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We investigate the anisotropic effect of magnetization plateaus in the antiferromagnetic Heisenberg model on a kagome strip chain. The kagome strip chain Heisenberg model, composed of a hexagonal net of triangles forming five-site unit cells, exhibits four magnetization plateaus in the presence of an applied magnetic field. Using numerical density matrix renormalization group method, we find that the magnetization plateaus are stable against anisotropic interactions in the same direction of the applied magnetic field but the plateaus vanish with strong anisotropic interactions in other directions. We further analyze the stability of the magnetic plateaus with spin wave theory. The emergence of the lowest flat magnon band and its evolution with the anisotropic interactions can explain the robustness of magnetization plateaus, which is consistent with our numerical findings. In addition, upon tuning down the interaction strength for the two lower legs below a critical value, the kagome strip chain decouples into two spin chains, which can be used to determine the effective lattice structure in materials with strong distortions. Our results enhance the theoretical understanding of the anisotropic effect and the nature of magnetization plateaus in frustrated kagome lattice materials, which can contribute to the design and manipulation of kagome materials with tailored properties., Comment: 8 pages, 7 figures

Let $G$ be a graph (with multiple edges allowed) and let $T$ be a tree in $G$. We say that $T$ is $\textit{even}$ if every leaf of $T$ belongs to the same part of the bipartition of $T$, and that $T$ is $\textit{weakly even}$ if every leaf of $T$ that has maximum degree in $G$ belongs to the same part of the bipartition of $T$. We confirm two recent conjectures of Jackson and Yoshimoto by showing that every connected graph that is not a regular bipartite graph has a spanning weakly even tree., Comment: 6 pages. This article represents a merger of arXiv:2409.15522v1 and arxiv:2408.07056

We present Points2Plans, a framework for composable planning with a relational dynamics model that enables robots to solve long-horizon manipulation tasks from partial-view point clouds. Given a language instruction and a point cloud of the scene, our framework initiates a hierarchical planning procedure, whereby a language model generates a high-level plan and a sampling-based planner produces constraint-satisfying continuous parameters for manipulation primitives sequenced according to the high-level plan. Key to our approach is the use of a relational dynamics model as a unifying interface between the continuous and symbolic representations of states and actions, thus facilitating language-driven planning from high-dimensional perceptual input such as point clouds. Whereas previous relational dynamics models require training on datasets of multi-step manipulation scenarios that align with the intended test scenarios, Points2Plans uses only single-step simulated training data while generalizing zero-shot to a variable number of steps during real-world evaluations. We evaluate our approach on tasks involving geometric reasoning, multi-object interactions, and occluded object reasoning in both simulated and real-world settings. Results demonstrate that Points2Plans offers strong generalization to unseen long-horizon tasks in the real world, where it solves over 85% of evaluated tasks while the next best baseline solves only 50%. Qualitative demonstrations of our approach operating on a mobile manipulator platform are made available at sites.google.com/stanford.edu/points2plans., Comment: Under review

Integrated sensing and communication (ISAC) is a main application scenario of the sixth-generation mobile communication systems. Due to the fast-growing number of antennas and subcarriers in cellular systems, the computational complexity of joint azimuth-range-velocity estimation (JARVE) in ISAC systems is extremely high. This paper studies the JARVE problem for a monostatic ISAC system with orthogonal frequency division multiplexing (OFDM) waveform, in which a base station receives the echos of its transmitted cellular OFDM signals to sense multiple targets. The Cramer-Rao bounds are first derived for JARVE. A low-complexity algorithm is further designed for super-resolution JARVE, which utilizes the proposed iterative subspace update scheme and Levenberg-Marquardt optimization method to replace the exhaustive search of spatial spectrum in multiple-signal-classification (MUSIC) algorithm. Finally, with the practical parameters of 5G New Radio, simulation results verify that the proposed algorithm can reduce the computational complexity by three orders of magnitude and two orders of magnitude compared to the existing three-dimensional MUSIC algorithm and estimation-of-signal-parameters-using-rotational-invariance-techniques (ESPRIT) algorithm, respectively, and also improve the estimation performance., Comment: 16 pages, 12 figures, submitted to IEEE journal

Radio imaging is rapidly gaining prominence in the design of future communication systems, with the potential to utilize reconfigurable intelligent surfaces (RISs) as imaging apertures. Although the sparsity of targets in three-dimensional (3D) space has led most research to adopt compressed sensing (CS)-based imaging algorithms, these often require substantial computational and memory burdens. Drawing inspiration from conventional Fourier transform (FT)-based imaging methods, our research seeks to accelerate radio imaging in RIS-aided communication systems. To begin, we introduce a two-stage wavenumber domain 3D imaging technique: first, we modify RIS phase shifts to recover the equivalent channel response from the user equipment to the RIS array, subsequently employing traditional FT-based wavenumber domain methods to produce target images. We also determine the diffraction resolution limits of the system through k-space analysis, taking into account factors including system bandwidth, transmission direction, operating frequency, and the angle subtended by the RIS. Addressing the challenge of limited pilots in communication systems, we unveil an innovative algorithm that merges the strengths of both FT- and CS-based techniques by substituting the expansive sensing matrix with FT-based operators. Our simulation outcomes confirm that our proposed FT-based methods achieve high-quality images while demanding few time, memory, and communication resources., Comment: 16 pages, 11 figures, submitted to IEEE for possible publication

Retrieving range information in three-dimensional (3D) radio imaging is particularly challenging due to the limited communication bandwidth and pilot resources. To address this issue, we consider a reconfigurable intelligent surface (RIS)-aided uplink communication scenario, generating multiple measurements through RIS phase adjustment. This study successfully realizes 3D single-frequency imaging by exploiting the near-field multi-view image correlations deduced from user mobility. We first highlight the significance of considering anisotropy in multi-view image formation by investigating radar cross-section properties and diffraction resolution limits. We then propose a novel model for joint multi-view 3D imaging that incorporates occlusion effects and anisotropic scattering. These factors lead to slow image support variation and smooth coefficient evolution, which are mathematically modeled as Markov processes. Based on this model, we employ the Expectation Maximization-Turbo-Generalized Approximate Message Passing algorithm for joint multi-view single-frequency 3D imaging with limited measurements. Simulation results reveal the superiority of joint multi-view imaging in terms of enhanced imaging ranges, accuracies, and anisotropy characterization compared to single-view imaging. Combining adjacent observations for joint multi-view imaging enables a reduction in the measurement overhead by 80%., Comment: 16 pages, 12 figures, accepted by IEEE Transactions on Communications

We study the spin-$1/2$ Heisenberg model on the square lattice with the first and second nearest-neighbor antiferromagnetic couplings $J_1$, $J_2$, as well as the three-spin scalar chiral coupling $J_{\chi}$. Using density matrix renormalization group calculations, we obtain a quantum phase diagram of this system for $0 \leq J_2/J_1 \leq 1.0$ and $0 \leq J_{\chi}/J_1 \leq 1.5$. We identify the N\'eel and stripe magnetic order phase at small $J_{\chi}$ coupling. With growing $J_{\chi}$, we identify the emergent chiral spin liquid (CSL) phase characterized by the quantized spin Chern number $C = 1/2$ and entanglement spectrum with the quasidegenerate group of levels agreeing with chiral SU(2)$_1$ conformal field theory, which is an analog of the $\nu = 1/2$ Laughlin state in spin system. In the vicinity of the N\'eel and CSL phase boundary, our numerical results do not find evidence to support the phase coexistence of N\'eel order and topological order that was conjectured by mean-field calculations. In the larger $J_2$ and $J_{\chi}$ coupling regime, the entanglement spectrum of the ground state also exhibits the chiral quasidegeneracy consistent with a CSL, but the adiabatic flux insertion simulations fail to obtain the quantized Chern number. By analyzing the finite-size scaling of magnetic order parameter, we find the vanished magnetic order suggesting a magnetic disorder phase, whose nature needs further studies. Different from the spin-$1$ $J_1$-$J_2$-$J_\chi$ model, we do not find the coexistent stripe magnetic order and topological order. We also investigate the $J_{\chi}$ dominant regime and find a strong tendency of the system to develop a dimer order rather than the chiral spin magnetic order observed in the spin-$1$ model., Comment: 16 pages, 17 figures

A recent study has demonstrated that a fermionic two-leg ladder model, threaded by a flux and characterized by a spatially varying interleg hopping term, gives rise to a quasiflat low-energy band. This band exhibits an unusual ground state at half filling in the presence of interaction -- a ferromagnetic Mott insulator. In this paper, we extend the study of this model to other fillings of the quasiflat band and explore the magnetic properties of the ground state at these fillings. In particular, we study four fillings: one-quarter, three-quarters, slightly above half filling (half filling plus two electrons), and slightly below half-filling (half filling minus two electrons). Incorporating interaction within the Hubbard model and using the Density Matrix Renormalization Group method to find the ground states, we find that the spin-spin correlation is ferromagnetic at fillings less than half, similar to that observed at half filling, but is antiferromagnetic beyond half filling. Interestingly, these results hold only when mixing between the lowest quasiflat band and the next-to-lowest dispersive band is negligible; once mixing between the two bands is facilitated by increasing the interaction strength, the correlation becomes ferromagnetic above half filling as well. Additionally, by reducing the strength of the interaction in comparison to the bandwidth, a transition from the ferromagnetic to the antiferromagnetic state is observed in all the cases.

Orthogonal frequency division multiplexing (OFDM)-based integrated sensing and communication (ISAC) is promising for future sixth-generation mobile communication systems. Existing works focus on the joint estimation of the targets' range and velocity for OFDM-based ISAC systems. In contrast, this paper studies the three-dimensional joint estimation (3DJE) of range, velocity, and azimuth for OFDM-based ISAC systems with multiple receive antennas. First, we establish the signal model and derive the Cramer-Rao bounds (CRBs) on the 3DJE. Furthermore, an auto-paired super-resolution 3DJE algorithm is proposed by exploiting the reconstructed observation sub-signal's translational invariance property in the time, frequency, and space domains. Finally, with the 5G New Radio parameter setup, simulation results show that the proposed algorithm achieves better estimation performance and its root mean square error is closer to the root of CRBs than existing methods., Comment: This manuscript has been submitted to the IEEE journal in 09-Aug-2023

We prove that the native space of a Wu function is a dense subspace of a Sobolev space. An explicit characterization of the native spaces of Wu functions is given. Three definitions of Wu functions are introduced and proven to be equivalent. Based on these new equivalent definitions and the so called $f$-form tricks, we can generalize the Wu functions into the even-dimensional spaces $\R^{2k}$, while the original Wu functions are only defined in the odd-dimensional spaces $\R^{2k+1}$. Such functions in even-dimensional spaces are referred to as the `missing Wu functions'. Furthermore we can generalize the Wu functions into `fractional'-dimensional spaces. We call all these Wu functions the generalized Wu functions. The closed form of the generalized Wu functions are given in terms of hypergeometric functions. Finally we prove that the Wu functions and the missing Wu functions can be written as linear combinations of the generalized Wendland functions.

Robots need to have a memory of previously observed, but currently occluded objects to work reliably in realistic environments. We investigate the problem of encoding object-oriented memory into a multi-object manipulation reasoning and planning framework. We propose DOOM and LOOM, which leverage transformer relational dynamics to encode the history of trajectories given partial-view point clouds and an object discovery and tracking engine. Our approaches can perform multiple challenging tasks including reasoning with occluded objects, novel objects appearance, and object reappearance. Throughout our extensive simulation and real-world experiments, we find that our approaches perform well in terms of different numbers of objects and different numbers of distractor actions. Furthermore, we show our approaches outperform an implicit memory baseline., Comment: Presented at IEEE Conference on Robotics and Automation (ICRA) 2024. Website: https://sites.google.com/view/rdmemory

We present a theory describing the single-ion anisotropy of rare earth (RE) magnets in the presence of point defects. Taking the RE-lean 1:12 magnet class as a prototype, we use first-principles calculations to show how the introduction of Ti substitutions into SmFe$_{12}$ perturbs the crystal field, generating new coefficients due to the lower symmetry of the RE environment. We then demonstrate that these perturbations can be described extremely efficiently using a screened point charge model. We provide analytical expressions for the anisotropy energy which can be straightforwardly implemented in atomistic spin dynamics simulations, meaning that such simulations can be carried out for an arbitrary arrangement of point defects. The significant crystal field perturbations calculated here demonstrate that a sample which is single-phase from a structural point of view can nonetheless have a dramatically varying anisotropy profile at the atomistic level if there is compositional disorder, which may influence localized magnetic objects like domain walls or skyrmions., Comment: 14 pages, 3 figures

Variance reduction is a crucial idea for Monte Carlo simulation and the stochastic Lanczos quadrature method is a dedicated method to approximate the trace of a matrix function. Inspired by their advantages, we combine these two techniques to approximate the log-determinant of large-scale symmetric positive definite matrices. Key questions to be answered for such a method are how to construct or choose an appropriate projection subspace and derive guaranteed theoretical analysis. This paper applies some probabilistic approaches including the projection-cost-preserving sketch and matrix concentration inequalities to construct a suboptimal subspace. Furthermore, we provide some insights on choosing design parameters in the underlying algorithm by deriving corresponding approximation error and probabilistic error estimations. Numerical experiments demonstrate our method's effectiveness and illustrate the quality of the derived error bounds.

The stochastic Lanczos quadrature method has garnered significant attention recently. Upon examination of the error analyses given by Ubaru, Chen and Saad and Cortinovis and Kressner, certain notable inconsistencies arise. It turns out that the former's results are valid for cases with symmetric quadrature nodes and may not be adequate for many practical cases such as estimating log determinant of matrices. This paper analyzes probabilistic error bound of the stochastic Lanczos quadrature method for cases with asymmetric quadrature nodes. Besides, an optimized error allocation technique is employed to minimize the overall number of matrix vector multiplications required by the stochastic Lanczos quadrature method., Comment: 20 pages, 3 figures

As one of the most intriguing states of matter, the chiral spin liquid (CSL) has attracted much scientific interest while its existence and mechanism in crystalline strongly correlated systems remain hotly debated. On the other hand, strong correlation driven emergent phenomena can be realized in twisted transition metal dichalcogenide bilayers with a tremendously tunable large length scale providing a new platform for the emergence of CSLs. We focus on a strongly correlated model relevant to heterobilayer $\textrm{WSe}_{2}/\textrm{MoSe}_{2}$ and investigate the Mott insulating phase at half filling under an out-of-plane magnetic field. Considering both its orbital and spin Zeeman effects we identify three conventionally ordered phases including a $120^{\circ}$ N\'{e}el phase, a stripe phase, and an up-up-down phase. For intermediate fields an emergent quantum spin liquid phase is identified with partial spin polarization. We further characterize its topological nature as the $\nu$ = 1/2 Laughlin CSL through the topological entanglement spectrum and quantized spin pumping under spin flux insertion. In addition, we map out the quantum phase diagram for different twisted angles in an experimentally accessible parameter regime., Comment: 7+9 pages, 5+14 figures

This study explores the use of non-line-of-sight (NLOS) components in millimeter-wave (mmWave) communication systems for joint localization and environment sensing. The radar cross section (RCS) of a reconfigurable intelligent surface (RIS) is calculated to develop a general path gain model for RISs and traditional scatterers. The results show that RISs have a greater potential to assist in localization due to their ability to maintain high RCSs and create strong NLOS links. A one-stage linear weighted least squares estimator is proposed to simultaneously determine user equipment (UE) locations, velocities, and scatterer (or RIS) locations using line-of-sight (LOS) and NLOS paths. The estimator supports environment sensing and UE localization even using only NLOS paths. A second-stage estimator is also introduced to improve environment sensing accuracy by considering the nonlinear relationship between UE and scatterer locations. Simulation results demonstrate the effectiveness of the proposed estimators in rich scattering environments and the benefits of using NLOS paths for improving UE location accuracy and assisting in environment sensing. The effects of RIS number, size, and deployment on localization performance are also analyzed., Comment: 32 pages, 12 figures, accepted by IEEE Transactions on Wireless Communications

Objects rarely sit in isolation in everyday human environments. If we want robots to operate and perform tasks in our human environments, they must understand how the objects they manipulate will interact with structural elements of the environment for all but the simplest of tasks. As such, we'd like our robots to reason about how multiple objects and environmental elements relate to one another and how those relations may change as the robot interacts with the world. We examine the problem of predicting inter-object and object-environment relations between previously unseen objects and novel environments purely from partial-view point clouds. Our approach enables robots to plan and execute sequences to complete multi-object manipulation tasks defined from logical relations. This removes the burden of providing explicit, continuous object states as goals to the robot. We explore several different neural network architectures for this task. We find the best performing model to be a novel transformer-based neural network that both predicts object-environment relations and learns a latent-space dynamics function. We achieve reliable sim-to-real transfer without any fine-tuning. Our experiments show that our model understands how changes in observed environmental geometry relate to semantic relations between objects. We show more videos on our website: https://sites.google.com/view/erelationaldynamics., Comment: Accepted at IEEE Transactions on Robotics (T-RO). arXiv admin note: text overlap with arXiv:2209.11943

We predict the magnetic and electronic properties of a novel metal-organic framework. By combining density functional theory and density matrix renormalization group approaches, we find the diatomic Kagome crystal structure of the metal-semiquinoid framework (H$_2$NMe$_2$)$_2$M$_2$(Cl$_2$dhbq)$_3$ (M = Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) to host a rich variety of antiferromagnetic (AFM) and ferromagnetic (FM) Dirac semimetallic, spin-polarized Dirac fermions, and flat band magnetic insulators and metallic phases. Concomitantly, the spin excitation spectrum of the various magnetic systems display multiple Dirac-like and nodal-ring crossings. This suggests that the metal-semiquinoid system is an ideal platform for examining the intertwining of Dirac fermions and magnons., Comment: main text: 7 pages, 3 figures; SI: 4 pages, 2 figures

Since strong quantum fluctuations are essential for the emergence of quantum spin liquids, there have been extensive exploration and identification of spin liquid candidates in spin-$1/2$ systems, while such activities are rare in higher spin systems. Here we report an example of non-Abelian chiral spin liquid emerging in spin-$3/2$ Heisenberg model on a square lattice. By tuning Heisenberg exchange interaction and scalar chirality interaction, we map out a quantum phase diagram enclosing three conventional magnetic orders and a chiral spin liquid based on density matrix renormalization group studies. The nature of the spin liquid is identified as a long-sought bosonic version of Read-Rezayi state that supports non-Abelian Fibonacci anyonic statistics, identified by the ground state entanglement spectrum. Significantly, we establish that the non-Abelian CSL emerges through the enlarged local degrees of freedom and enhanced quantum fluctuations near the classical phase boundaries of competing magnetic orders. Our numerical discovery of an exotic quantum spin liquid in spin-$3/2$ system suggests a new route for discovering fractionalized quantum phases in frustrated higher spin magnetic compounds., Comment: LA-UR-22-33202

Objects rarely sit in isolation in human environments. As such, we'd like our robots to reason about how multiple objects relate to one another and how those relations may change as the robot interacts with the world. To this end, we propose a novel graph neural network framework for multi-object manipulation to predict how inter-object relations change given robot actions. Our model operates on partial-view point clouds and can reason about multiple objects dynamically interacting during the manipulation. By learning a dynamics model in a learned latent graph embedding space, our model enables multi-step planning to reach target goal relations. We show our model trained purely in simulation transfers well to the real world. Our planner enables the robot to rearrange a variable number of objects with a range of shapes and sizes using both push and pick and place skills., Comment: 10 pages, 7 figures, to be published in the proceedings of the IEEE Conference on Robotics and Automation (ICRA) 2023. Robot Demos: https://robot-learning.cs.utah.edu/project/graph_nets

The topological superconducting state is a highly sought-after quantum state hosting topological order and Majorana excitations. In this work, we explore the mechanism to realize the topological superconductivity (TSC) in the doped Mott insulators with time-reversal symmetry (TRS). Through large-scale density matrix renormalization group study of an extended triangular-lattice $t$-$J$ model on the six- and eight-leg cylinders, we identify a $d+id$-wave chiral TSC with spontaneous TRS breaking, which is characterized by a Chern number $C=2$ and quasi-long-range superconducting order. We map out the quantum phase diagram by tuning the next-nearest-neighbor (NNN) electron hopping and spin interaction. In the weaker NNN-coupling regime, we identify a pseudogaplike phase with a charge stripe order coexisting with fluctuating superconductivity, which can be tuned into $d$-wave superconductivity by increasing the doping level and system width. The TSC emerges in the intermediate-coupling regime, which has a transition to a $d$-wave superconducting phase with larger NNN couplings. The emergence of the TSC is driven by geometrical frustrations and hole dynamics which suppress spin correlation and charge order, leading to a topological quantum phase transition., Comment: 6+12 pages, 5+11 figures

The mechanism of the unconventional topological superconductivity (TSC) remains a long-standing issue. We investigate the quantum phase diagram of the extended $t$-$J$-$J_{\chi}$ model including spin chiral interactions on triangular lattice based on the state-of-the-art density matrix renormalization group simulations. We identify distinct classes of superconducting phases characterized by nonzero topological Chern numbers $C=1$ and $2$, and a nematic d-wave superconducting phase with a zero Chern number. The TSC states are shown to emerge from doping either a magnetic insulator or chiral spin liquid, which opens new opportunities for experimental discovery. In addition, we further classify the $C=2$ class of TSC phases into an isotropic and a nematic TSC phases, and present evidence of continuous quantum phase transitions from the nematic TSC phase to both isotropic TSC and nematic d-wave phases. These results provide new insight into the mechanism of TSC with an emphasis on the role played by hole dynamics, which changes spin background and drives a topological phase transition at a hole doping level around $3\%$ upon doping a magnetic insulator to enable the emergence of the TSC., Comment: 11+16 pages, 7+16 figures

Tendon-driven robots, a type of continuum robot, have the potential to reduce the invasiveness of surgery by enabling access to difficult-to-reach anatomical targets. In the future, the automation of surgical tasks for these robots may help reduce surgeon strain in the face of a rapidly growing population. However, directly encoding surgical tasks and their associated context for these robots is infeasible. In this work we take steps toward a system that is able to learn to successfully perform context-dependent surgical tasks by learning directly from a set of expert demonstrations. We present three models trained on the demonstrations conditioned on a vector encoding the context of the demonstration. We then use these models to plan and execute motions for the tendon-driven robot similar to the demonstrations for novel context not seen in the training set. We demonstrate the efficacy of our method on three surgery-inspired tasks., Comment: 7 pages, 6 figures, to be published in the proceedings of the 2021 International Symposium on Medical Robotics (ISMR)

We study the ground-state properties of a spin-1 Heisenberg model on a square lattice with the first- and second-nearest-neighbor antiferromagnetic couplings $J_1$ and $J_2$ and a three-spin scalar chirality term $J_\chi$. Using the density matrix renormalization group calculation, we map out a global phase diagram including various magnetic order phases and an emergent quantum spin liquid phase. The nature of the spin liquid is identified as a bosonic non-Abelian Moore-Read state from the fingerprint of the entanglement spectra and identification of a full set of topological sectors. We further unveil a stripe magnetic order coexisting with this spin liquid. Our results not only establish a rare example of non-Abelian spin liquids in simple spin systems but also demonstrate the coexistence of fractionalized excitations and magnetic order beyond mean-field descriptions., Comment: 5+6 pages, 6+9 figures