional ferroelectric tunnel junctions are appealing for the realization of nanoscale nonvolatile memory devices due to their inherent advantage of device miniaturization. Those based on current mechanisms still have restrictions including low tunneling electroresistance (TER) effects and complex heterostructures. Here, we introduce an entirely new TER mechanism to construct the nanotube ferroelectric tunnel junction with ferroelectric nanotubes as the tunneling region. When rolling a ferroelectric monolayer into a nanotube, due to the coexistence of its intrinsic ferroelectric polarization with the flexoelectric polarization induced by bending, there occurs metal-insulator transition depending on radiative polarization states. For the pristine monolayer, its out-of-plane polarization is tunable by an in-plane electric field, the conducting states of the ferroelectric nanotube can thus be tuned between metallic and insulating via axial electric means. Using {\alpha}-In2Se3 as an example, our first-principles density functional theory calculations and nonequilibrium Green's function formalism confirm the feasibility of the TER mechanism and indicate an ultrahigh TER ratio exceeding 9.9*10^10% of the proposed nanotube ferroelectric tunnel junctions. Our findings provide a promising approach based on simple homogeneous structures for high density ferroelectric microelectronic devices with excellent ON/OFF performance., Comment: 15 pages, 5 figures

We discover a universal scaling law for the quasiparticle Nernst coefficient in underdoped cuprates, whose magnitude decreases exponentially with increasing temperature as confirmed in YBa$_2$Cu$_3$O$_y$. We attribute it to the basic mathematical structure of the conductivity formula with a narrow effective bandwidth of nonzero Berry curvatures associated with the pseudogap. A unified scheme is then developed to analyze transverse transport in hole-doped cuprates and clarify the puzzling disparity in determining the pseudogap temperature from different measurements. Our proposal opens the avenue for exploring potential scaling laws in the intermediate temperature region and may have broad applications in strongly correlated or narrow band systems., Comment: 4 pages, 3 figures

We propose an auxiliary-bath algorithm for the numerical renormalization group (NRG) method to solve multi-impurity models with shared electron baths. The method allows us to disentangle the electron baths into independent Wilson chains to perform standard NRG procedures beyond the widely adopted independent bath approximation. Its application to the 2-impurity model immediately reproduces the well-known even- and odd-parity channels. For 3-impurity Kondo models, we find successive screening of collective degrees of freedom such as the helicity and the cluster spin, and clarify the false prediction of a non-Fermi liquid ground state in unphysical parameter region in previous literature due to improper treatment of disentanglement. Our work highlights the importance of nonlocal spatial correlations due to shared baths and reveals a generic picture of successive collective screening for the entropy depletion that is crucial in real correlated systems. Our method greatly expands the applicability of the NRG and opens an avenue for its further development.