arXiv subjects

Linhao Li

Publications and source records attributed to Linhao Li.

32 records · Page 2Linked to original sources

arXiv2024

Anomaly in open quantum systems and its implications on mixed-state quantum phases

In this paper, we develop a systematic approach to characterize the 't Hooft anomaly in open quantum systems. Owing to nontrivial couplings to the environment, symmetries in such systems manifest as either strong or weak type. By representing their symmetry transformation through superoperators, we incorporate them in a unified framework that enables a direct calculation of their anomalies. In the case where the full symmetry group is $K\times G$, with $K$ the strong symmetry and $G$ the weak symmetry, we find that anomalies of bosonic systems are classified by $H^{d+2}(K\times G,U(1))/H^{d+2}(G,U(1))$ in $d$ spatial dimensions. To illustrate the power of anomalies in open quantum systems, we generally prove that anomaly must lead to nontrivial mixed-state quantum phases as long as the weak symmetry is imposed. Analogous to the ``anomaly matching" condition ensuring nontrivial low-energy physics in closed systems, anomaly also guarantees nontrivial steady states and long-time dynamics for open quantum systems governed by Lindbladians. Notably, we identify a novel $(1+1)$-D mixed-state quantum phase that has no counterpart in closed systems, where the steady state shows no nontrivial correlation function in the bulk, but displays spontaneous symmetry breaking order on the boundary, which is enforced by anomalies. We further establish the general relations between mixed-state anomalies and such unconventional boundary correlation. Finally, we explore the generalization of the ``anomaly inflow" mechanism in open quantum systems. We construct $(1+1)$-D and $(2+1)$-D Lindbladians whose steady states have mixed-state symmetry-protected-topological order in the bulk, with corresponding edge theories characterized by nontrivial anomalies.

quant-ph↗

arXiv2024

Decorated Defect Construction of Gapless-SPT States

Symmetry protected topological (SPT) phases are one of the simplest, yet nontrivial, gapped systems that go beyond the Landau paradigm. In this work, we study an extension of the notion of SPT for gapless systems, namely, gapless symmetry protected topological states. We construct several simple gapless-SPT models using the decorated defect construction, which allow analytical understanding of non-trivial topological features including the symmetry charge under twisted boundary conditions, and boundary (quasi)-degeneracy under open boundary conditions. We also comment on the stability of the gapless-SPT models under symmetric perturbations, and apply small-scale exact diagonalization when direct analytic understanding is not available.

cond-mat.str-el↗

arXiv2024

Non-Invertible Duality Transformation Between SPT and SSB Phases

In 1992, Kennedy and Tasaki constructed a non-local unitary transformation that maps between a $\mathbb{Z}_2\times \mathbb{Z}_2$ spontaneously symmetry breaking phase and the Haldane gap phase, which is a prototypical Symmetry-Protected Topological phase in modern framework, on an open spin chain. In this work, we propose a way to define it on a closed chain, by sacrificing unitarity. The operator realizing such a non-unitary transformation satisfies non-invertible fusion rule, and implements a generalized gauging of the $\mathbb{Z}_2\times \mathbb{Z}_2$ global symmetry. These findings connect the Kennedy-Tasaki transformation to numerous other concepts developed for SPT phases, and opens a way to construct SPT phases systematically using the duality mapping.

cond-mat.str-el↗

arXiv2023

Subsystem Non-Invertible Symmetry Operators and Defects

We explore non-invertible symmetries in two-dimensional lattice models with subsystem $\mathbb Z_2$ symmetry. We introduce a subsystem $\mathbb Z_2$-gauging procedure, called the subsystem Kramers-Wannier transformation, which generalizes the ordinary Kramers-Wannier transformation. The corresponding duality operators and defects are constructed by gaugings on the whole or half of the Hilbert space. By gauging twice, we derive fusion rules of duality operators and defects, which enriches ordinary Ising fusion rules with subsystem features. Subsystem Kramers-Wannier duality defects are mobile in both spatial directions, unlike the defects of invertible subsystem symmetries. We finally comment on the anomaly of the subsystem Kramers-Wannier duality symmetry, and discuss its subtleties.

cond-mat.str-el↗

arXiv2023

Intrinsically/Purely Gapless-SPT from Non-Invertible Duality Transformations

The Kennedy-Tasaki (KT) transformation was used to construct the gapped symmetry protected topological (SPT) phase from the symmetry breaking phase with open boundary condition, and was generalized in our proceeding work [L. Li et al. arXiv:2301.07899] on a ring by sacrificing the unitarity, and should be understood as a non-invertible duality transformation. In this work, we further apply the KT transformation to systematically construct gapless symmetry protected topological phases. This construction reproduces the known examples of (intrinsically) gapless SPT where the non-trivial topological features come from the gapped sectors by means of decorated defect constructions. We also construct new (intrinsically) purely gapless SPTs where there are no gapped sectors, hence are beyond the decorated defect construction. This construction elucidates the field theory description of the various gapless SPTs, and can also be applied to analytically study the stability of various gapless SPT models on the lattice under certain symmetric perturbations.

cond-mat.str-el↗

arXiv2023

Stability and fine structure of symmetry-enriched quantum criticality in a spin ladder triangular model

In this letter, we propose and study a ladder triangular cluster model which possesses a $\mathbb{Z}_2$ symmetry and an anti-unitary $\mathbb{Z}^{\mathbb{T}}_2$ symmetry generated by the spin-flip and complex conjugation, respectively. The phase diagram of the model hosts a critical line between a spontaneous symmetry breaking phase and a symmetry protected topological phase. Along the critical line, one endpoint exhibits symmetry-enriched Ashkin-Teller universality (SEATU), while other critical points fall into the symmetry-enriched Ising universality (SEIU). Both universality classes accommodate symmetry protected degenerate edge modes under open boundary conditions. This degeneracy can be lifted with a gap opening when proper perturbation is applied to the boundary. With system size ($L$) increasing, at the point of SEATU, the gap closes following $L^{-1}$. In contrast, for the critical points of SEIU apart from a point with the known gap closing as $L^{-14}$, other points surprisingly show exponentially gap closing. The coexistence of different gap closing behaviors for critical points of the same symmetry-enriched universality goes beyond the the usual understanding of symmetry-enriched universality class, implying a fine and rich structure of phase transition and universality class.

cond-mat.str-el↗

arXiv2023

Duality, Criticality, Anomaly, and Topology in Quantum Spin-1 Chains

In quantum spin-1 chains, there is a nonlocal unitary transformation known as the Kennedy-Tasaki transformation $U_{\text{KT}}$, which defines a duality between the Haldane phase and the $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry-breaking phase. In this paper, we find that $U_{\text{KT}}$ also defines a duality between a topological Ising critical phase and a trivial Ising critical phase, which provides a "hidden symmetry breaking" interpretation for the topological criticality. Moreover, since the duality relates different phases of matter, we argue that a model with self-duality (i.e., invariant under $U_{\text{KT}}$) is natural to be at a critical or multicritical point. We study concrete examples to demonstrate this argument. In particular, when $H$ is the Hamiltonian of the spin-1 antiferromagnetic Heisenberg chain, we prove that the self-dual model $H + U_{\text{KT}} H U_{\text{KT}}$ is exactly equivalent to a gapless spin-$1/2$ XY chain, which also implies an emergent quantum anomaly. On the other hand, we show that the topological and trivial Ising criticalities that are dual to each other meet at a multicritical point which is indeed self-dual.

cond-mat.str-el↗

arXiv2023

Duality viewpoint of criticality

In this work, we study quantum many-body systems which are self-dual under duality transformation connecting different symmetry protected topological (SPT) phases. We provide a geometric explanation of the criticality of these self-dual models. More precisely, we show a ground state (quasi-)degeneracy under the periodic boundary conditions,i.e., the ingappability of the bulk spectrum. Equivalently, the symmetry group at criticality, including the duality symmetry, has a mixed 't Hooft anomaly. This approach can not only predict the spectrum of the self-dual model with ordinary 0-form symmetry, but also be applied to that with generalized symmetry, such as higher form and subsystem symmetry. As an application, we illustrate our results with several examples in one and two dimensions, which separate two different SPTs.

quant-ph↗

arXiv2022

Interactive Model with Structural Loss for Language-based Abductive Reasoning

The abductive natural language inference task ($α$NLI) is proposed to infer the most plausible explanation between the cause and the event. In the $α$NLI task, two observations are given, and the most plausible hypothesis is asked to pick out from the candidates. Existing methods model the relation between each candidate hypothesis separately and penalize the inference network uniformly. In this paper, we argue that it is unnecessary to distinguish the reasoning abilities among correct hypotheses; and similarly, all wrong hypotheses contribute the same when explaining the reasons of the observations. Therefore, we propose to group instead of ranking the hypotheses and design a structural loss called ``joint softmax focal loss'' in this paper. Based on the observation that the hypotheses are generally semantically related, we have designed a novel interactive language model aiming at exploiting the rich interaction among competing hypotheses. We name this new model for $α$NLI: Interactive Model with Structural Loss (IMSL). The experimental results show that our IMSL has achieved the highest performance on the RoBERTa-large pretrained model, with ACC and AUC results increased by about 1\% and 5\% respectively.

cs.CL↗

arXiv2022

Dual topological nonlinear sigma models of $\text{QED}$ theory by dimensional reduction and monopole operators

Nonlinear $σ$ models (NLSM) with topological terms, i.e., Wess-Zumino-Witten (WZW) terms, or topological NLSM, are potent descriptions of many critical points and phases beyond the Landau paradigm. These critical systems include the deconfined quantum critical points (DQCP) between the Neel order and valance bond solid, and the Dirac spin liquid, in which the topological NLSMs are dual descriptions of the corresponding fermionic models or $\text{QED}$ theory. In this paper, we propose a dimensional reduction scheme to derive the $\text{U}(1)$ gauged topological NLSM in $n$-dimensional spacetime on a general target space represented by a Hermitian matrix from the dual QED theory. Compared with the famous Abanov-Wiegmann (AW) mechanism, which generally requires the fermions to be Dirac fermions in the infrared (IR), our method is also applicable to non-relativistic fermions in IR, which can have quadratic dispersion or even a Fermi surface. As concrete examples, we construct several two dimensional lattice models, whose IR theories are all the $N_f=4$ $\text{QED}_3$ with fermions of quadratic dispersion and show that its topological NLSM dual description has level-2 WZW terms on the Grassmannian manifold $\frac{\text{U(4)}}{\text{U(2)}\times \text{U(2)}}$ coupled with a dynamical $\text{U(1)}$ gauge field. We also study 't Hooft anomaly matching and the same effect of defects in both theories, such as interface, gauge monopoles and skyrmions, which further support our duality. Finally, we discuss how the macroscopic symmetries act on the $\text{U(1)}$ monopole operators and the corresponding quantum number.

cond-mat.str-el↗

arXiv2022

Fracton Topological Order at Finite Temperature

As new kinds of stabilizer code models, fracton models have been promising in realizing quantum memory or quantum hard drives. However, it has been shown that the fracton topological order of 3D fracton models occurs only at zero temperature. In this Letter, we show that higher dimensional fracton models can support a fracton topological order below a nonzero critical temperature $T_c$. Focusing on a typical 4D X-cube model, we show that there is a finite critical temperature $T_c$ by analyzing its free energy from duality. We also obtained the expectation value of the 't Hooft loops in the 4D X-cube model, which directly shows a confinement-deconfinement phase transition at finite temperature. This finite-temperature phase transition can be understood as spontaneously breaking the $\mathbb{Z}_2$ one-form subsystem symmetry. Moreover, we propose a new no-go theorem for finite-temperature quantum fracton topological order.

cond-mat.str-el↗

arXiv2020

Dynamic Anchor Learning for Arbitrary-Oriented Object Detection

Arbitrary-oriented objects widely appear in natural scenes, aerial photographs, remote sensing images, etc., thus arbitrary-oriented object detection has received considerable attention. Many current rotation detectors use plenty of anchors with different orientations to achieve spatial alignment with ground truth boxes, then Intersection-over-Union (IoU) is applied to sample the positive and negative candidates for training. However, we observe that the selected positive anchors cannot always ensure accurate detections after regression, while some negative samples can achieve accurate localization. It indicates that the quality assessment of anchors through IoU is not appropriate, and this further lead to inconsistency between classification confidence and localization accuracy. In this paper, we propose a dynamic anchor learning (DAL) method, which utilizes the newly defined matching degree to comprehensively evaluate the localization potential of the anchors and carry out a more efficient label assignment process. In this way, the detector can dynamically select high-quality anchors to achieve accurate object detection, and the divergence between classification and regression will be alleviated. With the newly introduced DAL, we achieve superior detection performance for arbitrary-oriented objects with only a few horizontal preset anchors. Experimental results on three remote sensing datasets HRSC2016, DOTA, UCAS-AOD as well as a scene text dataset ICDAR 2015 show that our method achieves substantial improvement compared with the baseline model. Besides, our approach is also universal for object detection using horizontal bound box. The code and models are available at https://github.com/ming71/DAL.

cs.CV↗

arXiv2020

A Novel CNN-based Method for Accurate Ship Detection in HR Optical Remote Sensing Images via Rotated Bounding Box

Currently, reliable and accurate ship detection in optical remote sensing images is still challenging. Even the state-of-the-art convolutional neural network (CNN) based methods cannot obtain very satisfactory results. To more accurately locate the ships in diverse orientations, some recent methods conduct the detection via the rotated bounding box. However, it further increases the difficulty of detection, because an additional variable of ship orientation must be accurately predicted in the algorithm. In this paper, a novel CNN-based ship detection method is proposed, by overcoming some common deficiencies of current CNN-based methods in ship detection. Specifically, to generate rotated region proposals, current methods have to predefine multi-oriented anchors, and predict all unknown variables together in one regression process, limiting the quality of overall prediction. By contrast, we are able to predict the orientation and other variables independently, and yet more effectively, with a novel dual-branch regression network, based on the observation that the ship targets are nearly rotation-invariant in remote sensing images. Next, a shape-adaptive pooling method is proposed, to overcome the limitation of typical regular ROI-pooling in extracting the features of the ships with various aspect ratios. Furthermore, we propose to incorporate multilevel features via the spatially-variant adaptive pooling. This novel approach, called multilevel adaptive pooling, leads to a compact feature representation more qualified for the simultaneous ship classification and localization. Finally, detailed ablation study performed on the proposed approaches is provided, along with some useful insights. Experimental results demonstrate the great superiority of the proposed method in ship detection.

cs.CV↗

arXiv2016

Efficient Background Modeling Based on Sparse Representation and Outlier Iterative Removal

Background modeling is a critical component for various vision-based applications. Most traditional methods tend to be inefficient when solving large-scale problems. In this paper, we introduce sparse representation into the task of large scale stable background modeling, and reduce the video size by exploring its 'discriminative' frames. A cyclic iteration process is then proposed to extract the background from the discriminative frame set. The two parts combine to form our Sparse Outlier Iterative Removal (SOIR) algorithm. The algorithm operates in tensor space to obey the natural data structure of videos. Experimental results show that a few discriminative frames determine the performance of the background extraction. Further, SOIR can achieve high accuracy and high speed simultaneously when dealing with real video sequences. Thus, SOIR has an advantage in solving large-scale tasks.

cs.CV↗