arXiv subjects

Shang Liu

Publications and source records attributed to Shang Liu.

At least 91 records · Page 5Linked to original sources

arXiv2022

Non-stationary Bandits with Knapsacks

In this paper, we study the problem of bandits with knapsacks (BwK) in a non-stationary environment. The BwK problem generalizes the multi-arm bandit (MAB) problem to model the resource consumption associated with playing each arm. At each time, the decision maker/player chooses to play an arm, and s/he will receive a reward and consume certain amount of resource from each of the multiple resource types. The objective is to maximize the cumulative reward over a finite horizon subject to some knapsack constraints on the resources. Existing works study the BwK problem under either a stochastic or adversarial environment. Our paper considers a non-stationary environment which continuously interpolates between these two extremes. We first show that the traditional notion of variation budget is insufficient to characterize the non-stationarity of the BwK problem for a sublinear regret due to the presence of the constraints, and then we propose a new notion of global non-stationarity measure. We employ both non-stationarity measures to derive upper and lower bounds for the problem. Our results are based on a primal-dual analysis of the underlying linear programs and highlight the interplay between the constraints and the non-stationarity. Finally, we also extend the non-stationarity measure to the problem of online convex optimization with constraints and obtain new regret bounds accordingly.

cs.LG↗

arXiv2022

Observation of entanglement negativity transition of pseudo-random mixed states

Multipartite entanglement is a key resource for quantum computation. It is expected theoretically that entanglement transition may happen for multipartite random quantum states, however, which is still absent experimentally. Here, we report the observation of entanglement transition quantified by negativity using a fully connected 20-qubit superconducting processor. We implement multi-layer pseudo-random circuits to generate pseudo-random pure states of 7 to 15 qubits. Then, we investigate negativity spectra of reduced density matrices obtained by quantum state tomography for 6 qubits.Three different phases can be identified by calculating logarithmic negativities based on the negativity spectra. We observe the phase transitions by changing the sizes of environment and subsystems. The randomness of our circuits can be also characterized by quantifying the distance between the distribution of output bit-string probabilities and Porter-Thomas distribution. Our simulator provides a powerful tool to generate random states and understand the entanglement structure for multipartite quantum systems.

quant-ph↗

arXiv2022

Center-of-Mass-based Robust Grasp Pose Adaptation Using RGBD Camera and Force/Torque Sensing

Object dropping may occur when the robotic arm grasps objects with uneven mass distribution due to additional moments generated by objects' gravity. To solve this problem, we present a novel work that does not require extra wrist and tactile sensors and large amounts of experiments for learning. First, we obtain the center-of-mass position of the rod object using the widely fixed joint torque sensors on the robot arm and RGBD camera. Further, we give the strategy of grasping to improve grasp stability. Simulation experiments are performed in "Mujoco". Results demonstrate that our work is effective in enhancing grasping robustness.

cs.RO↗

arXiv2022

Tunable Confinement-Deconfinement Transition in an Ultracold Atom Quantum Simulator

The one-dimensional lattice Schwinger model has recently been realized by using bosons in optical lattices. This model contains both confinement and deconfinement phases, whose phase diagram is controlled by the mass of the matter field and the topological angle. Since varying the mass of matter field is straightforward experimentally, we propose how to tune the topological angle, allowing accessing the entire phase diagram. We propose that direct experimental evidence of confinement and deconfinement can be obtained by measuring whether a physical charge is localized around a fixed gauge charge to screen it. We also discuss the PXP model realized in the Rydberg atoms array, which is equivalent to the lattice Schwinger model when all local gauge charges are fixed as zero. Although the gauge charges are fixed, we can alternatively probe the confinement and the deconfinement in the PXP model by studying the relative motion of a pair of a physical charge and an anti-charge. Our scheme can be directly implemented in these two relevant experimental platforms of ultracold atom quantum simulators.

cond-mat.quant-gas↗

arXiv2022

3D Nanoscale Mapping of Short-Range Order in GeSn Alloys

GeSn on Si has attracted much research interest due to its tunable direct bandgap for mid-infrared applications. Recently, short-range order (SRO) in GeSn alloys has been theoretically predicted, which profoundly impacts the band structure. However, characterizing SRO in GeSn is challenging. Guided by physics-informed Poisson statistical analyses of Kth-nearest neighbors (KNN) in atom probe tomography, a new approach is demonstrated here for 3D nanoscale SRO mapping and semi-quantitative strain mapping in GeSn. For GeSn with ~14 at.% Sn, the SRO parameters of Sn-Sn 1NN in 10x10x10 nm$^{3}$ nanocubes can deviate from that of the random alloys by $\pm$15%. The relatively large fluctuation of the SRO parameters contributes to band-edge softening observed optically. Sn-Sn 1NN also tends to be more favored towards the surface, less favored under strain relaxation or tensile strain, while almost independent of local Sn composition. An algorithm based on least square fit of atomic positions further verifies this Poisson-KNN statistical method. Compared to existing macroscopic spectroscopy or electron microscopy techniques, this new APT statistical analysis uniquely offers 3D SRO mapping at nanoscale resolution in a relatively large volume with millions of atoms. It can also be extended to investigate SRO in other alloy systems.

cond-mat.mtrl-sci↗

arXiv2022

Points-of-Interest Relationship Inference with Spatial-enriched Graph Neural Networks

As a fundamental component in location-based services, inferring the relationship between points-of-interests (POIs) is very critical for service providers to offer good user experience to business owners and customers. Most of the existing methods for relationship inference are not targeted at POI, thus failing to capture unique spatial characteristics that have huge effects on POI relationships. In this work we propose PRIM to tackle POI relationship inference for multiple relation types. PRIM features four novel components, including a weighted relational graph neural network, category taxonomy integration, a self-attentive spatial context extractor, and a distance-specific scoring function. Extensive experiments on two real-world datasets show that PRIM achieves the best results compared to state-of-the-art baselines and it is robust against data sparsity and is applicable to unseen cases in practice.

cs.AI↗

arXiv2021

Online Bin Packing with Known T

In the online bin packing problem, a sequence of items is revealed one at a time, and each item must be packed into an available bin instantly upon its arrival. In this paper, we revisit the problem under a setting where the total number of items T is known in advance, also known as the closed online bin packing problem. Specifically, we study both the stochastic model and the random permutation model. We develop and analyze an adaptive algorithm that solves an offline bin packing problem at geometric time intervals and uses the offline optimal solution to guide online packing decisions. Under both models, we show that the algorithm achieves C\sqrt{T} regret (in terms of the number of used bins) compared to the hindsight optimal solution, where C is a universal constant (<= 13) that bears no dependence on the underlying distribution or the item sizes. The result shows the lower bound barrier of Ω(\sqrt{T \log T}) in Shor (1986) can be broken with solely the knowledge of the horizon T, but without a need of knowing the underlying distribution. As to the algorithm analysis, we develop a new approach to analyzing the packing dynamic using the notion of exchangeable random variables. The approach creates a symmetrization between the offline solution and the online solution, and it is used to analyze both the algorithm performance and various benchmarks related to the bin packing problem. For the latter one, our analysis provides an alternative (probably simpler) treatment and tightens the analysis of the asymptotic benchmark of the stochastic bin packing problem in Rhee and Talagrand (1989a,b). As the analysis only relies on a symmetry between the offline and online problems, the algorithm and benchmark analyses can be naturally extended from the stochastic model to the random permutation model.

cs.DS↗

arXiv2021

Magnetic impurities at quantum critical points: large-$N$ expansion and SPT connections

In symmetry protected topological (SPT) phases, the combination of symmetries and a bulk gap stabilizes protected modes at surfaces or at topological defects. Understanding the fate of these modes at a quantum critical point, when the protecting symmetries are on the verge of being broken, is an outstanding problem. This interplay of topology and criticality must incorporate both the bulk dynamics of critical points, often described by nontrivial conformal field theories, and SPT physics. Here, we study the simplest nontrivial setting - that of a 0+1 dimensional topological mode - a quantum spin - coupled to a 2+1D critical bulk. Using the large-$N$ technique we solve a series of models which, as a consequence of topology, demonstrate intermediate coupling fixed points. We compare our results to previous numerical simulations and find good agreement. We also point out intriguing connections to generalized Kondo problems and Sachdev-Ye-Kitaev (SYK) models. In particular, we show that a Luttinger theorem derived for the complex SYK models, that relates the charge density to particle-hole asymmetry, also holds in our setting. These results should help stimulate further analytical study of the interplay between SPT physics and quantum criticality.

cond-mat.str-el↗

arXiv2021

Pascal's Triangle Fractal Symmetries

We introduce a model of interacting bosons exhibiting an infinite collection of fractal symmetries -- termed "Pascal's triangle symmetries" -- which provides a natural $U(1)$ generalization of a spin-(1/2) system with Sierpinski triangle fractal symmetries. The Pascal's triangle symmetry gives rise to exact degeneracies, as well as a manifold of low-energy states which are absent in the Sierpinski triangle model. Breaking the $U(1)$ symmetry of this model to $Z_p$, with prime integer $p$, yields a lattice model with a unique fractal symmetry which is generated by an operator supported on a fractal subsystem with Hausdorff dimension $d_H = \ln (p(p+1)/2)/\ln p$. The Hausdorff dimension of the fractal can be probed through correlation functions at finite temperature. The phase diagram of these models at zero temperature in the presence of quantum fluctuations, as well as the potential physical construction of the $U(1)$ model are discussed.

cond-mat.str-el↗

arXiv2021

Nematic topological semimetal and insulator in magic angle bilayer graphene at charge neutrality

We report on a fully self-consistent Hartree-Fock calculation of interaction effects on the Moiré flat bands of twisted bilayer graphene, assuming that valley U(1) symmetry is respected. We use realistic band structures and interactions and focus on the charge neutrality point, where experiments have variously reported either insulating or semimetallic behavior. Restricting the search to orders for which the valley U(1) symmetry remains unbroken, we find three types of self-consistent solutions with competitive ground state energy (i) insulators that break $C_2 {\mathcal T}$ symmetry, including valley Chern insulators (ii) spin or valley polarized insulators and (iii) rotation $C_3$ symmetry breaking semimetals whose gaplessness is protected by the topology of the Moiré flat bands. We find that the relative stability of these states can be tuned by weak strains that break $C_3$ rotation. The nematic semimetal and also, somewhat unexpectedly, the $C_2 {\mathcal T}$ breaking insulators, are stabilized by weak strain. These ground states may be related to the semi-metallic and insulating behaviors seen at charge neutrality, and the sample variability of their observation. We also compare with the results of STM measurements near charge neutrality.

cond-mat.str-el↗

arXiv2021

LUAI Challenge 2021 on Learning to Understand Aerial Images

This report summarizes the results of Learning to Understand Aerial Images (LUAI) 2021 challenge held on ICCV 2021, which focuses on object detection and semantic segmentation in aerial images. Using DOTA-v2.0 and GID-15 datasets, this challenge proposes three tasks for oriented object detection, horizontal object detection, and semantic segmentation of common categories in aerial images. This challenge received a total of 146 registrations on the three tasks. Through the challenge, we hope to draw attention from a wide range of communities and call for more efforts on the problems of learning to understand aerial images.

cs.CV↗

arXiv2021

Entanglement negativity spectrum of random mixed states: A diagrammatic approach

The entanglement properties of random pure states are relevant to a variety of problems ranging from chaotic quantum dynamics to black hole physics. The averaged bipartite entanglement entropy of such states admits a volume law and upon increasing the subregion size follows the Page curve. In this paper, we generalize this setup to random mixed states by coupling the system to a bath and use the partial transpose to study their entanglement properties. We develop a diagrammatic method to incorporate partial transpose within random matrix theory and formulate a perturbation theory in $1/L$, the inverse of the Hilbert space dimension. We compute several quantities including the spectral density of partial transpose (or entanglement negativity spectrum), two-point correlator of eigenvalues, and the logarithmic negativity. As long as the bath is smaller than the system, we find that upon sweeping the subregion size, the logarithmic negativity shows an initial increase and a final decrease similar to the Page curve, while it admits a plateau in the intermediate regime where the logarithmic negativity only depends on the size of the system and of the bath but not on how the system is partitioned. This intermediate phase has no analog in random pure states, and is separated from the two other regimes by a critical point. We further show that when the bath is larger than the system by at least two extra qubits the logarithmic negativity is identically zero which implies that there is no distillable entanglement. Using the diagrammatic approach, we provide a simple derivation of the semi-circle law of the entanglement negativity spectrum in the latter two regimes. We show that despite the appearance of a semicircle distribution, reminiscent of Gaussian unitary ensemble (GUE), the higher order corrections to the negativity spectrum and two-point correlator deviate from those of GUE.

cond-mat.str-el↗

arXiv2021

Quantum Many-Body Scars and Quantum Criticality

In this letter, we study the PXP Hamiltonian with an external magnetic field that exhibits both quantum scar states and quantum criticality. It is known that this model hosts a series of quantum many-body scar states violating quantum thermalization at zero magnetic field, and it also exhibits an Ising quantum phase transition driven by finite magnetic field. Although the former involves the properties of generic excited states and the latter concerns the low-energy physics, we discover two surprising connections between them, inspired by the observation that both states possess log-volume law entanglement entropies. First, we show that the quantum many-body scar states can be tracked to a set of quantum critical states, whose nature can be understood as pair-wisely occupied Fermi sea states. Second, we show that the partial violation of quantum thermalization diminishes in the quantum critical regime. We envision that these connections can be extended to general situations and readily verified in existing cold atom experimental platforms.

cond-mat.quant-gas↗

arXiv2020

Ground State and Hidden Symmetry of Magic Angle Graphene at Even Integer Filling

In magic angle twisted bilayer graphene, electron-electron interactions play a central role resulting in correlated insulating states at certain integer fillings. Identifying the nature of these insulators is a central question and potentially linked to the relatively high temperature superconductivity observed in the same devices. Here we address this question using a combination of analytical strong-coupling arguments and a comprehensive Hartree-Fock numerical calculation which includes the effect of remote bands. The ground state we obtain at charge neutrality is an unusual ordered state which we call the Kramers intervalley-coherent (K-IVC) insulator. In its simplest form, the K-IVC exhibits a pattern of alternating circulating currents which triples the graphene unit cell leading to an "orbital magnetization density wave". Although translation and time reversal symmetry are broken, a combined `Kramers' time reversal symmetry is preserved. Our analytic arguments are built on first identifying an approximate ${\rm U}(4) \times {\rm U}(4)$ symmetry, resulting from the remarkable properties of the tBG band structure, which helps select a low energy manifold of states, which are further split to favor the K-IVC. This low energy manifold is also found in the Hartree-Fock numerical calculation. We show that symmetry lowering perturbations can stabilize other insulators and the semi-metallic state, and discuss the ground state at half filling and a comparison with experiments.

cond-mat.str-el↗

arXiv2020

Quantum Magnetism in Wannier-Obstructed Mott Insulators

We develop a strong coupling approach towards quantum magnetism in Mott insulators for Wannier obstructed bands. Despite the lack of Wannier orbitals, electrons can still singly occupy a set of exponentially-localized but nonorthogonal orbitals to minimize the repulsive interaction energy. We develop a systematic method to establish an effective spin model from the electron Hamiltonian using a diagrammatic approach. The nonorthogonality of the Mott basis gives rise to multiple new channels of spin-exchange (or permutation) interactions beyond Hartree-Fock and superexchange terms. We apply this approach to a Kagome lattice model of interacting electrons in Wannier obstructed bands (including both Chern bands and fragile topological bands). Due to the orbital nonorthogonality, as parameterized by the nearest neighbor orbital overlap $g$, this model exhibits stable ferromagnetism up to a finite bandwidth $W\sim U g$, where $U$ is the interaction strength. This provides an explanation for the experimentally observed robust ferromagnetism in Wannier obstructed bands. The effective spin model constructed through our approach also opens up the possibility for frustrated quantum magnetism around the ferromagnet-antiferromagnet crossover in Wannier obstructed bands.

cond-mat.str-el↗

arXiv2019

Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene

Two monolayers of graphene twisted by a small `magic' angle exhibit nearly flat bands leading to correlated electronic states and superconductivity, whose precise nature including possible broken symmetries, remain under debate. Here we theoretically study a related but different system with reduced symmetry - twisted {\em double} bilayer graphene (TDBLG), consisting of {\em two} Bernal stacked bilayer graphene sheets, twisted with respect to one another. Unlike the monolayer case, we show that isolated flat bands only appear on application of a vertical displacement field $D$. We construct a phase diagram as a function of twist angle and $D$, incorporating interactions via a Hartree-Fock approximation. At half filling, ferromagnetic insulators are stabilized, typically with valley Chern number $C_v=2$. Ferromagnetic fluctuations in the metallic state are argued to lead to spin triplet superconductivity from pairing between electrons in opposite valleys. Response of these states to a magnetic field applied either perpendicular or parallel to the graphene sheets is obtained, and found to compare favorably with a recent experiment. We highlight a novel orbital effect arising from in-plane fields that can exceed the Zeeman effect and plays an important role in interpreting experiments.

cond-mat.str-el↗

arXiv2019

Shift insulators: rotation-protected two-dimensional topological crystalline insulators

We study a two-dimensional (2D) tight-binding model of a topological crystalline insulator (TCI) protected by rotation symmetry. The model is built by stacking two Chern insulators with opposite Chern numbers which transform under conjugate representations of the rotation group, e.g. $p_\pm$ orbitals. Despite its apparent similarity to the Kane-Mele model, it does not host stable gapless surface states. Nevertheless the model exhibits topological responses including the appearance of quantized fractional charge bound to rotational defects (disclinations) and the pumping of angular momentum in response to threading an elementary magnetic flux, which are described by a mutual Chern-Simons coupling between the electromagnetic gauge field and an effective gauge field corresponding to the rotation symmetry. In addition, we show that although the filled bands of the model do not admit a symmetric Wannier representation, this obstruction is removed upon the addition of appropriate atomic orbitals, which implies `fragile' topology. As a result, the response of the model can be derived by representing it as a superposition of atomic orbitals with positive and negative integer coefficients. Following the analysis of the model, which serves as a prototypical example of 2D TCIs protected by rotation, we show that all TCIs protected by point group symmetries which do not have protected surface states are either atomic insulators or fragile phases. Remarkably, this implies that gapless surface states exist in free electron systems if and only if there is a stable Wannier obstruction. We then use dimensional reduction to map the problem of classifying 2D TCIs protected by rotation to a zero-dimensional (0D) problem which is then used to obtain the complete non-interacting classification of such TCIs as well as the reduction of this classification in the presence of interactions.

cond-mat.mes-hall↗

arXiv2018

Complementary relation of quantum coherence and quantum correlations in multiple measurements

Quantum coherence and quantum correlations lie in the center of quantum information science, since they both are considered as fundamental reasons for significant features of quantum mechanics different from classical mechanics. We present a group of complementary relations for quantum coherence and quantum correlations; specifically, we focus on thermal discord and conditional information in scenarios of multiple measurements. We show that the summation of quantum coherence quantified in different bases has a lower bound, resulting from entropic uncertainty relations with multiple measurements. Similar results are also obtained for thermal discord and for post-measurement conditional information with multiple measurements in a multipartite system. These results indicate the general applications of the uncertainty principle to various concepts of quantum information.

quant-ph↗