arXiv subjects

Zheng Zhou

Publications and source records attributed to Zheng Zhou.

At least 73 records · Page 4Linked to original sources

arXiv2024

The $g$-function and Defect Changing Operators from Wavefunction Overlap on a Fuzzy Sphere

Defects are common in physical systems with boundaries, impurities or extensive measurements. The interaction between bulk and defect can lead to rich physical phenomena. Defects in gapless phases of matter with conformal symmetry usually flow to a defect conformal field theory (dCFT). Understanding the universal properties of dCFTs is a challenging task. In this paper, we propose a computational strategy applicable to a line defect in arbitrary dimensions. Our main assumption is that the defect has a UV description in terms of a local modification of the Hamiltonian so that we can compute the overlap between low-energy eigenstates of a system with or without the defect insertion. We argue that these overlaps contain a wealth of conformal data, including the $g$-function, which is an RG monotonic quantity that distinguishes different dCFTs, the scaling dimensions of defect creation operators $Δ^{+0}_α$ and changing operators $Δ^{+-}_α$ that live on the intersection of different types of line defects, and various OPE coefficients. We apply this method to the fuzzy sphere regularization of 3D CFTs and study the magnetic line defect of the 3D Ising CFT. Using exact diagonalization and DMRG, we report the non-perturbative results $g=0.602(2),Δ^{+0}_0=0.108(5)$ and $Δ^{+-}_0=0.84(5)$ for the first time. We also obtain other OPE coefficients and scaling dimensions. Our results have significant physical implications. For example, they constrain the possible occurrence of spontaneous symmetry breaking at line defects of the 3D Ising CFT. Our method can be potentially applied to various other dCFTs, such as plane defects and Wilson lines in gauge theories.

hep-th↗

arXiv2024

BACON: Bayesian Optimal Condensation Framework for Dataset Distillation

Dataset Distillation (DD) aims to distill knowledge from extensive datasets into more compact ones while preserving performance on the test set, thereby reducing storage costs and training expenses. However, existing methods often suffer from computational intensity, particularly exhibiting suboptimal performance with large dataset sizes due to the lack of a robust theoretical framework for analyzing the DD problem. To address these challenges, we propose the BAyesian optimal CONdensation framework (BACON), which is the first work to introduce the Bayesian theoretical framework to the literature of DD. This framework provides theoretical support for enhancing the performance of DD. Furthermore, BACON formulates the DD problem as the minimization of the expected risk function in joint probability distributions using the Bayesian framework. Additionally, by analyzing the expected risk function for optimal condensation, we derive a numerically feasible lower bound based on specific assumptions, providing an approximate solution for BACON. We validate BACON across several datasets, demonstrating its superior performance compared to existing state-of-the-art methods. For instance, under the IPC-10 setting, BACON achieves a 3.46% accuracy gain over the IDM method on the CIFAR-10 dataset and a 3.10% gain on the TinyImageNet dataset. Our extensive experiments confirm the effectiveness of BACON and its seamless integration with existing methods, thereby enhancing their performance for the DD task. Code and distilled datasets are available at BACON.

cs.CV↗

arXiv2024

Sj$\ddot{\text{o}}$qvist quantum geometric tensor of finite-temperature mixed states

The quantum geometric tensor (QGT) reveals local geometric properties and associated topological information of quantum states. Here a generalization of the QGT to mixed quantum states at finite temperatures based on the Sj$\ddot{\text{o}}$qvist distance is developed. The resulting Sj$\ddot{\text{o}}$qvist QGT is invariant under gauge transformations of individual spectrum levels of the density matrix. A Pythagorean-like relation connects the distances and gauge transformations, which clarifies the role of the parallel-transport condition. The real part of the QGT naturally decomposes into a sum of the Fisher-Rao metric and Fubini-Study metric, allowing a distinction between different contributions to the quantum distance. The imaginary part of the QGT is proportional to a weighted summation of the Berry curvatures, which leads to a geometric phase for mixed states under certain conditions. We present three examples of different dimensions to illustrate the temperature dependence of the QGT and a discussion on possible implications.

quant-ph↗

arXiv2024

Ultrafast Electron Diffraction with MeV Electron Source from a Laser Wakefield Accelerator

MeV ultrafast electron diffraction (UED) is a widely used technology for ultrafast structural dynamic studies of matters in numerous areas. The development of laser wakefield accelerator (LWFA) envisions great potential of advanced all-optical electron source based on LWFA in UED applications. We experimentally demonstrated that an LWFA-based device with a miniaturized permanent magnet beamline can generate and manipulate electron beams suitable for UED. In the beam transmission, the LWFA electron beams with intrinsic short duration stretch due to energy spread and then are compressed by a following double bend achromat. The optimized double bend achromat can make the beamline isochronous such that the arrival time jitter induced by the shot-to-shot energy fluctuation can be eliminated, and allow the advantage of the natural laser-beam synchronization for LWFAs to emerge. With the energy filtering, the beam energy spread can be reduced to 3% (FWHM) while a sufficient amount of charge (11.9 fC) per bunch for diffraction is retained. Start-to-end simulations showed that the bunch length reaches ~30 fs (rms) with the same experimental configuration. Clear single-shot and multi-shot diffraction patterns of single-crystalline gold samples are obtained and the derived lattice constant agrees excellently with the real value. Our proof-of-principle experiments open the door to the detection of ultrafast structural dynamics using MeV LWFA beams, and pave the way for the UED applications with sub-10-fs temporal resolution.

physics.acc-ph↗

arXiv2024

On the Connection between the Repeated X-ray Quasi-periodic Oscillation and Warm Absorber in the Active Galaxy RE~J1034+396

We conduct an in-depth spectral analysis of $\sim1{\rm ~Ms}$ XMM-Newton data of the narrow line Seyfert 1 galaxy RE J1034+396. The long exposure ensures high spectral quality and provides us with a detailed look at the intrinsic absorption and emission features toward this target. Two warm-absorber (WA) components with different ionization states ($\log (ξ/{\rm erg~cm~s}^{-1}) \sim 4$ and $\log (ξ/{\rm erg~cm~s}^{-1}) \sim 2.5-3$) are required to explain the intrinsic absorption features in the RGS spectra. The estimated outflow velocities are around $-1400{\rm ~km~s}^{-1}$ and $-(100-300){\rm ~km~s}^{-1}$ for the high- and low-ionization WA components, respectively. Both absorbers are located beyond the broad-line region and cannot significantly affect the host environment. We analyze the warm absorbers in different flux states. We also examine the May-2007 observation in the low and high phases of quasi-periodic oscillation (QPO). In contrast to previous analyses showing a negative correlation between the high-ionization WA and the QPO phase, we have found no such variation in this WA component. We discover a broad emission bump in the spectral range of $\sim12-18$ Angstrom, covering the primary features of the high-ionization WA. This emission bump shows a dramatic change in different source states, and its intensity may positively correlate with the QPO phase. The absence of this emission bump in previous work may contribute to the suggested WA-QPO connection.

astro-ph.HE↗

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

Interferometric Geometric Phases of $\mathcal{PT}$-symmetric Quantum Mechanics

We present a generalization of the geometric phase to pure and thermal states in $\mathcal{PT}$-symmetric quantum mechanics (PTQM) based on the approach of the interferometric geometric phase (IGP). The formalism first introduces the parallel-transport conditions of quantum states and reveals two geometric phases, $θ^1$ and $θ^2$, for pure states in PTQM according to the states under parallel-transport. Due to the non-Hermitian Hamiltonian in PTQM, $θ^1$ is complex and $θ^2$ is its real part. The imaginary part of $θ^1$ plays an important role when we generalize the IGP to thermal states in PTQM. The generalized IGP modifies the thermal distribution of a thermal state, thereby introducing effective temperatures. At certain critical points, the generalized IGP exhibits discrete jumps at finite temperatures, signaling a geometric phase transition. We demonstrate the finite-temperature geometric phase transition in PTQM by a two-level system and visualize its results.

quant-ph↗

arXiv2023

Geometric phases of mixed quantum states: A comparative study of interferometric and Uhlmann phases

Two geometric phases of mixed quantum states, known as the interferometric phase and Uhlmann phase, are generalizations of the Berry phase of pure states. After reviewing the two geometric phases and examining their parallel-transport conditions, we specify a class of cyclic processes that are compatible with both conditions and therefore accumulate both phases through their definitions, respectively. Those processes then facilitate a fair comparison between the two phases. We present exact solutions of two-level and three-level systems to contrast the two phases. While the interferometric phase exhibits finite-temperature transitions only in the three-level system but not the two-level system, the Uhlmann phase shows finite-temperature transitions in both cases. Thus, using the two geometric phases as finite-temperature topological indicators demonstrates the rich physics of topology of mixed states.

quant-ph↗

arXiv2023

Quantum optimization within lattice gauge theory model on a quantum simulator

Simulating lattice gauge theory (LGT) Hamiltonian and its nontrivial states by programmable quantum devices has attracted numerous attention in recent years. Rydberg atom arrays constitute one of the most rapidly developing arenas for quantum simulation and quantum computing. The $\mathbb{Z}_2$ LGT and topological order has been realized in experiments while the $U(1)$ LGT is being worked hard on the way. States of LGT have local constraint and are fragmented into several winding sectors with topological protection. It is therefore difficult to reach the ground state in target sector for experiments, and it is also an important task for quantum topological memory. Here, we propose a protocol of sweeping quantum annealing (SQA) for searching the ground state among topological sectors. With the quantum Monte Carlo method, we show that this SQA has linear time complexity of size with applications to the antiferromagnetic transverse field Ising model, which has emergent $U(1)$ gauge fields. This SQA protocol can be realized easily on quantum simulation platforms such as Rydberg array and D-wave annealer. We expect this approach would provide an efficient recipe for resolving the topological hindrances in quantum optimization and the preparation of quantum topological state.

quant-ph↗

arXiv2023

X-Ray Detection of the Galaxy's Missing Baryons in the Circum-Galactic Medium of L$^*$ Galaxies

The amount of baryons hosted in the disks of galaxies is lower than expected based on the mass of their dark-matter halos and the fraction of baryon-to-total matter in the universe, giving rise to the so called galaxy missing-baryon problem. The presence of cool circum-galactic matter gravitationally bound to its galaxy's halo up to distances of at least ten times the size of the galaxy's disk, mitigates the problem but is far from being sufficient for its solution. It has instead been suggested, that the galaxy missing baryons may hide in a much hotter gaseous phase of the circum-galactic medium, possibly near the halo virial temperature and co-existing with the cool phase. Here we exploit the best available X-ray spectra of known cool circum-galactic absorbers of L$^*$ galaxies to report the first direct high-statistical-significance (best estimates ranging from $4.2-5.6σ$, depending on fitting methodology)} detection of associated OVII absorption in the stacked XMM and Chandra spectra of three quasars. We show that these absorbers trace hot medium in the X-ray halo of these systems, at logT(in k)$\simeq 5.8-6.3$ K (comprising the halo virial temperature T$_{vir} \simeq 10^6$ K). We estimate masses of the X-ray halo within 1 virial radius within the interval M$_{hot-CGM}\simeq (1-1.7)\times 10^{11} (Z/0.3 Z_{\odot})^{-1}$ M$_{\odot}$. For these systems, this corresponds to galaxy missing baryon fractions in the range $ξ_b = M_{hot-CGM}/M_{missing}\simeq (0.7-1.2) (Z/0.3 Z_{\odot})^{-1}$, thus potentially closing the galaxy baryon census in typical L$^*$ galaxies. Our measurements contribute significantly to the solution of the long-standing galaxy missing baryon problem and to the understanding of the continuous cycle of baryons in-and-out of galaxies throughout the life of the universe.

astro-ph.GA↗

arXiv2023

Slightly broken higher-spin current in bosonic and fermionic QED in the large-$N$ limit

We study the slightly broken higher-spin currents in various CFTs with $\mathrm{U}(1)$ gauge field, including the tricritical QED, scalar QED, fermionic QED and QED-Gross-Neveu-Yukawa theory. We calculate their anomalous dimension by making use of the classical non-conservation equation and the equations of motion. We find a logarithmic asymptotic behaviour ($γ_s\sim 16/(Nπ^2) \log s $) of the anomalous dimension at large spin $s$, which is different from other interacting CFTs without gauge fields and may indicate certain unique features of gauge theories. We also study slightly broken higher-spin currents of the $\mathrm{SU}(N)_1$ WZW model at $d=2+ε$ dimensions by formulating them as the QED theory, and we again find its anomalous dimension has a logarithmic asymptotic behaviour with respect to spin. This result resolves the mystery regarding the mechanism of breaking higher spin currents of Virasoro symmetry at $d=2+ε$ dimensions, and may be applicable to other interesting problems such as the $2+ε$ expansion of Ising CFT.

hep-th↗

arXiv2022

Uhlmann phase of coherent states and the Uhlmann-Berry correspondence

We first compare the geometric frameworks behind the Uhlmann and Berry phases in a fiber-bundle language and then evaluate the Uhlmann phases of bosonic and fermionic coherent states. The Uhlmann phases of both coherent states are shown to carry geometric information and decrease smoothly with temperature. Importantly, the Uhlmann phases approach the corresponding Berry phases as temperature decreases. Together with previous examples in the literature, we propose a correspondence between the Uhlmann and Berry phases in the zero-temperature limit as a general property except some special cases and present a conditional proof of the correspondence.

quant-ph↗

arXiv2022

Quantum tricriticality of incommensurate phase induced by quantum domain walls in frustrated Ising magnetism

Incommensurability plays a critical role in many strongly correlated systems. In some cases, the origin of such exotic order can be theoretically understood in the framework of 1d line-like topological excitations known as ``quantum strings''. Here we study an extended transverse field Ising model on a triangular lattice. Using the large scale quantum Monte Carlo simulations, we find that the spatial anisotropy can stabilize an incommensurate phase out of the commensurate clock order. Our results for the structure factor and the string density exhibit a linear relationship between incommensurate ordering wave vector and the density of quantum strings, which is reminiscent of hole density in under-doped cuprate superconductors. When introducing the next-nearest-neighbor interaction, we observe a quantum tricritical point out of the incommensurate phase. After carefully analyzing the ground state energies within different string topological sectors, we conclude that this tricriticality is non-trivially caused by effective long-range inter-string interactions with two competing terms following different decaying behaviors.

cond-mat.str-el↗

arXiv2022

Model-free Subsampling Method Based on Uniform Designs

Subsampling or subdata selection is a useful approach in large-scale statistical learning. Most existing studies focus on model-based subsampling methods which significantly depend on the model assumption. In this paper, we consider the model-free subsampling strategy for generating subdata from the original full data. In order to measure the goodness of representation of a subdata with respect to the original data, we propose a criterion, generalized empirical F-discrepancy (GEFD), and study its theoretical properties in connection with the classical generalized L2-discrepancy in the theory of uniform designs. These properties allow us to develop a kind of low-GEFD data-driven subsampling method based on the existing uniform designs. By simulation examples and a real case study, we show that the proposed subsampling method is superior to the random sampling method. Moreover, our method keeps robust under diverse model specifications while other popular subsampling methods are under-performing. In practice, such a model-free property is more appealing than the model-based subsampling methods, where the latter may have poor performance when the model is misspecified, as demonstrated in our simulation studies.

stat.ME↗

arXiv2022

Generalizations of Berry phase and differentiation of purified state and thermal vacuum of mixed states

Two representations of mixed states by state-vectors, known as purified state and thermal vacuum, have been realized on quantum computers. While the two representations look similar, they differ by a partial transposition in the ancilla space. While ordinary observables cannot discern the two representations, we generalize the Berry phase of pure quantum states to mixed states and construct two geometric phases that can reflect the partial transposition. By generalizing the adiabatic condition, we construct the thermal Berry phase, whose values from the two representations can be different, However, the thermal Berry phase may contain non-geometrical contributions. Alternatively, we generalize the parallel-transport condition to include the system and ancilla and show the dynamical phase is excluded under parallel transport. The geometrical phase accumulated in parallel transport is the generalized Berry phase, which may or may not differentiate a purified state from a thermal vacuum depending on the protocol. The generalizations of the Berry phase to mixed states may be realized and measured on quantum computers via the two representations to reveal the rich physics of finite-temperature quantum systems.

quant-ph↗

arXiv2022

EEG4Students: An Experimental Design for EEG Data Collection and Machine Learning Analysis

Using Machine Learning and Deep Learning to predict cognitive tasks from electroencephalography (EEG) signals has been a fast-developing area in Brain-Computer Interfaces (BCI). However, during the COVID-19 pandemic, data collection and analysis could be more challenging. The remote experiment during the pandemic yields several challenges, and we discuss the possible solutions. This paper explores machine learning algorithms that can run efficiently on personal computers for BCI classification tasks. The results show that Random Forest and RBF SVM perform well for EEG classification tasks. Furthermore, we investigate how to conduct such BCI experiments using affordable consumer-grade devices to collect EEG-based BCI data. In addition, we have developed the data collection protocol, EEG4Students, that grants non-experts who are interested in a guideline for such data collection. Our code and data can be found at https://github.com/GuangyaoDou/EEG4Students.

cs.LG↗

arXiv2022

Unbalanced-basis-misalignment tolerant measurement-device-independent quantum key distribution

Measurement-device-independent quantum key distribution (MDIQKD) is a revolutionary protocol since it is physically immune to all attacks on the detection side. However, the protocol still keeps the strict assumptions on the source side that the four BB84-states must be perfectly prepared to ensure security. Some protocols release part of the assumptions in the encoding system to keep the practical security, but the performance would be dramatically reduced. In this work, we present a MDIQKD protocol that requires less knowledge of encoding system to combat the troublesome modulation errors and fluctuations. We have also experimentally demonstrated the protocol. The result indicates the high-performance and good security for its practical applications. Besides, its robustness and flexibility exhibit a good value for complex scenarios such as the QKD networks.

quant-ph↗

arXiv2022

BrainActivity1: A Framework of EEG Data Collection and Machine Learning Analysis for College Students

Using Machine Learning and Deep Learning to predict cognitive tasks from electroencephalography (EEG) signals has been a fast-developing area in Brain-Computer Interfaces (BCI). However, during the COVID-19 pandemic, data collection and analysis could be more challenging than before. This paper explored machine learning algorithms that can run efficiently on personal computers for BCI classification tasks. Also, we investigated a way to conduct such BCI experiments remotely via Zoom. The results showed that Random Forest and RBF SVM performed well for EEG classification tasks. The remote experiment during the pandemic yielded several challenges, and we discussed the possible solutions; nevertheless, we developed a protocol that grants non-experts who are interested a guideline for such data collection.

cs.DB↗