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Efimov effect in Dirac semi-metals

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Frontiers of physics 2018年第5期13卷 55-61页

作者： Pengfei Zhang hui zhai Institute for Advanced Study Tsinghua University Beijing 100084 China Collaborative Innovation Center of Quantum Matter Beijing 100084 China

The Efimov effect is defined as a quantum state with discrete scaling symmetry and a universal scaling factor. It has attracted considerable interests from nuclear to atomic physics communities. In a Dirac semi-metal, when an electron interacts with a static impurity through a Coulombic interaction, the same kinetic scaling and the interaction energy results in the Efimov effect. However, even when the Fermi energy lies exactly at the Dirac point, the vacuum polarization of the electron-hole pair fluctuation can still screen the Coulombic interaction, which leads to deviations from the scaling symmetry and eventually breaks down of the Efimov effect. This energy distortion of the Efimov states due to vacuum polarization is a relativistic electron analogy of the Lamb shift for the hydrogen atom. Motivated by the recent experimental observations in two- and three-dimensional Dirac semi-metals, we herein investigate this many-body correction to the Efimov effect and the conditions that allow some of the Efimov-like quasi-bound states to be observed in these condensed matter experiments.

关键词： Dirac semi-metal Efimov effect screening

Machine learning of frustrated classical spin models （II）： Kernel principal component analysis

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Frontiers of physics 2018年第5期13卷 23-29页

作者： Ce Wang hui zhai Institute for Advanced Study Tsinghua University Beijing 100084 China Collaborative Innovation Center of Quantum Matter Beijing 100084 China

In this work, we apply a principal component analysis （PCA） method with a kernel trick to study the classification of phases and phase transitions in classical XY models of frustrated lattices. Compared to our previous work with the linear PCA method, the kernel PCA can capture nonlinear functions. In this case, the Z2 chiral order of the classical spins in these lattices is indeed a nonlinear function of the input spin configurations. In addition to the principal component revealed by the linear PCA, the kernel PCA can find two more principal components using the data generated by Monte Carlo simulation for various temperatures as the input. One of them is related to the strength of the U（1） order parameter, and the other directly manifests the chiral order parameter that characterizes the Z2 symmetry breaking. For a temperature-resolved study, the temperature dependence of the principal eigenvalue associated with the Z2 symmetry breaking clearly shows second-order phase transition behavior.

关键词： machine learning classical XY model kernel PCA frustrated lattice

Emergent symmetry at superradiance transition of a Bose condensate in two crossed beam cavities

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Science Bulletin 2018年第9期63卷 542-547页

作者： Zhigang Wu Yu Chen hui zhai Shenzhen Institute for Quantum Science and Engineering and Department of Physics Southern University of Science and Technology Shenzhen 518000 China Institute for Advanced Study Tsinghua University Beijing 100084 China Department of Physics Capital Normal University Beijing 100048 China Collaborative Innovation Center of Quantum Matter Beijing 100084 China

Recently an experiment on superradiant transition of a Bose condensate in two crossed beam cavities has been reported by Leonard et al. in Nature 543, 87 （2017）. The surprise is they find that across the superradiant transition, the cavity light can be emitted in any superposition of these two cavity modes. This indicates an additional U（1） symmetry that does not exist in the full Hamiltonian. In this paper we show that this symmetry is an emergent symmetry in the vicinity of the phase transition. We identify all the necessary conditions that are required for this emergent U（I ） symmetry and show that this experiment is a special case that satisfies these conditions. We further show that the superradiant transition in this system can also be driven to a first order one when the system is tuned away from the point having the emergent svmmetrv.

关键词： Bose-Einstein condensate Emergent symmetry Superradiance transition Cavity

Scaling symmetry meets topology

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Science Bulletin 2019年第5期64卷 289-290页

作者： Pengfei Zhang hui zhai Institute for Advanced Study Tsinghua University

In 1970,Vitaly Efimov found an interesting phenomenon in a quantum three-body problem,which is now known as the Efimov *** found that when the two-body in teraction potential is short-ranged and is tuned to the vicinity of an s-wave resonance,an inhnite number of three-body bound states emerge and their eigenenergies En form a geometric sequence as En=-|Eo|exp(—2m/So).

关键词： Scaling symmetry meets topology In 1970

Emergent Schr?dinger equation in an introspective machine learning architecture

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Science Bulletin 2019年第17期64卷 1228-1233页

作者： Ce Wang hui zhai Yi-Zhuang You Institute for Advanced Study Tsinghua University Beijing 100084 China Department of Physics University o f California San Diego CA 92093 USA

Can physical concepts and laws emerge in a neural network as it learns to predict the observation data of physical systems? As a benchmark and a proof-of-principle study of this possibility, here we show an introspective learning architecture that can automatically develop the concept of the quantum wave function and discover the Schr?dinger equation from simulated experimental data of the potential-todensity mappings of a quantum particle. This introspective learning architecture contains a machine translator to perform the potential to density mapping, and a knowledge distiller auto-encoder to extract the essential information and its update law from the hidden states of the translator, which turns out to be the quantum wave function and the Schr?dinger equation. We envision that our introspective learning architecture can enable machine learning to discover new physics in the future.

关键词： Quantum physics Machine learning Potential-to-density mapping Neural network Recurrent autoencoder

The quantum cocktail party problem

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Science China(Physics,Mechanics & Astronomy) 2020年第5期63卷 2-5页

作者： Xiao Liang YaDong Wu hui zhai Institute for Advanced Study Tsinghua UniversityBeijing 100084China Laboratory of Quantum Information University of Science and Technology of ChinoHefei 230026China

The cocktail party problem refers to the phenomenon that the brain of a listener can focus on a single voice while filtering out a range of other voices in a multi-talker situation,say,in a cocktail party[1].This selective attention problem was firstly defined as the"cocktail party problem"(CPP)by Cherry[2]in *** recent years,machine-learning based approaches to solve the CPP were essential for many industrial applications such as automated speech *** independent component analysis(ICA)is such an algorithm particularly suitable for the *** CPP also has applications in physical science such as astrophysics data analysis[3,4].

关键词： quantum problem filtering

Out-of-time-order correlation for many-body localization

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Science Bulletin 2017年第10期62卷 707-711页

作者： Ruihua Fan Pengfei Zhang huitao Shen hui zhai lnstitute for Advanced Study Tsinghua University Beijing 100084 China Department of Physics Peking University Beijing 100871 China Department of Physics Massachusetts Institute of Technology Cambridge MA 02139 USA Collaborative Innovation Center of Quantum Matter Beijing 100084 China

In this paper we first compute the out-of-time-order correlators （OTOC） for both a phenomenological model and a random-field XXZ model in the many-body localized phase. We show that the OTOC decreases in power law in a many-body localized system at the scrambling time. We also find that the OTOC can also be used to distinguish a many-body localized phase from an Anderson localized phase, while a normal correlator cannot. Furthermore, we prove an exact theorem that relates the growth of the second Renyi entropy in the quench dynamics to the decay of the OTOC in equilibrium. This theorem works for a generic quantum system. We discuss various implications of this theorem.

关键词： Out-of-time-order correlationMany-body localizationR6nyi entropy

Low-Complexity DOA Estimation of Noncircular Signals for Coprime Sensor Arrays

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Transactions of Nanjing University of Aeronautics and Astronautics 2019年第4期36卷 599-608页

作者： zhai hui CHEN Weiyang ZHANG Xiaofei ZHENG Wang College of Electronic and Information Engineering Nanjing University of Aeronautics and AstronauticsNanjing 210016P.R.China

This paper presents a low?complexity method for the direction?of?arrival(DOA)estimation of noncircular signals for coprime sensor *** noncircular property is exploited to improve the performance of DOA *** reduce the computational complexity,the rotational invariance propagator method(RIPM)is included in the ***,the extended array output is reconstructed by combining the array output and its conjugated ***,the RIPM is utilized to obtain two sets of DOA estimates for two ***,the true DOAs are estimated by combining the consistent results of the two *** illustrates the potential gain that both noncircularity and coprime arrays provide when considered *** proposed algorithm has a lower computational complexity and a better DOA estimation performance than the standard estimation of signal parameters by the rotational invariance technique and Capon *** simulation results illustrate the effectiveness and superiority of the proposed algorithm.

关键词： sensor array direction of arrival estimation coprime sensor arrays noncircular signals rotational invariance propagator method

The Characterization of p-factor-critical Graphs

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Acta Mathematicae Applicatae Sinica 2022年第1期38卷 154-158页

作者： Shao-hui zhai Er-ling WEI Fu-ji ZHANG School of Applied Mathematics Xiamen University of TechnologyXiamen 361024China School of Mathematics Renmin University of ChinaBeijing 100872China School of Mathematical Sciences Xiamen UniversityXiamen 361005China

A graph G is said to be p-factor-critical if G-u1-u2-···-up has a perfect matching for any u1,u2,···,up∈V(G).The concept of p-factor-critical is a generalization of the concepts of factor-critical and bicritical for p=1 and p=2,*** Zhang and Fuji Zhang[Construction for bicritical graphs and k-extendable bipartite graphs,Discrete Math.,306(2006)1415–1423]gave a concise structure characterization of bicritical *** this paper,we present the characterizations of p-factor-critical graphs and minimal p-factorcritical graphs for p≥*** an application,we also obtain a class of graphs which are minimal p-factor-critical for p≥1.

关键词： perfect matching,p-factor-critical graph transversal