arXiv subjects

W. Zhu

Publications and source records attributed to W. Zhu.

At least 37 records · Page 2Linked to original sources

arXiv2024

Entropic $F$-function of 3D Ising conformal field theory via the fuzzy sphere regularization

The $F$-function, the three-dimensional counterpart of the central charge in the 2D conformal field theory, measures the effective number of degrees of freedom in 3D quantum field theory, and it is monotonically decreasing under the renormalization group flow. However, unlike the 2D central charge, the $F$-function is a non-local quantity and cannot be computed using correlators of local operators. Utilizing the recently proposed fuzzy sphere regularization, we have performed the first non-perturbative computation of the $F$-function for the paradigmatic 3D Ising conformal field theory through entanglement entropy. Our estimate yields $F_{\text{Ising}} \approx 0.0612(5)$, slightly smaller than the $F$-function of a real free scalar, $F_{\text{free}} = \frac{\log 2}{8} - \frac{3ζ(3)}{16π^2} \approx 0.0638$, consistent with the $F$-theorem, and close to the $4-ε$ expansion estimates of $F_{\text{Ising}} \approx 0.0610 \sim 0.0623$.

hep-th↗

arXiv2024

The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum

The deconfined quantum critical point (DQCP) is an example of phase transitions beyond the Landau symmetry breaking paradigm that attracts wide interest. However, its nature has not been settled after decades of study. In this paper, we apply the recently proposed fuzzy sphere regularization to study the $\mathrm{SO}(5)$ non-linear sigma model (NL$σ$M) with a topological Wess-Zumino-Witten term, which serves as a dual description of the DQCP with an exact $\mathrm{SO}(5)$ symmetry. We demonstrate that the fuzzy sphere functions as a powerful microscope, magnifying and revealing a wealth of crucial information about the DQCP, ultimately paving the way towards its final answer. In particular, through exact diagonalization, we provide clear evidence that the DQCP exhibits approximate conformal symmetry. The evidence includes the existence of a conserved $\mathrm{SO}(5)$ symmetry current, a stress tensor, and integer-spaced levels between conformal primaries and their descendants. Most remarkably, we have identified 23 primaries and 76 conformal descendants. Furthermore, by examining the renormalization group flow of the lowest symmetry singlet as well as other primaries, we provide numerical evidence in favour of DQCP being pseudo-critical, with the approximate conformal symmetry plausibly emerging from nearby complex fixed points. The primary spectrum we compute also has important implications, including the conclusion that the $\mathrm{SO}(5)$ DQCP cannot describe a direct transition from the Néel to valence bond solid phase on the honeycomb lattice.

cond-mat.str-el↗

arXiv2024

Self-organizing Nervous Systems for Robot Swarms

The system architecture controlling a group of robots is generally set before deployment and can be either centralized or decentralized. This dichotomy is highly constraining, because decentralized systems are typically fully self-organized and therefore difficult to design analytically, whereas centralized systems have single points of failure and limited scalability. To address this dichotomy, we present the Self-organizing Nervous System (SoNS), a novel robot swarm architecture based on self-organized hierarchy. The SoNS approach enables robots to autonomously establish, maintain, and reconfigure dynamic multi-level system architectures. For example, a robot swarm consisting of $n$ independent robots could transform into a single $n$-robot SoNS and then into several independent smaller SoNSs, where each SoNS uses a temporary and dynamic hierarchy. Leveraging the SoNS approach, we show that sensing, actuation, and decision-making can be coordinated in a locally centralized way, without sacrificing the benefits of scalability, flexibility, and fault tolerance, for which swarm robotics is usually studied. In several proof-of-concept robot missions -- including binary decision-making and search-and-rescue -- we demonstrate that the capabilities of the SoNS approach greatly advance the state of the art in swarm robotics. The missions are conducted with a real heterogeneous aerial-ground robot swarm, using a custom-developed quadrotor platform. We also demonstrate the scalability of the SoNS approach in swarms of up to 250 robots in a physics-based simulator, and demonstrate several types of system fault tolerance in simulation and reality.

cs.RO↗

arXiv2024

Chirality-2 fermion induced anti-Klein tunneling in 2D checkerboard lattice

The quantum tunneling effect in the two-dimensional (2D) checkerboard lattice is investigated. By analyzing the pseudospin texture of the states in a 2D checkerboard lattice based on the low-energy effective Hamiltonian, we find that this system has a chiral symmetry with chirality equal to 2. Although compared to regular chiral fermions, its pseudospin orientation does not vary uniformly. This suggests that the perfect reflection chiral tunneling, also known as the anti-Klein tunneling, is expected to appear in checkerboard lattice as well. In order to verify the conjecture, we calculate the transmission probability and find that normally incident electron states can be perfectly reflected by the barrier with hole states inside, and vice versa. Furthermore, we also numerically calculate the tunneling conductance of the checkerboard nanotube using the recursive Green's function method. The results show that a perfect on-off ratio can be achieved by confining the energy of the incident states within a certain range. It also suggests that, by tuning the barrier, the checkerboard nanotube is able to work as a perfect ``band filter" or ``tunneling field effect transistor", which transmits electrons selectively with respect to the pseudospin of the incident electrons.

cond-mat.mes-hall↗

arXiv2024

Universal entanglement signatures of interface conformal field theories

An interface connecting two distinct conformal field theories hosts rich critical behaviors. In this work, we investigate the entanglement properties of such critical interface theories for probing the underlying universality. As inspired by holographic perspectives, we demonstrate vital features of various entanglement measures regarding such interfaces based on several paradigmatic lattice models. Crucially, for two subsystems adjacent at the interface, the mutual information and the reflected entropy exhibit identical leading logarithmic scaling, giving an effective interface central charge that takes the same value as the smaller central charge of the two conformal field theories. Our work demonstrates that the entanglement measure offers a powerful tool to explore the rich physics in critical interface theories.

cond-mat.stat-mech↗

arXiv2023

Long-Term Rate-Fairness-Aware Beamforming Based Massive MIMO Systems

This is the first treatise on multi-user (MU) beamforming designed for achieving long-term rate-fairness in fulldimensional MU massive multi-input multi-output (m-MIMO) systems. Explicitly, based on the channel covariances, which can be assumed to be known beforehand, we address this problem by optimizing the following objective functions: the users' signal-toleakage-noise ratios (SLNRs) using SLNR max-min optimization, geometric mean of SLNRs (GM-SLNR) based optimization, and SLNR soft max-min optimization. We develop a convex-solver based algorithm, which invokes a convex subproblem of cubic time-complexity at each iteration for solving the SLNR maxmin problem. We then develop closed-form expression based algorithms of scalable complexity for the solution of the GMSLNR and of the SLNR soft max-min problem. The simulations provided confirm the users' improved-fairness ergodic rate distributions.

cs.IT↗

arXiv2023

Conformal Operator Content of the Wilson-Fisher Transition on Fuzzy Sphere Bilayers

The Wilson-Fisher criticality provides a paradigm for a large class of phase transitions in nature (e.g., helium, ferromagnets). In the three dimension, Wilson-Fisher critical points are not exactly solvable due to the strongly-correlated feature, so one has to resort to non-perturbative tools such as numerical simulations. Here, we design a microscopic model of Heisenberg magnet bilayer and study the underlying Wilson-Fisher $\mathrm{O}(3)$ transition through the lens of fuzzy sphere regularization. We uncover a wealth of crucial information which directly reveals the emergent conformal symmetry regarding this fixed point. In specific, we accurately calculate and analyze the energy spectra at the transition, and explicitly identify the existence of a conserved Noether current, a stress tensor and relevant primary fields. Most importantly, the primaries and their descendants form a fingerprint conformal tower structure, pointing to an almost perfect state-operator correspondence. Furthermore, by examining the leading rank-4 symmetric tensor operator, we demonstrate the cubic perturbation is relevant, implying the critical $\mathrm{O}(3)$ model is unstable to cubic anisotropy, in agreement with the renormalization group and bootstrap calculations. The successful dissection of conformal content of the Wilson-Fisher universality class extends the horizon of the fuzzy sphere method and paves the way for exploring higher dimensional conformal field theories.

cond-mat.str-el↗

arXiv2023

Max-min Rate Optimization of Low-Complexity Hybrid Multi-User Beamforming Maintaining Rate-Fairness

A wireless network serving multiple users in the millimeter-wave or the sub-terahertz band by a base station is considered. High-throughput multi-user hybrid-transmit beamforming is conceived by maximizing the minimum rate of the users. For the sake of energy-efficient signal transmission, the array-of-subarrays structure is used for analog beamforming relying on low-resolution phase shifters. We develop a convexsolver based algorithm, which iteratively invokes a convex problem of the same beamformer size for its solution. We then introduce the soft max-min rate objective function and develop a scalable algorithm for its optimization. Our simulation results demonstrate the striking fact that soft max-min rate optimization not only approaches the minimum user rate obtained by max-min rate optimization but it also achieves a sum rate similar to that of sum-rate maximization. Thus, the soft max-min rate optimization based beamforming design conceived offers a new technique of simultaneously achieving a high individual quality-of-service for all users and a high total network throughput.

cs.IT↗

arXiv2023

Non-Hermitian Parent Hamiltonian from Generalized Quantum Covariance Matrix

Quantum inverse problem is defined as how to determine a local Hamiltonian from a single eigenstate? This question is valid not only in Hermitian system but also in non-Hermitian system. So far, most attempts are limited to Hermitian systems, while the possible non-Hermitian solution remains outstanding. In this work, we generalize the quantum covariance matrix method to the cases that are applicable to non-Hermitian systems, through which we are able to explicitly reconstruct the non-Hermitian parent Hamiltonian from an arbitrary pair of biorthogonal eigenstates. As concrete examples, we successfully apply our approach in spin chain with Lee-Yang singularity and a non-Hermitian interacting fermion model. Some generalization and further application of our approach are also discussed. Our work provides a systematical and efficient way to construct non-Hermitian Hamiltonian from a single pair of biorthogonal eigenstates and shed light on future exploration on non-Hermitian physics.

quant-ph↗

arXiv2023

Conformal four-point correlators of the 3D Ising transition via the quantum fuzzy sphere

In conformal field theory (CFT), the four-point correlator is a fundamental object that encodes CFT properties, constrains CFT structures, and connects to the gravitational scattering amplitude in holography theory. However, the four-point correlator of CFTs in dimensions higher than 2D remains largely unexplored due to the lack of non-perturbative tools. In this paper, we introduce a new approach for directly computing four-point correlators of 3D CFTs. Our method employs the recently proposed fuzzy (non-commutative) sphere regularization, and we apply it to the paradigmatic 3D Ising CFT. Specifically, we have computed three different four-point correlators: $\langle σσσσ\rangle$, $\langle σσεε\rangle$, and $\langle σσT_{μν} T_{ρη}\rangle$. Additionally, we verify the crossing symmetry of $\langle σσσσ\rangle$, which is a notable property arising from conformal symmetry. Remarkably, the computed four-point correlators exhibit continuous crossing ratios, showcasing the continuum nature of the fuzzy sphere regularization scheme. This characteristic renders them highly suitable for future theoretical applications, enabling further advancements and insights in 3D CFT.

cond-mat.stat-mech↗

arXiv2023

Operator Product Expansion Coefficients of the 3D Ising Criticality via Quantum Fuzzy Sphere

Conformal field theory (CFT) is the key to various critical phenomena. So far, most of studies focus on the critical exponents of various universalities, corresponding to conformal dimensions of CFT primary fields. However, other important yet intricate data such as the operator product expansion (OPE) coefficients governing the fusion of two primary fields, is largely unexplored before, specifically in dimensions higher than 2D (or equivalently $1+1$D). Here, motivated by the recently-proposed fuzzy sphere regularization, we investigate the operator content of 3D Ising criticality starting from a microscopic description. We first outline the procedure of extracting OPE coefficients on the fuzzy sphere, and then compute 13 OPE coefficients of low-lying CFT primary fields. The obtained results are in agreement with the numerical conformal bootstrap data of 3D Ising CFT within a high accuracy. In addition, we also manage to obtain 4 OPE coefficients including $f_{T_{μν} T_{ρη} ε}$ that were not available before, which demonstrates the superior capabilities of our scheme. By expanding the horizon of the fuzzy sphere regularization from the state perspective to the operator perspective, we expect a lot of new physics ready for exploration.

cond-mat.stat-mech↗

arXiv2023

Low-Complexity Pareto-Optimal 3D Beamforming for the Full-Dimensional Multi-User Massive MIMO Downlink

Full-dimensional (FD) multi-user massive multiple input multiple output (m-MIMO) systems employ large two-dimensional (2D) rectangular antenna arrays to control both the azimuth and elevation angles of signal transmission. We introduce the sum of two outer products of the azimuth and elevation beamforming vectors having moderate dimensions as a new class of FD beamforming. We show that this low-complexity class is capable of outperforming 2D beamforming relying on the single outer product of the azimuth and elevation beamforming vectors. It is also capable of performing close to its FD counterpart of massive dimensions in terms of either the users minimum rate or their geometric mean rate (GM-rate), or sum rate (SR). Furthermore, we also show that even FD beamforming may be outperformed by our outer product-based improper Gaussian signaling solution. Explicitly, our design is based on low-complexity algorithms relying on convex problems of moderate dimensions for max-min rate optimization or on closed-form expressions for GM-rate and SR maximization.

cs.IT↗

arXiv2023

Modular transformation and anyonic statistics of multi-component fractional quantum Hall states

We investigate the response to modular transformations and the fractional statistics of Abelian multi-component fractional quantum Hall (FQH) states. In particular, we analytically derive the modular matrices encoding the statistics of anyonic excitations for general Halperin states using the conformal field theories (CFTs). We validate our theory by several microscopic examples, including the spin-singlet state using anyon condensation picture and the Halperin (221) state in a topological flat-band lattice model using numerical calculations. Our results, uncovering that the modular matrices and associated fractional statistics are solely determined by the $K$-matrix, further strengthens the correspondence between the 2D CFTs and (2+1)D topological orders for multi-component FQH states.

cond-mat.str-el↗

arXiv2022

Global quantum phase diagram and non-Abelian chiral spin liquid in a spin-3/2 square lattice antiferromagnet

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.

cond-mat.str-el↗

arXiv2022

Entanglement Entropy of $(2+1)$D Quantum Critical Points with Quenched Disorder: Dimensional Reduction Approach

A formidable perspective in understanding quantum criticality of a given many-body system is through its entanglement contents. Until now, most progress are only limited to the disorder-free case. Here, we develop an efficient scheme to compute the entanglement entropy of $(2+1)$-dimensional quantum critical points with randomness, from a conceptually novel angle where the quenched disorder can be considered as dimensionally reducible interactions. As a concrete example, we reveal novel entanglement signatures of $(2+1)$-dimensional Dirac fermion exposed to a random magnetic field, which hosts a class of emergent disordered quantum critical points. We demonstrate that the entanglement entropy satisfies the area-law scaling, and observe a modification of the area-law coefficient that points to the emergent disordered quantum criticality. Moreover, we also obtain the sub-leading correction to the entanglement entropy due to a finite correlation length. This sub-leading correction is found to be a universal function of the correlation length and disorder strength. We discuss its connection to the renormalization group flows of underlying theories.

cond-mat.str-el↗

arXiv2022

On the sample-dependent minimal conductivity in weakly disordered graphene

We present a unified understanding of the experimentally observed minimal dc conductivity in weakly disordered graphene. Firstly, based on linear response theory, we reveal that randomness or disorder inevitably induces momentum dependent corrections to the electron self-energy function, which naturally yields a sample-dependent minimal conductivity. Taking the long-ranged Gaussian and Coulomb potentials as examples, we derive the momentum dependent self-energy function within the Born approximation, and further validate it via numerical simulations using the large-scale Lanczos algorithm. The explicit momentum dependences of the self-energy on the intensity, concentration and range of potential are critically addressed. Therefore, our results provide a reasonable interpretation of the sample-dependent minimal conductivity observed in graphene samples.

cond-mat.mes-hall↗

arXiv2022

Ferromagnetic Negative Charge-Transfer Insulator: from Theoretical Proposal to Material Realization

Here we propose another type of ferromagnetic semiconductors: ferromagnetic negative charge-transfer insulator (FNCTI). In FNCTI, the negative charge-transfer states strongly enhance the ferromagnetic (FM) exchange interactions and the orbital hybridization gap permits the magnetic molecular orbitals as the underlying magnetic units rather than local atomic orbitals. Thus the FM exchange interactions are rather strong and decay slowly due to the large spearding of magnetic molecular orbitals. This is distinct from the superexchange mechanism where FM exchange interactions are quite weak as summarized in the well-known Goodenough-Kanamori-Anderson semi-empirical rules.Through first-principle calculations with the hybrid functional, PbO-type CrAs monolayer is mapped out to be a FNCTI, which possesses a band gap $\sim$ 0.35 eV, FM nearest-/next-nearest-neighbor exchange coupling strength $\sim$ 57/40 meV, and a high $T_c$ $\sim$ 1500 K respectively. It is believed that the existence of FNCTI validates the long-pending hypothesis by D. I. Khomskii and G. A. Sawatzky in 1997 [Solid State Commun. 102, 87 (1997)].

cond-mat.str-el↗

arXiv2022

Thermal Correction to Entanglement Spectrum for Conformal Field Theories

We calculate the thermal correction to the entanglement spectrum for separating a single interval of two dimensional conformal field theories. Our derivation is a direct extension of the thermal correction to the Rényi entropy. Within a low-temperature expansion by including only the first excited state in the thermal density matrix, we approach analytical results of the thermal correction to the entanglement spectrum at both of the small and large interval limit. We find the temperature correction reduces the large eigenvalues in the entanglement spectrum while increases the small eigenvalues in the entanglement spectrum, leading to an overall crossover changing pattern of the entanglement spectrum. Crucially, at low-temperature limit, the thermal corrections are dominated by the first excited state and depend on its scaling dimension $Δ$ and degeneracy $g$. This opens an avenue to extract universal information of underlying conformal data via the thermal entanglement spectrum. All of these analytical computation is supported from numerical simulations using 1+1 dimensional free fermion. Finally, we extend our calculation to resolve the thermal correction to the symmetry-resolved entanglement spectrum.

hep-th↗