arXiv subjects

Meng Cheng

Publications and source records attributed to Meng Cheng.

At least 55 records · Page 3Linked to original sources

arXiv2023

Continuous phase transitions between fractional quantum Hall states and symmetry-protected topological states

We study quantum phase transitions in Bose-Fermi mixtures driven by interspecies interaction in the quantum Hall regime. In the absence of such an interaction, the bosons and fermions form their respective fractional quantum Hall (FQH) states at certain filling factors. A symmetry-protected topological (SPT) state is identified as the ground state for strong interspecies interaction. The phase transitions between them are proposed to be described by Chern-Simons-Higgs field theories. For a simple microscopic Hamiltonian, we present numerical evidence for the existence of the SPT state and a continuous transition to the FQH state. It is also found that the entanglement entropy between the bosons and fermions exhibits scaling behavior in the vicinity of this transition.

cond-mat.str-el↗

arXiv2023

Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities

The fermion disorder operator has been shown to reveal the entanglement information in 1D Luttinger liquids and 2D free and interacting Fermi and non-Fermi liquids emerging at quantum critical points(QCP). Here we study, by means of large-scale quantum Monte Carlo simulation, the scaling behavior of disorder operator in correlated Dirac systems. We first demonstrate the logarithmic scaling behavior of the disorder operator at the Gross-Neveu (GN) chiral Ising and Heisenberg QCPs, where consistent conformal field theory (CFT) content of the GN-QCP in its coefficient is found. Then we study a 2D monopole free deconfined quantum critical point (DQCP) realized between a quantum-spin Hall insulator and a superconductor. Our data point to negative values of the logarithmic coefficients such that the DQCP does not correspond to a unitary CFT. Density matrix renormalization group calculations of the disorder operator on a 1D DQCP model also detect emergent continuous symmetries.

cond-mat.str-el↗

arXiv2023

Many versus one: the disorder operator and entanglement entropy in fermionic quantum matter

Motivated by recent development of the concept of the disorder operator and its relation with entanglement entropy in bosonic systems, here we show the disorder operator successfully probes many aspects of quantum entanglement in fermionic many-body systems. From both analytical and numerical computations in free and interacting fermion systems in 1D and 2D, we find the disorder operator and the entanglement entropy exhibit similar universal scaling behavior, as a function of the boundary length of the subsystem, but with subtle yet important differences. In 1D they both follow the $\log{L}$ scaling behavior with the coefficient determined by the Luttinger parameter for disorder operator, and the conformal central charge for entanglement entropy. In 2D they both show the universal $L\log L$ scaling behavior in free and interacting Fermi liquid states, with the coefficients depending on the geometry of the Fermi surfaces. However at a 2D quantum critical point with non-Fermi-liquid state, extra symmetry information is needed in the design of the disorder operator, so as to reveal the critical fluctuations as does the entanglement entropy. Our results demonstrate the fermion disorder operator can be used to probe quantum many-body entanglement related to global symmetry, and provides new tools to explore the still largely unknown territory of highly entangled fermion quantum matter in 2 or higher dimensions.

cond-mat.str-el↗

arXiv2023

Ground state degeneracy on torus in a family of $\mathbb{Z}_N$ toric code

Topologically ordered phases in $2+1$ dimensions are generally characterized by three mutually-related features: fractionalized (anyonic) excitations, topological entanglement entropy, and robust ground state degeneracy that does not require symmetry protection or spontaneous symmetry breaking. Such degeneracy is known as topological degeneracy and usually can be seen under the periodic boundary condition regardless of the choice of the system size $L_1$ and $L_2$ in each direction. In this work we introduce a family of extensions of the Kitaev toric code to $N$ level spins ($N\geq2$). The model realizes topologically ordered phases or symmetry-protected topological phases depending on parameters in the model. The most remarkable feature of the topologically ordered phases is that the ground state may be unique, depending on $L_1$ and $L_2$, despite that the translation symmetry of the model remains unbroken. Nonetheless, the topological entanglement entropy takes the nontrivial value. We argue that this behavior originates from the nontrivial action of translations permuting anyon species.

cond-mat.other↗

arXiv2023

Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems

We analyze lattice Hamiltonian systems whose global symmetries have 't Hooft anomalies. As is common in the study of anomalies, they are probed by coupling the system to classical background gauge fields. For flat fields (vanishing field strength), the nonzero spatial components of the gauge fields can be thought of as twisted boundary conditions, or equivalently, as topological defects. The symmetries of the twisted Hilbert space and their representations capture the anomalies. We demonstrate this approach with a number of examples. In some of them, the anomalous symmetries are internal symmetries of the lattice system, but they do not act on-site. (We clarify the notion of "on-site action.") In other cases, the anomalous symmetries involve lattice translations. Using this approach we frame many known and new results in a unified fashion. In this work, we limit ourselves to 1+1d systems with a spatial lattice. In particular, we present a lattice system that flows to the $c=1$ compact boson system with any radius (no BKT transition) with the full internal symmetry of the continuum theory, with its anomalies and its T-duality. As another application, we analyze various spin chain models and phrase their Lieb-Shultz-Mattis theorem as an 't Hooft anomaly matching condition. We also show in what sense filling constraints like Luttinger theorem can and cannot be viewed as reflecting an anomaly. As a by-product, our understanding allows us to use information from the continuum theory to derive some exact results in lattice model of interest, such as the lattice momenta of the low-energy states.

cond-mat.str-el↗

arXiv2023

YOLOv6 v3.0: A Full-Scale Reloading

The YOLO community has been in high spirits since our first two releases! By the advent of Chinese New Year 2023, which sees the Year of the Rabbit, we refurnish YOLOv6 with numerous novel enhancements on the network architecture and the training scheme. This release is identified as YOLOv6 v3.0. For a glimpse of performance, our YOLOv6-N hits 37.5% AP on the COCO dataset at a throughput of 1187 FPS tested with an NVIDIA Tesla T4 GPU. YOLOv6-S strikes 45.0% AP at 484 FPS, outperforming other mainstream detectors at the same scale (YOLOv5-S, YOLOv8-S, YOLOX-S and PPYOLOE-S). Whereas, YOLOv6-M/L also achieve better accuracy performance (50.0%/52.8% respectively) than other detectors at a similar inference speed. Additionally, with an extended backbone and neck design, our YOLOv6-L6 achieves the state-of-the-art accuracy in real-time. Extensive experiments are carefully conducted to validate the effectiveness of each improving component. Our code is made available at https://github.com/meituan/YOLOv6.

cs.CV↗

arXiv2022

Gauging Lie group symmetry in (2+1)d topological phases

We present a general algebraic framework for gauging a 0-form compact, connected Lie group symmetry in (2+1)d topological phases. Starting from a symmetry fractionalization pattern of the Lie group $G$, we first extend $G$ to a larger symmetry group $\tilde{G}$, such that there is no fractionalization with respect to $\tilde{G}$ in the topological phase, and the effect of gauging $\tilde{G}$ is to tensor the original theory with a $\tilde{G}$ Chern-Simons theory. To restore the desired gauge symmetry, one then has to gauge an appropriate one-form symmetry (or, condensing certain Abelian anyons) to obtain the final result. Studying the consistency of the gauging procedure leads to compatibility conditions between the symmetry fractionalization pattern and the Hall conductance. When the gauging can not be consistently done (i.e. the compatibility conditions can not be satisfied), the symmetry $G$ with the fractionalization pattern has an 't Hooft anomaly and we present a general method to determine the (3+1)d topological term for the anomaly. We provide many examples, including projective simple Lie groups and unitary groups to illustrate our approach.

cond-mat.str-el↗

arXiv2022

Classification and construction of interacting fractonic higher-order topological phases

The notion of higher-order topological phases can have interesting generalizations to systems with subsystem symmetries that exhibit fractonic dynamics for charged excitations. In this work, we systematically study the higher-order topological phases protected by a combination of subsystem symmetries and ordinary global symmetries in two and three-dimensional interacting boson systems, with some interacting fermionic examples.

cond-mat.str-el↗

arXiv2022

Topological Disorder Parameter

We introduce a many-body topological invariant, called the topological disorder parameter (TDP), to characterize gapped quantum phases with global internal symmetry in (2+1)d. TDP is defined as the constant correction that appears in the ground state expectation value of a partial symmetry transformation applied to a connected spatial region $M$, the absolute value of which scales generically as $\exp(-αl+γ)$ where $l$ is the perimeter of $M$ and $γ$ is the TDP. Motivated by a topological quantum field theory interpretation of the operator, we show that $e^γ$ can be related to the quantum dimension of the symmetry defect, and provide a general formula for $γ$ when the entanglement Hamiltonian of the topological phase can be described by a (1+1)d conformal field theory (CFT). A special case of TDP is equivalent to the topological Rényi entanglement entropy when the symmetry is the cyclic permutation of the replica of the gapped phase. We then investigate several examples of lattice models of topological phases, both analytically and numerically, in particular when the assumption of having a CFT edge theory is not satisfied. We also consider an example of partial translation symmetry in Wen's plaquette model and show that the result can be understood using the edge CFT. Our results establish a new tool to detect quantum topological order.

cond-mat.str-el↗

arXiv2022

YOLOv6: A Single-Stage Object Detection Framework for Industrial Applications

For years, the YOLO series has been the de facto industry-level standard for efficient object detection. The YOLO community has prospered overwhelmingly to enrich its use in a multitude of hardware platforms and abundant scenarios. In this technical report, we strive to push its limits to the next level, stepping forward with an unwavering mindset for industry application. Considering the diverse requirements for speed and accuracy in the real environment, we extensively examine the up-to-date object detection advancements either from industry or academia. Specifically, we heavily assimilate ideas from recent network design, training strategies, testing techniques, quantization, and optimization methods. On top of this, we integrate our thoughts and practice to build a suite of deployment-ready networks at various scales to accommodate diversified use cases. With the generous permission of YOLO authors, we name it YOLOv6. We also express our warm welcome to users and contributors for further enhancement. For a glimpse of performance, our YOLOv6-N hits 35.9% AP on the COCO dataset at a throughput of 1234 FPS on an NVIDIA Tesla T4 GPU. YOLOv6-S strikes 43.5% AP at 495 FPS, outperforming other mainstream detectors at the same scale~(YOLOv5-S, YOLOX-S, and PPYOLOE-S). Our quantized version of YOLOv6-S even brings a new state-of-the-art 43.3% AP at 869 FPS. Furthermore, YOLOv6-M/L also achieves better accuracy performance (i.e., 49.5%/52.3%) than other detectors with a similar inference speed. We carefully conducted experiments to validate the effectiveness of each component. Our code is made available at https://github.com/meituan/YOLOv6.

cs.CV↗

arXiv2022

Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations

We develop a nonequilibrium increment method in quantum Monte Carlo simulations to obtain the Rényi entanglement entropy of various quantum many-body systems with high efficiency and precision. To demonstrate its power, we show the results on a few important yet difficult $(2+1)d$ quantum lattice models, ranging from the Heisenberg quantum antiferromagnet with spontaneous symmetry breaking, the quantum critical point with O(3) conformal field theory (CFT) to the toric code $\Z_2$ topological ordered state and the Kagome $\Z_2$ quantum spin liquid model with frustration and multi-spin interactions. In all these cases, our method either reveals the precise CFT data from the logarithmic correction or extracts the quantum dimension in topological order, from the dominant area law in finite-size scaling, with very large system sizes, controlled errorbars and minimal computational costs. Our method therefore establishes a controlled and practical computation paradigm to obtain the difficult yet important universal properties in highly entangled quantum matter.

cond-mat.str-el↗

arXiv2022

Scaling of disorder operator at deconfined quantum criticality

We study scaling behavior of the disorder parameter, defined as the expectation value of a symmetry transformation applied to a finite region, at the deconfined quantum critical point in (2+1)$d$ in the $J$-$Q_3$ model via large-scale quantum Monte Carlo simulations. We show that the disorder parameter for U(1) spin rotation symmetry exhibits perimeter scaling with a logarithmic correction associated with sharp corners of the region, as generally expected for a conformally-invariant critical point. However, for large rotation angle the universal coefficient of the logarithmic corner correction becomes negative, which is not allowed in any unitary conformal field theory. We also extract the current central charge from the small rotation angle scaling, whose value is much smaller than that of the free theory.

cond-mat.str-el↗

arXiv2022

Gauging U(1) symmetry in (2+1)d topological phases

We study the gauging of a global U(1) symmetry in a gapped system in (2+1)d. The gauging procedure has been well-understood for a finite global symmetry group, which leads to a new gapped phase with emergent gauge structure and can be described algebraically using the mathematical framework of modular tensor category (MTC). We develop a categorical description of U(1) gauging in an MTC, taking into account the dynamics of U(1) gauge field absent in the finite group case. When the ungauged system has a non-zero Hall conductance, the gauged theory remains gapped and we determine the complete set of anyon data for the gauged theory. On the other hand, when the Hall conductance vanishes, we argue that gauging has the same effect of condensing a special Abelian anyon nucleated by inserting $2π$ U(1) flux. We apply our procedure to the SU(2)$_k$ MTCs and derive the full MTC data for the $\mathbb{Z}_k$ parafermion MTCs. We also discuss a dual U(1) symmetry that emerges after the original U(1) symmetry of an MTC is gauged.

cond-mat.str-el↗

arXiv2022

Rotation Symmetry-Protected Topological Phases of Fermions

We study classification of interacting fermionic symmetry-protected topological (SPT) phases with both rotation symmetry and Abelian internal symmetries in one, two, and three dimensions. By working out this classification, on the one hand, we demonstrate the recently proposed correspondence principle between crystalline topological phases and those with internal symmetries through explicit block-state constructions. We find that for the precise correspondence to hold it is necessary to change the central extension structure of the symmetry group by the $\mathbb{Z}_2$ fermion parity. On the other hand, we uncover new classes of intrinsically fermionic SPT phases that are only enabled by interactions, both in 2D and 3D with four-fold rotation. Moreover, several new instances of Lieb-Schultz-Mattis-type theorems for Majorana-type fermionic SPTs are obtained and we discuss their interpretations from the perspective of bulk-boundary correspondence.

cond-mat.str-el↗

arXiv2022

Scaling of entanglement entropy at deconfined quantum criticality

We develop a nonequilibrium increment method to compute the Rényi entanglement entropy and investigate its scaling behavior at the deconfined critical (DQC) point via large-scale quantum Monte Carlo simulations. To benchmark the method, we first show that at an conformally-invariant critical point of O(3) transition, the entanglement entropy exhibits universal scaling behavior of area law with logarithmic corner corrections and the obtained correction exponent represents the current central charge of the critical theory. Then we move on to the deconfined quantum critical point, where although we still observe similar scaling behavior but with a very different exponent. Namely, the corner correction exponent is found to be negative. Such a negative exponent is in sharp contrast with positivity condition of the Rényi entanglement entropy, which holds for unitary conformal field theories(CFT). Our results unambiguously reveal fundamental differences between DQC and quantum critical points(QCPs) described by unitary CFTs.

cond-mat.str-el↗

arXiv2021

Exactly solvable lattice models for interacting electronic insulators in two dimensions

In the past decade, tremendous efforts have been made towards understanding fermionic symmetry protected topological (FSPT) phases in interacting systems. Nevertheless, for systems with continuum symmetry, e.g., electronic insulators, it is still unclear how to construct an exactly solvable model with a finite dimensional Hilbert space in general. In this paper, we give a lattice model construction and classification for 2D interacting electronic insulators. Based on the physical picture of $\mathrm{U(1)}_f$-charge decorations, we illustrate the key idea by considering the well known 2D interacting topological insulator. Then we generalize our construction to an arbitrary 2D interacting electronic insulator with symmetry $G_f=\mathrm{U(1)}_f \rtimes_{ρ_1,ω_2} G$, where $\mathrm{U(1)}_f$ is the charge conservation symmetry and $ρ_1, ω_2$ are additional data which fully characterize the group structure of $G_f$. Finally we study more examples, including the full interacting classification of 2D crystalline topological insulators.

cond-mat.str-el↗

arXiv2021

Weak symmetry breaking and topological order in a 3D compressible quantum liquid

We introduce a new type of 3D compressible quantum phase, in which the U(1) charge conservation symmetry is weakly broken by a rigid string-like order parameter, and no local order parameter exists. We show that this gapless phase is completely stable and described at low energy by an infinite-component Chern-Simons-Maxwell theory. We determine the emergent symmetry group, which contains U(1) 0-form planar symmetries and an unusual subgroup of the dual U(1) 1-form symmetry supported on cylindrical surfaces. Through the associated 't Hooft anomaly, we examine how the filling condition is fulfilled in the low-energy theory. We also demonstrate that the phase exhibits a kind of fractonic topological order, signified by extensively many different types of topologically nontrivial quasiparticles formed out of vortices of the weak superfluid. A microscopic model realizing the weak superfluid phase is constructed using an array of strongly coupled Luttinger liquid wires, and the connection to the field theory is established through boson-vortex duality.

cond-mat.str-el↗

arXiv2021

Fractionalized conductivity and emergent self-duality near topological phase transitions

The experimental discovery of the fractional Hall conductivity in two-dimensional electron gases revealed new types of quantum particles, called anyons, which are beyond bosons and fermions as they possess fractionalized exchange statistics. These anyons are usually studied deep inside an insulating topological phase. It is natural to ask whether such fractionalization can be detected more broadly, say near a phase transition from a conventional to a topological phase. To answer this question, we study a strongly correlated quantum phase transition between a topological state, called a $\mathbb{Z}_2$ quantum spin liquid, and a conventional superfluid using large-scale quantum Monte Carlo simulations. Our results show that the universal conductivity at the quantum critical point becomes a simple fraction of its value at the conventional insulator-to-superfluid transition. Moreover, a dynamically self-dual optical conductivity emerges at low temperatures above the transition point, indicating the presence of the elusive vison particles. Our study opens the door for the experimental detection of anyons in a broader regime, and has ramifications in the study of quantum materials, programmable quantum simulators, and ultra-cold atomic gases. In the latter case, we discuss the feasibility of measurements in optical lattices using current techniques.

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