Search

Azimuthal modulations are crucial for the phenomenological extraction and separation of various generalized parton distributions. We provide a new choice of frame and corresponding formalism to describe the azimuthal distributions, based on the separation of physics occurring at different momentum scales. We demonstrate that this new description is not only well-suited for experimental analysis, but also advantageous in separating contributions from different subprocesses to the same physical cross section., Comment: 5 pages, 3 figures, plus a 3-page supplemental material

The physics case for quarkonium-production studies accessible at the US Electron Ion Collider is described., Comment: Latex, 84 pages. Review prepared for Progress in Particle and Nuclear Physics

We present the first calculation of next-to-leading order (NLO) factorized QED contributions to the short-distance hard coefficients of inclusive lepton-hadron deep inelastic scattering (DIS) in a joint QCD and QED factorization approach. We demonstrate how the joint factorization consistently factorize all perturbative collinear sensitivities of partonic scattering in both QCD and QED into corresponding universal hadron and lepton distribution functions without the need of any parameters other than the standard factorization scale. We discuss the necessary modification to DGLAP-type evolution of the parton and lepton distribution functions in this joint factorization approach. We also discuss the potential impact of this joint factorization approach on the extraction of partonic information from lepton-hadron DIS., Comment: 6 pages, 2 figures; contributed talk to DIS2024

We introduce a new type of exclusive processes for a better study of generalized parton distributions (GPDs), which we refer to as single-diffractive hard exclusive processes (SDHEPs). We advocate a two-stage framework for picturing SDHEPs based on the separation of scales, which gives a clear description both kinematically and dynamically. We examine the sensitivity of the SDHEP to the parton momentum fraction $x$-dependence of GPDs, and demonstrate it quantitatively with two specific processes that can be readily measured at J-PARC or AMBER using a pion beam and at JLab using a photon beam, respectively. Both processes are capable of providing enhanced sensitivity to the $x$-dependence, overcoming the problem of shadow GPDs, and disentangling different types of GPDs with various spin asymmetries., Comment: 5 pages, 2 figures; contributed talk to DIS2024

In a PN junction, the separation between positive and negative charges leads to diode transport. In the past few years, the intrinsic diode transport in noncentrosymmetric polar conductors has attracted great interest, because it suggests novel nonlinear applications and provides a symmetry-sensitive probe of Fermi surface. Recently, such studies have been extended to noncentrosymmetric superconductors, realizing the superconducting diode effect. Here, we show that, even in a centrosymmetric crystal without directional charge separation, the spins of an antiferromagnet (AFM) can generate a spatial directionality, leading to an AFM diode effect. We observe large second-harmonic transport in a nonlinear electronic device enabled by the compensated AFM state of even-layered MnBi2Te4. We also report a novel electrical sum-frequency generation (SFG), which has been rarely explored in contrast to the well-known optical SFG in wide-gap insulators. We demonstrate that the AFM enables an in-plane field-effect transistor and harvesting of wireless electromagnetic energy. The electrical SFG establishes a powerful method to study nonlinear electronics built by quantum materials. The AFM diode effect paves the way for potential device concepts including AFM logic circuits, self-powered AFM spintronics, and other applications that potentially bridge nonlinear electronics with AFM spintronics., Comment: 33+8 pages, 14+2 figures

We study the extraction of transition generalized parton distributions (GPDs) from production of two back-to-back high transverse momentum photons ($\gamma\gamma$) and a massive pair of leptons ($\ell^+\ell^-$) in hard exclusive pion-nucleon scattering. We argue that the exclusive scattering amplitude of both processes could be factorized into nonperturbative pion distribution amplitude and nucleon transition GPDs that are convoluted with perturbatively calculable short-distance matching coefficients. We demonstrate that the exclusive diphoton production not only is complementary to the Drell-Yan-type dilepton production for extracting the GPDs, but also provides enhanced sensitivities for extracting the parton momentum fraction $x$ dependence of the GPDs. We show that both exclusive observables are physically measurable at the J-PARC and AMBER experiment energies. If the target nucleon can be polarized, corresponding spin asymmetries can offer additional sensitivities for extracting transition GPDs., Comment: 7+2 pages, 9 figures; journal published version

It has been more than 30 years since the enigmatic 21 {\mu}m emission feature was first discovered in protoplanetary nebulae (PPNs). Although dozens of different dust carrier candidates have been proposed, there is as yet no widely accepted one. We present the results of molecular observations toward 21{\mu}m objects using the 10m Submillimeter Telescope of Arizona Radio Observatory at the 1.3 mm band and the 13.7 m telescope of Purple Mountain Observatory at the 3mm band, aiming to investigate whether the gas-phase environments of these unusual sources have some peculiarities compared to normal PPNs. We detect 31 emission lines belonging to seven different molecular species, most of which are the first detection in 21 {\mu}m PPNs. The observations provide clues on the identification of the 21 {\mu}m feature. We report a correlation study between the fractional abundance of gas-phase molecules and the strengths of the 21 {\mu}m emission. Our study shows that given the small sample size, the 21 {\mu}m feature has weak or no correlations with the gas-phase molecules. Future radio observations of high spatial and spectral resolution toward a large sample are desirable to elucidate the 21 {\mu}m emission phenomena., Comment: 40 pages, 10 figures, 11 tables, accepted for publication in The Astronomical Journal

Generative AI is a fast-growing area of research offering various avenues for exploration in high-energy nuclear physics. In this work, we explore the use of generative models for simulating electron-proton collisions relevant to experiments like CEBAF and the future Electron-Ion Collider (EIC). These experiments play a critical role in advancing our understanding of nucleons and nuclei in terms of quark and gluon degrees of freedom. The use of generative models for simulating collider events faces several challenges such as the sparsity of the data, the presence of global or event-wide constraints, and steeply falling particle distributions. In this work, we focus on the implementation of diffusion models for the simulation of electron-proton scattering events at EIC energies. Our results demonstrate that diffusion models can accurately reproduce relevant observables such as momentum distributions and correlations of particles, momentum sum rules, and the leading electron kinematics, all of which are of particular interest in electron-proton collisions. Although the sampling process is relatively slow compared to other machine learning architectures, we find diffusion models can generate high-quality samples. We foresee various applications of our work including inference for nuclear structure, interpretable generative machine learning, and searches of physics beyond the Standard Model., Comment: 14 pages, 10 figures, journal version

Water fountains (WFs) are thought to be objects in the morphological evolution of the circumstellar envelopes of low- and intermediate-mass evolved stars, transitioning from spherically symmetric to asymmetric shapes. We used databases of circumstellar 1612 MHz OH and 22.235 GHz H$_2$O maser sources to search for new WF candidates using the criterion of a larger velocity range of the H$_2$O maser emission compared to that of the OH maser emission. Thus, it is in principle possible to identify WFs with an H$_2$O velocity ranges smaller than those for the previously known WFs. For the OH maser line, we analyzed database entries of 8,474 observations from 2,195 sources, and 6,085 observations from 3,642 sources for H$_2$O maser line. After a close examination of the velocity ranges and line profiles, we identified 11 sources that meet the criterion mentioned above. We examined the IRAS colors of the selected sources and found that two of them (IRAS 19069+0916 and IRAS 19319+2214) are in the color region for post-AGB stars. We find that the maser velocity criterion can discover other astrophysically interesting objects than just WFs. Such objects may include peculiar planetary nebulae with maser emissions and stellar merger remnants., Comment: 34 pages, 10 figures, Accepted for publication in ApJS

We present an unbiased molecular line survey toward the carbon-rich circumstellar envelope CIT 6 carried out between 90 and 116 GHz with the Arizona Radio Observatory 12 m telescope. A total of 42 lines assigned to 10 molecular species and 4 isotopologues are detected. Despite the absence of any newly identified circumstellar molecules, several transitions are freshly reported for this object. This work is a complement to our previous line survey toward CIT 6 in the frequency ranges of 36-49 GHz and 131-268 GHz. Based on the measurements and in combination with previously published data, we perform a rotation-diagram analysis to determine the column densities, excitation temperatures, and fractional abundances of the molecules. The excitation temperature varies along the radius. The abundance pattern of CIT6 is broadly consistent with that of the prototype C-star IRC+10216 at the specified detection sensitivity, indicating that the molecular richness in IRC+10216 cannot be attributed to an interpretation of unusual chemistry. Nevertheless, subtle distinctions between the two C-stars are found. The higher abundance of carbon-chain molecules and lower 12C/13C ratio in CIT 6 compared to IRC+10216 imply that the former is more massive or in a more evolved phase than the latter., Comment: 34 pages, 14 figures, 5 tables

Diode effects are of great interest for both fundamental physics and modern technologies. Electrical diode effects (nonreciprocal transport) have been observed in Weyl systems. Optical diode effects arising from the Weyl fermions have been theoretically considered but not probed experimentally. Here, we report the observation of a nonlinear optical diode effect (NODE) in the magnetic Weyl semimetal CeAlSi, where the magnetization introduces a pronounced directionality in the nonlinear optical second-harmonic generation (SHG). We show demonstrate a six-fold change of the measured SHG intensity between opposite propagation directions over a bandwidth exceeding 250 meV. Supported by density-functional theory, we establish the linearly dispersive bands emerging from Weyl nodes as the origin of this broadband effect. We further demonstrate current-induced magnetization switching and thus electrical control of the NODE. Our results advance ongoing research to identify novel nonlinear optical/transport phenomena in magnetic topological materials and further opens new pathways for the unidirectional manipulation of light., Comment: 20 pages, 4 figures, SI included

Quantum geometry - the geometry of electron Bloch wavefunctions - is central to modern condensed matter physics. Due to the quantum nature, quantum geometry has two parts, the real part quantum metric and the imaginary part Berry curvature. The studies of Berry curvature have led to countless breakthroughs, ranging from the quantum Hall effect in 2DEGs to the anomalous Hall effect (AHE) in ferromagnets. However, in contrast to Berry curvature, the quantum metric has rarely been explored. Here, we report a new nonlinear Hall effect induced by quantum metric by interfacing even-layered MnBi2Te4 (a PT-symmetric antiferromagnet (AFM)) with black phosphorus. This novel nonlinear Hall effect switches direction upon reversing the AFM spins and exhibits distinct scaling that suggests a non-dissipative nature. Like the AHE brought Berry curvature under the spotlight, our results open the door to discovering quantum metric responses. Moreover, we demonstrate that the AFM can harvest wireless electromagnetic energy via the new nonlinear Hall effect, therefore enabling intriguing applications that bridges nonlinear electronics with AFM spintronics., Comment: 19 pages, 4 figures and a Supplementary Materials with 66 pages, 4 figures and 3 tables. Originally submitted to Science on Oct. 5, 2022

The $x$ dependence of hadrons' generalized parton distributions (GPDs) $\mathcal{F}(x,\xi,t)$ is the most difficult to extract from the existing known processes, while the $\xi$ and $t$ dependence are uniquely determined by the kinematics of the scattered hadron. We study the single diffractive hard exclusive processes for extracting GPDs in the photoproduction. We demonstrate quantitatively the enhanced sensitivity on extracting the $x$ dependence of various GPDs from the photoproduction cross sections, as well as the asymmetries constructed from photon polarization and hadron spin that could be measured at JLab Hall D by GlueX Collaboration and future facilities., Comment: 5 pages, 5 figures, plus a supplemental material that is 5 pages + 2 figures; to match the journal version

The `brane quantisation' procedure is developed by Gukov and Witten \cite{Gukov:2008ve}. We implement this idea by combining it with the tilting theory and the minimal resolutions. This way, we can realistically compute the deformation quantisation on the space of observables acting on the Hilbert space. We apply this procedure to certain quantisation problem in the context of generalised K\"ahler structure on $\mathbb{P}^2$. Our approach differs from and complements that of Bischoff and Gualtieri \cite{Bischoff:2021ixy}. We also benefitted from an important technical tool: a combinatorial criterion for the Maurer-Cartan equation, developed in \cite{BarmeierWang} by Barmeier and Wang., Comment: 39+9 pages, typos fixed, comments welcome

This handbook provides a comprehensive review of transverse-momentum-dependent parton distribution functions and fragmentation functions, commonly referred to as transverse momentum distributions (TMDs). TMDs describe the distribution of partons inside the proton and other hadrons with respect to both their longitudinal and transverse momenta. They provide unique insight into the internal momentum and spin structure of hadrons, and are a key ingredient in the description of many collider physics cross sections. Understanding TMDs requires a combination of theoretical techniques from quantum field theory, nonperturbative calculations using lattice QCD, and phenomenological analysis of experimental data. The handbook covers a wide range of topics, from theoretical foundations to experimental analyses, as well as recent developments and future directions. It is intended to provide an essential reference for researchers and graduate students interested in understanding the structure of hadrons and the dynamics of partons in high energy collisions., Comment: 471 pages, many figures

Using circularly-polarized light to control quantum matter is a highly intriguing topic in physics, chemistry and biology. Previous studies have demonstrated helicity-dependent optical control of spatial chirality and magnetization $M$. The former is central for asymmetric synthesis in chemistry and homochirality in bio-molecules, while the latter is of great interest for ferromagnetic spintronics. In this paper, we report the surprising observation of helicity-dependent optical control of fully-compensated antiferromagnetic (AFM) order in 2D even-layered MnBi$_2$Te$_4$, a topological Axion insulator with neither chirality nor $M$. We further demonstrate helicity-dependent optical creation of AFM domain walls by double induction beams and the direct reversal of AFM domains by ultrafast pulses. The control and reversal of AFM domains and domain walls by light helicity have never been achieved in any fully-compensated AFM. To understand this optical control, we study a novel type of circular dichroism (CD) proportional to the AFM order, which only appears in reflection but is absent in transmission. We show that the optical control and CD both arise from the optical Axion electrodynamics, which can be visualized as a Berry curvature real space dipole. Our Axion induction provides the possibility to optically control a family of $\mathcal{PT}$-symmetric AFMs such as Cr$_2$O$_3$, CrI$_3$ and possibly novel states in cuprates. In MnBi$_2$Te$_4$, this further opens the door for optical writing of dissipationless circuit formed by topological edge states.

Context. IRAS 19312+1950 is an isolated infrared source that exhibits a characteristic quasi-point-symmetric morphology in the near- and mid-infrared images and is also very bright in molecular radio lines. Because of its unique observational characteristics, various observational studies have been conducted and several hypotheses have been proposed regarding its origin, which is still unclear. So far, it has been suggested that it could be a peculiar evolved star, a young stellar object, or even a red nova remnant. Regardless of which type of object it is ultimately classified as, IRAS 19312+1950 is exceptionally bright in the infrared and molecular radio lines and therefore will undoubtedly be crucial as a prototype of this kind of object having a peculiar nature or unusual evolutionary phase. Aims. This study aims to reveal the molecular composition of the central part of IRAS 19312+1950 by performing an unbiased molecular radio line survey and discussing the origin of the object from a molecular chemical point of view. Methods. We carried out a spectral line survey with the IRAM 30 m telescope towards the center of IRAS 19312+1950 in the 3 and 1.3 mm windows. Results. In total, 28 transition lines of 22 molecular species and those isotopologues are detected towards IRAS 19312+1950, some of which exhibit a broad and a narrow components. Seventeen thermal lines and 1 maser line are newly detected. The molecular species of C$^{17}$O, $^{30}$SiO, HN$^{13}$C, HC$^{18}$O$^{+}$, H$_{2}$CO, and $c$-C$_{3}$H$_{2}$ are detected for the first time in this object. Conclusions. Our results, in combination with previous studies, favor the hypothesis that IRAS 19312+1950 might be a red nova remnant, in which the progenitors that merged to become a red nova may have contained at least two evolved stars with oxygen-rich and carbon-rich chemistry, respectively., Comment: 30 pages, 24 figures, accepted for publication in A&A

We report the current understanding of heavy quarkonium production at high transverse momentum ($p_T$) in hadronic collisions in terms of QCD factorization. In this presentation, we highlight the role of subleading power corrections to heavy quarkonium production, which are essential to describe the $p_T$ spectrum of quarkonium at a relatively lower $p_T$. We also introduce prescription to match QCD factorization to fixed-order NRQCD factorization calculations for quarkonium production at low $p_T$., Comment: 8 pages, 4 figures; talk given at the XVth Quark confinement and the Hadron spectrum conference, August 1st - 6th, 2022, University of Stavanger, Norway

Generalized parton distributions (GPDs) are important nonperturbative functions that provide tomographic images of partonic structures of hadrons. We introduce a type of exclusive processes, to be referred to as single diffractive hard exclusive processes (SDHEPs). We discuss the necessary and sufficient conditions for SDHEPs to be factorized into GPDs. We demonstrate that the SDHEP is not only sufficiently generic to cover all known processes for extracting GPDs, but is also well motivated for the search of new processes for the study of GPDs. We examine the sensitivity of the SDHEP to the parton momentum fraction $x$ dependence of GPDs., Comment: 26 pages, 26 figures. To match the journal version

We constructed a frequently updated, near-real-time global power generation dataset: Carbon Monitor-Power since January, 2016 at national levels with near-global coverage and hourly-to-daily time resolution. The data presented here are collected from 37 countries across all continents for eight source groups, including three types of fossil sources (coal, gas, and oil), nuclear energy and four groups of renewable energy sources (solar energy, wind energy, hydro energy and other renewables including biomass, geothermal, etc.). The global near-real-time power dataset shows the dynamics of the global power system, including its hourly, daily, weekly and seasonal patterns as influenced by daily periodical activities, weekends, seasonal cycles, regular and irregular events (i.e., holidays) and extreme events (i.e., the COVID-19 pandemic). The Carbon Monitor-Power dataset reveals that the COVID-19 pandemic caused strong disruptions in some countries (i.e., China and India), leading to a temporary or long-lasting shift to low carbon intensity, while it had only little impact in some other countries (i.e., Australia). This dataset offers a large range of opportunities for power-related scientific research and policy-making.

We show that exclusive production of a pair of high transverse momentum photons in pion-nucleon collisions can be systematically studied in QCD factorization approach if the photon's transverse momentum $q_T$ with respect to the colliding pion is much greater than $\Lambda_{\rm QCD}$. We demonstrate that the leading power non-perturbative contributions to the scattering amplitudes of this exclusive process are process-independent and can be systematically factorized into universal pion's distribution amplitudes (DAs) and nucleon's generalized parton distributions (GPDs), which are convoluted with corresponding infrared safe and perturbatively calculable short-distance hard parts. The correction to this factorized expression is suppressed by powers of $1/q_T$. We demonstrate quantitatively that this new type of exclusive processes is not only complementary to existing processes for extracting GPDs, but also capable of providing an enhanced sensitivity to the dependence of both DAs and GPDs on the active parton's momentum fraction $x$. We also introduce additional, but the same type of exclusive observables to enhance our capability to explore GPDs, in particular, their $x$-dependence., Comment: 60 pages, 28 figures; extended reference and some discussions, with the main results unchanged

We present observations of the carbon-rich protoplanetary nebula (PPN) CRL 2688 made with the Institut de Radioastronomie Millimetrique (IRAM) 30 m telescope in the 3mm and 2mm bands. In total, 196 transition lines belonging to 38 molecular species and isotopologues are detected, among which, to our best knowledge, 153 transition lines and 13 species are the first report for this object. Additionally, in order to contribute to future research, we have collected observational data on the molecular lines of CRL 2688 from the literature and compiled them into a single unified catalog. We find that the molecular abundance of CRL 2688 cannot be explained by the standard model of a circumstellar envelope. The implications of metal-bearing molecules on circumstellar chemistry are discussed., Comment: 55 pages, 10 figures, Accepted for publication in ApJS

We extract pion parton distribution functions (PDFs) in a Monte Carlo global QCD analysis of experimental data together with reduced Ioffe time pseudo-distributions and matrix elements of current-current correlators generated from lattice QCD. By including both experimental and lattice QCD data, our analysis rigorously quantifies both the uncertainties of the pion PDFs and systematic effects intrinsic to the lattice QCD observables. The reduced Ioffe time pseudo-distributions significantly decrease the uncertainties on the PDFs, while the current-current correlators are limited by the systematic effects associated with the lattice. Consistent with recent phenomenological determinations, the behavior of the valence quark distribution of the pion at large momentum fraction is found to be $\sim (1-x)^{ \beta_{\rm eff}}$ with $\beta_{\rm eff} \approx 1.0-1.2$., Comment: 47 pages, 15 figures

In this document, we summarize the status and challenges of calculating parton physics in lattice QCD for the US Particle Physics Community Planning Exercise (a.k.a. "Snowmass"). While PDF-moments calculations have been very successful and been continuously improved, new methods have been developed to calculate distributions directly in $x$-space. Many recent lattice studies have been focused on calculating isovector PDFs of the pion and nucleon, learning to control systematics associated with excited-state contamination, renormalization and continuum extrapolations, pion-mass and finite-volume effects, etc. Although in some cases, the lattice results are already competitive with experimental data, to reach the level of precision in a wide range of $x$ for unpolarized nucleon PDFs impactful for future collider physics remains a challenge, and may require exascale supercomputing power. The new theoretical methods open the door for calculating other partonic observables which will be the focus of the experimental program in nuclear physics, including generalized parton distributions and transverse-momentum dependent PDFs. A fruitful interplay between experimental data and lattice-QCD calculations will usher in a new era for parton physics and hadron structure., Comment: 14 pages

We discuss the diagonalization problem of the Nijenhuis tensor in a class of Poisson-Nijenhuis structures defined on compact hermitian symmetric spaces. We study its action on the ring of invariant polynomials of a Thimm chain of subalgebras. The existence of $\phi$-minimal representations defines a suitable basis of invariant polynomials that completely solves the diagonalization problem. We prove that such representations exist in the classical cases AIII, BDI, DIII and CI, and do not exist in the exceptional cases EIII and EVII. We discuss a second general construction that in these two cases computes partially the spectrum and hints at a different behavior with respect to the classical cases., Comment: 27 pages, 1 figure, 18 references

Single-table text-to-SQL aims to transform a natural language question into a SQL query according to one single table. Recent work has made promising progress on this task by pre-trained language models and a multi-submodule framework. However, zero-shot table, that is, the invisible table in the training set, is currently the most critical bottleneck restricting the application of existing approaches to real-world scenarios. Although some work has utilized auxiliary tasks to help handle zero-shot tables, expensive extra manual annotation limits their practicality. In this paper, we propose a new approach for the zero-shot text-to-SQL task which does not rely on any additional manual annotations. Our approach consists of two parts. First, we propose a new model that leverages the abundant information of table content to help establish the mapping between questions and zero-shot tables. Further, we propose a simple but efficient meta-learning strategy to train our model. The strategy utilizes the two-step gradient update to force the model to learn a generalization ability towards zero-shot tables. We conduct extensive experiments on a public open-domain text-to-SQL dataset WikiSQL and a domain-specific dataset ESQL. Compared to existing approaches using the same pre-trained model, our approach achieves significant improvements on both datasets. Compared to the larger pre-trained model and the tabular-specific pre-trained model, our approach is still competitive. More importantly, on the zero-shot subsets of both the datasets, our approach further increases the improvements., Comment: Accepted to AAAI 2021

We present the details of a new factorized approach to semi-inclusive deep-inelastic scattering which treats QED and QCD radiation on equal footing, and provides a systematically improvable approximation to the extraction of transverse momentum dependent parton distributions. We demonstrate how the QED contributions can be well approximated by collinear factorization, and illustrate the application of the factorized approach to QED radiation in inclusive scattering. For semi-inclusive processes, we show how radiation effects prevent a well-defined "photon-nucleon" frame, forcing one to use a two-step process to account for the radiation. We illustrate the utility of the new method by explicit application to the spin-dependent Sivers and Collins asymmetries., Comment: 55 pages, 23 figures, accepted for publication in J. High Energy Phys

Heavy quarkonium production at high transverse momentum ($p_T$) in hadronic collisions is explored in the QCD factorization approach. We find that the leading power in the $1/p_T$ expansion is responsible for high $p_T$ regime, while the next-to-leading power contribution is necessary for the low $p_T$ region. We present the first numerical analysis of the scale evolution of coupled twist-2 and twist-4 fragmentation functions (FFs) for heavy quarkonium production and demonstrate that the QCD factorization approach is capable of describing the $p_T$ spectrum of hadronic $J/\psi$ production at the LHC., Comment: 7 pages, 3 figures. Contribution to the XXVIII International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2021). SciPost Proceedings

While ferromagnets have been known and exploited for millennia, antiferromagnets (AFMs) were only discovered in the 1930s. The elusive nature indicates AFMs' unique properties: At large scale, due to the absence of global magnetization, AFMs may appear to behave like any non-magnetic material; However, such a seemingly mundane macroscopic magnetic property is highly nontrivial at microscopic level, where opposite spin alignment within the AFM unit cell forms a rich internal structure. In topological AFMs, such an internal structure leads to a new possibility, where topology and Berry phase can acquire distinct spatial textures. Here, we study this exciting possibility in an AFM Axion insulator, even-layered MnBi$_2$Te$_4$ flakes, where spatial degrees of freedom correspond to different layers. Remarkably, we report the observation of a new type of Hall effect, the layer Hall effect, where electrons from the top and bottom layers spontaneously deflect in opposite directions. Specifically, under no net electric field, even-layered MnBi$_2$Te$_4$ shows no anomalous Hall effect (AHE); However, applying an electric field isolates the response from one layer and leads to the surprising emergence of a large layer-polarized AHE (~50%$\frac{e^2}{h}$). Such a layer Hall effect uncovers a highly rare layer-locked Berry curvature, which serves as a unique character of the space-time $\mathcal{PT}$-symmetric AFM topological insulator state. Moreover, we found that the layer-locked Berry curvature can be manipulated by the Axion field, E$\cdot$B, which drives the system between the opposite AFM states. Our results achieve previously unavailable pathways to detect and manipulate the rich internal spatial structure of fully-compensated topological AFMs. The layer-locked Berry curvature represents a first step towards spatial engineering of Berry phase, such as through layer-specific moir\'e potential., Comment: A revised version of this article is published in Nature