Gapped Spin-1/2 Spinon Excitations in a New Kagome Quantum Spin Liquid Compound Cu_3Zn(OH)_6FBr

We report a new kagome quantum spin liquid candidate CuaZn（OH）6FBr, which does not experience any phase transition down to 50inK, more than three orders lower than the antiferromagnetic Curie-Weiss temperature （-200 K）. A clear gap opening at low temperature is observed in the uniform spin susceptibility obtained from 19F nuclear magnetic resonance measurements. We observe the characteristic magnetic field dependence of the gap as expected for fractionalized spin-1/2 spinon excitations. Our experimental results provide firm evidence for spin fractionalization in a topologically ordered spin system, resembling charge fraetionalization in the fractional quantum Hall state.

泵站深基坑管井降水替代围封结构施工技术

本文主要介绍了针对淮北平原地区复杂地质条件下超厚粉细砂层深基坑开挖施工技术,通过对工程施工区域地质条件的分析研究、施工经济效益、工期及技术方案的可行性等多方面进行比对,采用管井降水能够有效地解决粉细砂层地质深基坑开挖安全问题,为淮北平原复杂地质条件施工提供一定参考。

From Claringbullite to a New Spin Liquid Candidate Cu_3Zn(OH)_6FCl

The search for quantum spin liquid(QSL) materials has attracted significant attention in the field of condensed matter physics in recent years, however so far only a handful of them are considered as candidates hosting QSL ground state. Owning to their geometrically frustrated structures, Kagome materials are ideal systems to realize QSL. We synthesize the kagome structured material claringbullite(Cu_4(OH)_6FCl) and then replace inter-layer Cu with Zn to form Cu_3Zn(OH)_6FCl. Comprehensive measurements reveal that doping Zn^(2+) ions transforms magnetically ordered Cu_4(OH)_6FCl into a non-magnetic QSL candidate Cu_3Zn(OH)_6FCl. Therefore,the successful syntheses of Cu_4(OH)_6FCl and Cu_3Zn(OH)_6FCl provide not only a new platform for the study of QSL but also a novel pathway of investigating the transition between QSL and magnetically ordered systems.

Emergent O(4) symmetry at the phase transition from plaquette-singlet to antiferromagnetic order in quasi-two-dimensional quantum magnets

Recent experiments [Guo et al., Phys. Rev. Lett. 124 206602(2020)] on thermodynamic properties of the frustrated layered quantum magnet SrCu_(2)(BO_(3))_(2)-the Shastry–Sutherland material-have provided strong evidence for a lowtemperature phase transition between plaquette-singlet and antiferromagnetic order as a function of pressure. Further motivated by the recently discovered unusual first-order quantum phase transition with an apparent emergent O(4) symmetry of the antiferromagnetic and plaquette-singlet order parameters in a two-dimensional "checkerboard J-Q" quantum spin model[Zhao et al., Nat. Phys. 15 678(2019)], we here study the same model in the presence of weak inter-layer couplings. Our focus is on the evolution of the emergent symmetry as the system crosses over from two to three dimensions and the phase transition extends from strictly zero temperature in two dimensions up to finite temperature as expected in SrCu_(2)(BO_(3))_(2).Using quantum Monte Carlo simulations, we map out the phase boundaries of the plaquette-singlet and antiferromagnetic phases, with particular focus on the triple point where these two ordered phases meet the paramagnetic phase for given strength of the inter-layer coupling. All transitions are first-order in the neighborhood of the triple point. We show that the emergent O(4) symmetry of the coexistence state breaks down clearly when the interlayer coupling becomes sufficiently large, but for a weak coupling, of the magnitude expected experimentally, the enlarged symmetry can still be observed at the triple point up to significant length scales. Thus, it is likely that the plaquette-singlet to antiferromagnetic transition in SrCu_(2)(BO_(3))_(2) exhibits remnants of emergent O(4) symmetry, which should be observable due to additional weakly gapped Goldstone modes.

A sport and a pastime:Model design and computation in quantum many-body systems

We summarize the recent developments in the model design and computation for a few representative quantum manybody systems,encompassing quantum critical metals beyond the Hertz-Millis-Moriya framework with pseudogap and superconductivity,SYK non-Fermi-liquid with self-tuned quantum criticality and fluctuation induced superconductivity,and the flat-band quantum Moirélattice models in continuum where the interplay of quantum geometry of flat-band wave function and the long-range Coulomb interactions gives rise to novel insulating phases at integer fillings and superconductivity away from them.Although the narrative choreography seems simple,we show how important the appropriate model design and their tailor-made algorithmic developments-in other words,the scientific imagination inspired by the corresponding fast experimental developments in the aforementioned systems-compel us to invent and discover new knowledge and insights in the sport and pastime of quantum many-body research.

Quantum simulation of lattice gauge theories on superconducting circuits:Quantum phase transition and quench dynamics

Recently,quantum simulation of low-dimensional lattice gauge theories(LGTs)has attracted many interests,which may improve our understanding of strongly correlated quantum many-body systems.Here,we propose an implementation to approximate Z;LGT on superconducting quantum circuits,where the effective theory is a mixture of a LGT and a gauge-broken term.By using matrix product state based methods,both the ground state properties and quench dynamics are systematically investigated.With an increase of the transverse(electric)field,the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase.In the ordered phase,an approximate Gauss law of the Z;LGT emerges in the ground state.Moreover,to shed light on the experiments,we also study the quench dynamics,where there is a dynamical signature of the spontaneous translational symmetry breaking.The spreading of the single particle of matter degree is diffusive under the weak transverse field,while it is ballistic with small velocity for the strong field.Furthermore,due to the emergent Gauss law under the strong transverse field,the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping.Our results pave the way for simulating the LGT on superconducting circuits,including the quantum phase transition and quench dynamics.

Correlated insulating phases in the twisted bilayer graphene

We review analytical and numerical studies of correlated insulating states in twisted bilayer graphene, focusing on real-space lattice models constructions and their unbiased quantum many-body solutions. We show that by constructing localized Wannier states for the narrow bands, the projected Coulomb interactions can be approximated by interactions of cluster charges with assisted nearest neighbor hopping terms. With the interaction part only, the Hamiltonian is SU(4)symmetric considering both spin and valley degrees of freedom. In the strong coupling limit where the kinetic terms are neglected, the ground states are found to be in the SU(4) manifold with degeneracy. The kinetic terms, treated as perturbation, break this large SU(4) symmetry and propel the appearance of intervalley coherent state, quantum topological insulators, and other symmetry-breaking insulating states. We first present the theoretical analysis of moiré lattice model construction and then show how to solve the model with large-scale quantum Monte Carlo simulations in an unbiased manner. We further provide potential directions such that from the real-space model construction and its quantum many-body solutions how the perplexing yet exciting experimental discoveries in the correlation physics of twisted bilayer graphene can be gradually understood. This review will be helpful for the readers to grasp the fast growing field of the model study of twisted bilayer graphene.

Superconductivity near the(2+1)-Dimensional Ferromagnetic Quantum Critical Point

We utilize both analytical and numerical methods to study the superconducting transition temperature Tnear a fermionic quantum critical point(QCP) using a model constructed by Xu et al. [Phys. Rev. X 7, 031059(2017)] as an example. In this model, the bosonic critical fluctuation plays the role of pairing glue for the Cooper pairs, and we use a Bardeen–Cooper–Schrieffer-type mean-field theory to estimate T. We further argue that the Tc computed from the BCS theory approximates a pseudogap temperature TPG, instead of the Berezinskii–Kosterlitz–Thouless transition temperature T, which is confirmed by our determinant quantum Monte Carlo simulation. Moreover, due to the fact that electron density of state starts to deplete at T, the critical scaling of the underlying QCP is also affected below TPG. Thus, when studying the critical behavior of fermionic QCPs, we need to monitor that the temperature is above TPG instead of T. This was often ignored in previous studies.

Network-Initialized Monte Carlo Based on Generative Neural Networks

We design generative neural networks that generate Monte Carlo configurations with complete absence of autocorrelation from which only short Markov chains are needed before making measurements for physical observables,irrespective of the system locating at the classical critical point,fermionic Mott insulator,Dirac semimetal,or quantum critical point.We further propose a network-initialized Monte Carlo scheme based on such neural networks,which provides independent samplings and can accelerate the Monte Carlo simulations by significantly reducing the thermalization process.We demonstrate the performance of our approach on the two-dimensional Ising and fermion Hubbard models,expect that it can systematically speed up the Monte Carlo simulations especially for the very challenging many-electron problems.

Nonlocal Effects of Low-Energy Excitations in Quantum-Spin-Liquid Candidate Cu_(3)Zn(OH)_(6)FBr

We systematically study the low-temperature specific heats for the two-dimensional kagome antiferromagnet,Cu_(3)Zn(OH)_(6)FBr.The specific heat exhibits a T1.7 dependence at low temperatures and a shoulder-like feature above it.We construct a microscopic lattice model of Z_(2) quantum spin liquid and perform large-scale quantum Monte Carlo simulations to show that the above behaviors come from the contributions from gapped anyons and magnetic impurities.Surprisingly,we find the entropy associated with the shoulder decreases quickly with grain size d,although the system is paramagnetic to the lowest temperature.While this can be simply explained by a core-shell picture in that the contribution from the interior state disappears near the surface,the 5.9-nm shell width precludes any trivial explanations.Such a large length scale signifies the coherence length of the nonlocality of the quantum entangled excitations in quantum spin liquid candidate,similar to Pippard’s coherence length in superconductors.Our approach therefore offers a new experimental probe of the intangible quantum state of matter with topological order.

Momentum Space Quantum Monte Carlo on Twisted Bilayer Graphene

We report an implementation of the momentum space quantum Monte Carlo(QMC)method on the interaction model for the twisted bilayer graphene(TBG).The long-range Coulomb repulsion is treated exactly with the flat bands,spin and valley degrees of freedom of electrons taking into account.We prove the absence of the minus sign problem for QMC simulation when either the two valleys or the two spin degrees of freedom are considered.By taking the realistic parameters of the twist angle and interlayer tunnelings into the simulation,we benchmark the QMC data with the exact band gap obtained at the chiral limit,to reveal the insulating ground states at the charge neutrality point(CNP).Then,with the exact Green's functions from QMC,we perform stochastic analytic continuation to obtain the first set of single-particle spectral function for the TBG model at CNP.Our momentum space QMC scheme therefore offers the controlled computation pathway for systematic investigation of the electronic states in realistic TBG model at various electron fillings.

Metal to Orthogonal Metal Transition

Orthogonal metal is a new quantum metallic state that conducts electricity but acquires no Fermi surface(FS)or quasiparticles, and hence orthogonal to the established paradigm of Landau’s Fermi-liquid(FL). Such a state may hold the key of understanding the perplexing experimental observations of quantum metals that are beyond FL, i.e., dubbed non-Fermi-liquid(nFL), ranging from the Cu-and Fe-based oxides, heavy fermion compounds to the recently discovered twisted graphene heterostructures. However, to fully understand such an exotic state of matter, at least theoretically, one would like to construct a lattice model and to solve it with unbiased quantum many-body machinery. Here we achieve this goal by designing a 2D lattice model comprised of fermionic and bosonic matter fields coupled with dynamic Z2 gauge fields, and obtain its exact properties with sign-free quantum Monte Carlo simulations. We find that as the bosonic matter fields become disordered, with the help of deconfinement of the Z2 gauge fields, the system reacts with changing its nature from the conventional normal metal with an FS to an orthogonal metal of n FL without FS and quasiparticles and yet still responds to magnetic probe like an FL. Such a quantum phase transition from a normal metal to an orthogonal metal, with its electronic and magnetic spectral properties revealed, is calling for the establishment of new paradigm of quantum metals and their transition with conventional ones.

Magnetic Phase Diagram of Cu4-xZnx(OH)6FBr Studied by Neutron-Diffraction and μSR Techniques

We systematically investigate the magnetic properties of Cu4-xZnx(OH)6FBr using the neutron diffraction and muon spin rotation and relaxation(μSR) techniques.Neutron-diffraction measurements suggest that the longrange magnetic order and the orthorhombic nuclear structure in the x=0 sample can persist up to x=0.23 and 0.43,respectively.The temperature dependence of the zero-field μSR spectra provides two characteristic temperatures,TA0 and Tλ,which are associated with the initial drop close to zero time and the long-time exponential decay of the muon relaxation,respectively.Comparison between TA0 and TM from previously reported magnetic-susceptibility measurements suggest that the former comes from the short-range interlayer-spin clusters that persist up to x=0.82.On the other hand,the doping level where Tλ becomes zero is about 0.66,which is much higher than threshold of the long-range order,i.e.,~0.4.Our results suggest that the change in the nuclear structure may alter the spin dynamics of the kagome layers and a gapped quantum-spin-liquid state may exist above x=0.66 with the perfect kagome planes.

Solving quantum rotor model with different Monte Carlo techniques

We systematically test the performance of several Monte Carlo update schemes for the(2+1)d XY phase transition of quantum rotor model.By comparing the local Metropolis(LM),LM plus over-relaxation(OR),Wolff-cluster(WC),hybrid Monte Carlo(HM),hybrid Monte Carlo with Fourier acceleration(FA)schemes,it is clear that among the five different update schemes,at the quantum critical point,the WC and FA schemes acquire the smallest autocorrelation time and cost the least amount of CPU hours in achieving the same level of relative error,and FA enjoys a further advantage of easily implementable for more complicated interactions such as the long-range ones.These results bestow one with the necessary knowledge of extending the quantum rotor model,which plays the role of ferromagnetic/antiferromagnetic critical bosons or Z_(2)topological order,to more realistic and yet challenging models such as Fermi surface Yukawa-coupled to quantum rotor models.

Analytic Continuation with Pade Decomposition

The ill-posed analytic continuation problem for Green＇s functions or self-energies can be carried out using the Pade rational polynomial approximation. However, to extract accurate results from this approximation, high precision input data of the Matsubara Green function are needed. The calculation of the Matsubara Green function generally involves a Matsubara frequency summation, which cannot be evaluated analytically. Numerical summation is requisite but it converges slowly with the increase of the Matsubara frequency. Here we show that this slow convergence problem can be significantly improved by utilizing the Pade decomposition approach to replace the Matsubara frequency summation by a Pade frequency summation, and high precision input data can be obtained to successfully perform the Pade analytic continuation.

转角双层石墨烯中易调控的非线性霍尔效应

量子霍尔效应(quantum Hall effect,QHE)是霍尔效应的量子力学版本。一般分为整数量子霍尔效应(integer QHE)和分数量子霍尔效应(fractionQHE),其中整数量子霍尔效应由德国物理学家von Klitzing发现,他因此获得1985年诺贝尔物理学奖。分数量子霍尔效应由美籍华裔物理学家崔琦、德国物理学家Horst Störmer和美国材料学家Arthur Gossard发现,前两位因此与美国物理学家Robert Laughlin分享了1998年诺贝尔物理学奖。

海森伯模型的谱,到底有多靠谱?

1缘起 靠谱,还是不靠谱,这是一个值得思考的问题。这个问题不仅关乎哈姆雷特对于人生悖论的追问,其实在凝聚态物理学量子多体问题的动力学性质计算中,也是一个让多少仁人志士扼腕叹息的、带有希腊悲剧意味的、形而上的命题。

白马非马,非费米液体—非—费米液体

我承认,这是一个晦涩的题目。白马非马的故事见《公孙龙子·白马论》,是一个著名的哲学命题。故事来自于先秦诸子百家中的名家,其代表人物公孙龙子有这样一个悖论:白马有颜色(白)和外形(马)两种特征,而马只有外形一种特征,所以白马描述的范畴不同于马所描述的范畴,故而白马和马不是同一个事物。在我们现代人看来,这个故事显然是古人在和我们开诡辩的玩笑,混淆了词语的范畴,当然这也是名家做为诸子百家中诡辩家的老本行。

寂静春天里的动力学

解题北京的春天,短暂而狂躁,万物的复苏和生长都在让人猝不及防的时间中完成,该发生的和不该发生的事,都在一场沙尘暴、几场春雨和几场雾霾的夹裹之下,生生地走进这熙熙攘攘的世相里,让人只有接受的份儿。生活在这样狂躁之中的人,很难不被如此的气氛所影响和蛊惑,做出些本来可以不做、几年后回想会脸红追悔的事儿来。

西斯廷教堂中的对偶变换

题记这篇文字已写成数月,期间不断有热心的朋友给出反馈,从历史描述的准确性（如米氏的年龄）到科学内容的通俗性（如对偶变换在凝聚态物理学中更多的例子）,都在提醒、督促着笔者进一步将这篇小文扩展、充实。私心里,我也觉得原来的故事讲得有些仓促,情节太浓,呈现得不够从容,也总想找机会再修改一次。无奈几个月来俗务缠身,几近淹没在日常的熙熙攘攘、为稻粱谋之中,