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Variational quantum simulation of thermal statistical states on a superconducting quantum processer Xue-Yi Guo(郭学仪), Shang-Shu Li(李尚书), Xiao Xiao(效骁), Zhong-Cheng Xiang(相忠诚), Zi-Yong Ge(葛自勇), He-Kang Li(李贺康), Peng-Tao Song(宋鹏涛), Yi Peng(彭益), Zhan Wang(王战), Kai Xu(许凯), Pan Zhang(张潘), Lei Wang(王磊), Dong-Ning Zheng(郑东宁), and Heng Fan(范桁) Chin. Phys. B, 2023, 32 (1): 010307.   DOI: 10.1088/1674-1056/aca7f3 Abstract （170）      PDF （3465KB）（161）       Knowledge map    Quantum computers promise to solve finite-temperature properties of quantum many-body systems, which is generally challenging for classical computers due to high computational complexities. Here, we report experimental preparations of Gibbs states and excited states of Heisenberg $XX$ and $XXZ$ models by using a 5-qubit programmable superconducting processor. In the experiments, we apply a hybrid quantum-classical algorithm to generate finite temperature states with classical probability models and variational quantum circuits. We reveal that the Hamiltonians can be fully diagonalized with optimized quantum circuits, which enable us to prepare excited states at arbitrary energy density. We demonstrate that the approach has a self-verifying feature and can estimate fundamental thermal observables with a small statistical error. Based on numerical results, we further show that the time complexity of our approach scales polynomially in the number of qubits, revealing its potential in solving large-scale problems.

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Editorial: Celebrating the 30 Wonderful Year Journey of Chinese Physics B Hong-Jun Gao(高鸿钧), and Qihua Xiong(熊启华) Chin. Phys. B, 2022, 31 (12): 120101.   DOI: 10.1088/1674-1056/acaa95 Abstract （61）      PDF （195KB）（125）       Knowledge map    The year 2022 marks the 30th anniversary of Chinese Physics B. This editorial provides a brief history of the journal and introduces the anniversary theme collection comprising over 30 invited reviews and perspective articles from renowned scholars in various branches of physics.

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Computational studies on magnetism and ferroelectricity Ke Xu(徐可), Junsheng Feng(冯俊生), and Hongjun Xiang(向红军) Chin. Phys. B, 2022, 31 (9): 097505.   DOI: 10.1088/1674-1056/ac7b1b Abstract （138）   HTML （2）    PDF （2190KB）（141）       Knowledge map    Magnetics, ferroelectrics, and multiferroics have attracted great attentions because they are not only extremely important for investigating fundamental physics, but also have important applications in information technology. Here, recent computational studies on magnetism and ferroelectricity are reviewed. We first give a brief introduction to magnets, ferroelectrics, and multiferroics. Then, theoretical models and corresponding computational methods for investigating these materials are presented. In particular, a new method for computing the linear magnetoelectric coupling tensor without applying an external field in the first principle calculations is proposed for the first time. The functionalities of our home-made Property Analysis and Simulation Package for materials (PASP) and its applications in the field of magnetism and ferroelectricity are discussed. Finally, we summarize this review and give a perspective on possible directions of future computational studies on magnetism and ferroelectricity.

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Observation of nonlinearity and heating-induced frequency shifts in cavity magnonics Wei-Jiang Wu(吴维江), Da Xu(徐达), Jie Qian(钱洁), Jie Li(李杰), Yi-Pu Wang(王逸璞), and Jian-Qiang You(游建强) Chin. Phys. B, 2022, 31 (12): 127503.   DOI: 10.1088/1674-1056/ac9b02 Abstract （278）      PDF （1892KB）（273）       Knowledge map    When there is a certain amount of field inhomogeneity, the biased ferrimagnetic crystal can exhibit the higher-order magnetostatic (HMS) mode in addition to the uniform-precession Kittel mode. In cavity magnonics, we show the nonlinearity and heating-induced frequency shifts of the Kittel mode and HMS mode in a yttrium-iron-garnet (YIG) sphere. When the Kittel mode is driven to generate a certain number of excitations, the temperature of the whole YIG sample rises and the HMS mode can display an induced frequency shift, and vice versa. This cross effect provides a new method to study the magnetization dynamics and paves a way for novel cavity magnonic devices by including the heating effect as an operational degree of freedom.

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Superconducting properties of the C15-type Laves phase ZrIr2 with an Ir-based kagome lattice Qing-Song Yang(杨清松), Bin-Bin Ruan(阮彬彬), Meng-Hu Zhou(周孟虎), Ya-Dong Gu(谷亚东), Ming-Wei Ma(马明伟), Gen-Fu Chen(陈根富), and Zhi-An Ren(任治安) Chin. Phys. B, 2023, 32 (1): 017402.   DOI: 10.1088/1674-1056/aca3a2 Abstract （93）      PDF （2233KB）（70）       Knowledge map    We report systematic studies on superconducting properties of the Laves phase superconductor ZrIr$_2$. It crystallizes in a C15-type (cubic MgCu$_2$-type, space group $Fd\overline{3}m$) structure in which the Ir atoms form a kagome lattice, with cell parameters $a=b=c=7.3596(1)$ Å. Resistivity and magnetic susceptibility measurements indicate that ZrIr$_2$ is a type-II superconductor with a transition temperature of 4.0 K. The estimated lower and upper critical fields are 12.8 mT and 4.78 T, respectively. Heat capacity measurements confirm the bulk superconductivity in ZrIr$_2$. ZrIr$_2$ is found to possibly host strong-coupled s-wave superconductivity with the normalized specific heat change $\Delta C_{\rm e}/\gamma T_{\rm c} \sim 1.86$ and the coupling strength $\Delta_0/k_{\rm B}T_{\rm c} \sim 1.92$. First-principles calculations suggest that ZrIr$_2$ has three-dimensional Fermi surfaces with simple topologies, and the states at Fermi level mainly originate from the Ir-5d and Zr-4d orbitals. Similar to SrIr$_2$ and ThIr$_2$, spin--orbit coupling has dramatic influences on the band structure in ZrIr$_2$.

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A sport and a pastime: Model design and computation in quantum many-body systems Gaopei Pan(潘高培), Weilun Jiang(姜伟伦), and Zi Yang Meng(孟子杨) Chin. Phys. B, 2022, 31 (12): 127101.   DOI: 10.1088/1674-1056/aca083 Abstract （81）      PDF （6474KB）（105）       Knowledge map    We summarize the recent developments in the model design and computation for a few representative quantum many-body 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 Moiré lattice 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.

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Fabrication of Al/AlOx/Al Josephson junctions and superconducting quantum circuits by shadow evaporation and a dynamic oxidation process Wu Yu-Lin (吴玉林), Deng Hui (邓辉), Yu Hai-Feng (于海峰), Xue Guang-Ming (薛光明), Tian Ye (田野), Li Jie (李洁), Chen Ying-Fei (陈莺飞), Zhao Shi-Ping (赵士平), Zheng Dong-Ning (郑东宁) Chin. Phys. B, 2013, 22 (6): 060309.   DOI: 10.1088/1674-1056/22/6/060309 Abstract （654）      PDF （1978KB）（3533）       Knowledge map    Besides serving as promising candidates for realizing quantum computing, superconducting quantum circuits are one of a few macroscopic physical systems in which fundamental quantum phenomena can be directly demonstrated and tested, giving rise to a vast field of intensive research work both theoretically and experimentally. In this paper we report our work on the fabrication of superconducting quantum circuits, starting from its building blocks, Al/AlOx/Al Josephson junctions. By using electron beam lithography patterning and shadow evaporation, we have fabricated aluminum Josephson junctions with a controllable critical current density (jc) and wide range of junction sizes from 0.01 μm2 up to 1 μm2. We have carried out systematical studies on the oxidation process in fabricating Al/AlOx/Al Josephson junctions suitable for superconducting flux qubits. Furthermore, we have also fabricated superconducting quantum circuits such as superconducting flux qubit and charge-flux qubit.

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Bottom-up design and assembly with superatomic building blocks Famin Yu(于法民), Zhonghua Liu(刘中华), Jiarui Li(李佳芮), Wanrong Huang(黄婉蓉), Xinrui Yang(杨欣瑞), and Zhigang Wang(王志刚) Chin. Phys. B, 2022, 31 (12): 128107.   DOI: 10.1088/1674-1056/ac9e97 Abstract （307）      PDF （1170KB）（248）       Knowledge map    Constructing specific structures from the bottom up with artificial units is an important interdisciplinary topic involving physics, chemistry, materials, and so on. In this work, we theoretically demonstrated the feasibility of using superatoms as building blocks to assemble a complex at atomic-level precision. By using a series of actinide-based endohedral metallofullerene (EMF) superatoms that can form one, two, three and four chemical bonds, a planar complex with intra- and inter-molecular interactions was assembled on the Au(111) surface. This complex is composed of two parts, containing ten and eight superatoms, respectively. The electronic structure analysis shows that the electron density inside each part is connected and the closed-shell electronic arrangement system is designed. There is also an obvious van der Waals boundary by physical adsorption between the two parts, and a stable complex is formed. Since this complex is realized by the first-principles calculations of quantum mechanics, our results help not only achieve atomic-level precision construction with artificial superatomic units but also maintain atomic-level functional properties.

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Controlling acoustic orbital angular momentum with artificial structures: From physics to application Wei Wang(王未), Jingjing Liu(刘京京), Bin Liang (梁彬), and Jianchun Cheng(程建春) Chin. Phys. B, 2022, 31 (9): 094302.   DOI: 10.1088/1674-1056/ac7868 Abstract （121）   HTML （4）    PDF （11557KB）（94）       Knowledge map    Acoustic orbital angular momentum (OAM) associated with helicoidal wavefront recently attracts rapidly-growing attentions, offering a new degree of freedom for acoustic manipulation. Due to the unique dynamical behavior and inherent mode orthogonality of acoustic OAM, its harnessing is of fundamental interests for wave physics, with great potential in a plethora of applications. The recent advance in materials physics further boosts efforts into controlling OAM-carrying acoustic vortices, especially acoustic metasurfaces with planar profile and subwavelength thickness. Thanks to their unconventional acoustic properties beyond attainable in the nature, acoustic artificial structures provide a powerful platform for new research paradigm for efficient generation and diverse manipulation of OAM in ways not possible before, enabling novel applications in diverse scenarios ranging from underwater communication to object manipulation. In this article, we present a comprehensive view of this emerging field by delineating the fundamental physics of OAM-metasurface interaction and recent advances in the generation, manipulation, and application of acoustic OAM based on artificial structures, followed by an outlook for promising future directions and potential practical applications.

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Topological properties of non-Hermitian Creutz ladders Hui-Qiang Liang(梁辉强) and Linhu Li(李林虎) Chin. Phys. B, 2022, 31 (1): 010310.   DOI: 10.1088/1674-1056/ac3991 Abstract （214）   HTML （3）    PDF （7101KB）（151）       Knowledge map    We study topological properties of the one-dimensional Creutz ladder model with different non-Hermitian asymmetric hoppings and on-site imaginary potentials, and obtain phase diagrams regarding the presence and absence of an energy gap and in-gap edge modes. The non-Hermitian skin effect (NHSE), which is known to break the bulk-boundary correspondence (BBC), emerges in the system only when the non-Hermiticity induces certain unbalanced non-reciprocity along the ladder. The topological properties of the model are found to be more sophisticated than that of its Hermitian counterpart, whether with or without the NHSE. In one scenario without the NHSE, the topological winding is found to exist in a two-dimensional plane embedded in a four-dimensional space of the complex Hamiltonian vector. The NHSE itself also possesses some unusual behaviors in this system, including a high spectral winding without the presence of long-range hoppings, and a competition between two types of the NHSE, with the same and opposite inverse localization lengths for the two bands, respectively. Furthermore, it is found that the NHSE in this model does not always break the conventional BBC, which is also associated with whether the band gap closes at exceptional points under the periodic boundary condition.

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Topology of a parity-time symmetric non-Hermitian rhombic lattice Shumai Zhang(张舒迈), Liang Jin(金亮), and Zhi Song(宋智) Chin. Phys. B, 2022, 31 (1): 010312.   DOI: 10.1088/1674-1056/ac364a Abstract （210）   HTML （3）    PDF （888KB）（142）       Knowledge map    We investigate the topological properties of a trimerized parity-time ($ \mathcal{PT}$) symmetric non-Hermitian rhombic lattice. Although the system is $\mathcal{PT}$-symmetric, the topology is not inherited from the Hermitian lattice; in contrast, the topology can be altered by the non-Hermiticity and depends on the couplings between the sublattices. The bulk-boundary correspondence is valid and the Bloch bulk captures the band topology. Topological edge states present in the two band gaps and are predicted from the global Zak phase obtained through the Wilson loop approach. In addition, the anomalous edge states compactly localize within two diamond plaquettes at the boundaries when all bands are flat at the exceptional point of the lattice. Our findings reveal the topological properties of the $\mathcal{PT}$-symmetric non-Hermitian rhombic lattice and shed light on the investigation of multi-band non-Hermitian topological phases.

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Matrix integrable fifth-order mKdV equations and their soliton solutions Wen-Xiu Ma(马文秀) Chin. Phys. B, 2023, 32 (2): 020201.   DOI: 10.1088/1674-1056/ac7dc1 Abstract （39）      PDF （229KB）（43）       Knowledge map    We consider matrix integrable fifth-order mKdV equations via a kind of group reductions of the Ablowitz—Kaup—Newell—Segur matrix spectral problems. Based on properties of eigenvalue and adjoint eigenvalue problems, we solve the corresponding Riemann—Hilbert problems, where eigenvalues could equal adjoint eigenvalues, and construct their soliton solutions, when there are zero reflection coefficients. Illustrative examples of scalar and two-component integrable fifth-order mKdV equations are given.

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Correlated states in alternating twisted bilayer-monolayer-monolayer graphene heterostructure Ruirui Niu(牛锐锐), Xiangyan Han(韩香岩), Zhuangzhuang Qu(曲壮壮), Zhiyu Wang(王知雨), Zhuoxian Li(李卓贤), Qianling Liu(刘倩伶), Chunrui Han(韩春蕊), and Jianming Lu(路建明) Chin. Phys. B, 2023, 32 (1): 017202.   DOI: 10.1088/1674-1056/ac9de4 Abstract （97）      PDF （5804KB）（47）       Knowledge map    Highly controlled electronic correlation in twisted graphene heterostructures has gained enormous research interests recently, encouraging exploration in a wide range of moiré superlattices beyond the celebrated twisted bilayer graphene. Here we characterize correlated states in an alternating twisted Bernal bilayer-monolayer-monolayer graphene of ～ 1.74°, and find that both van Hove singularities and multiple correlated states are asymmetrically tuned by displacement fields. In particular, when one electron per moiré unit cell is occupied in the electron-side flat band, or the hole-side flat band (i.e., three holes per moiré unit cell), the correlated peaks are found to counterintuitively grow with heating and maximize around 20 K - a signature of Pomeranchuk effect. Our multilayer heterostructure opens more opportunities to engineer complicated systems for investigating correlated phenomena.

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Mottness, phase string, and high-Tc superconductivity Jing-Yu Zhao(赵靖宇) and Zheng-Yu Weng(翁征宇) Chin. Phys. B, 2022, 31 (8): 087104.   DOI: 10.1088/1674-1056/ac7a14 Abstract （153）   HTML （2）    PDF （969KB）（117）       Knowledge map    It is a great discovery in physics of the twentieth century that the elementary particles in nature are dictated by gauge forces, characterized by a nonintegrable phase factor that an elementary particle of charge $q$ acquires from $A$ to $B$ points: $P \exp \left( \text{i} \frac q {\hbar c}\int_A^B A_{\mu}\text{d} x^{\mu}\right),$ where $A_{\mu}$ is the gauge potential and $P$ stands for path ordering. In a many-body system of strongly correlated electrons, if the so-called Mott gap is opened up by interaction, the corresponding Hilbert space will be fundamentally changed. A novel nonintegrable phase factor known as phase-string will appear and replace the conventional Fermi statistics to dictate the low-lying physics. Protected by the Mott gap, which is clearly identified in the high-$T_{\rm c}$ cuprate with a magnitude $> 1.5$ eV, such a singular phase factor can enforce a fractionalization of the electrons, leading to a dual world of exotic elementary particles with a topological gauge structure. A non-Fermi-liquid "parent" state will emerge, in which the gapless Landau quasiparticle is only partially robust around the so-called Fermi arc regions, while the main dynamics are dominated by two types of gapped spinons. Antiferromagnetism, superconductivity, and a Fermi liquid with full Fermi surface can be regarded as the low-temperature instabilities of this new parent state. Both numerics and experiments provide direct evidence for such an emergent physics of the Mottness, which lies in the core of a high-$T_{\rm c}$ superconducting mechanism.

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Two-body exceptional points in open dissipative systems Peize Ding(丁霈泽) and Wei Yi(易为) Chin. Phys. B, 2022, 31 (1): 010309.   DOI: 10.1088/1674-1056/ac3396 Abstract （216）   HTML （2）    PDF （994KB）（151）       Knowledge map    We study two-body non-Hermitian physics in the context of an open dissipative system depicted by the Lindblad master equation. Adopting a minimal lattice model of a handful of interacting fermions with single-particle dissipation, we show that the non-Hermitian effective Hamiltonian of the master equation gives rise to two-body scattering states with state- and interaction-dependent parity-time transition. The resulting two-body exceptional points can be extracted from the trace-preserving density-matrix dynamics of the same dissipative system with three atoms. Our results not only demonstrate the interplay of parity-time symmetry and interaction on the exact few-body level, but also serve as a minimal illustration on how key features of non-Hermitian few-body physics can be probed in an open dissipative many-body system.

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Analytically determining frequency and amplitude of spontaneous alpha oscillation in Jansen's neural mass model using the describing function method Yao Xu(徐瑶), Chun-Hui Zhang(张春会), Ernst Niebur, Jun-Song Wang(王俊松) Chin. Phys. B, 2018, 27 (4): 048701.   DOI: 10.1088/1674-1056/27/4/048701 Abstract （508）   HTML    PDF （1787KB）（6159）       Knowledge map    Spontaneous alpha oscillations are a ubiquitous phenomenon in the brain and play a key role in neural information processing and various cognitive functions. Jansen's neural mass model (NMM) was initially proposed to study the origin of alpha oscillations. Most of previous studies of the spontaneous alpha oscillations in the NMM were conducted using numerical methods. In this study, we aim to propose an analytical approach using the describing function method to elucidate the spontaneous alpha oscillation mechanism in the NMM. First, the sigmoid nonlinear function in the NMM is approximated by its describing function, allowing us to reformulate the NMM and derive its standard form composed of one nonlinear part and one linear part. Second, by conducting a theoretical analysis, we can assess whether or not the spontaneous alpha oscillation would occur in the NMM and, furthermore, accurately determine its amplitude and frequency. The results reveal analytically that the interaction between linearity and nonlinearity of the NMM plays a key role in generating the spontaneous alpha oscillations. Furthermore, strong nonlinearity and large linear strength are required to generate the spontaneous alpha oscillations.

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Fabrication of honeycomb AuTe monolayer with Dirac nodal line fermions Qin Wang(汪琴), Jie Zhang(张杰), Jierui Huang(黄杰瑞), Jinan Shi(时金安), Shuai Zhang(张帅), Hui Guo(郭辉), Li Huang(黄立), Hong Ding(丁洪), Wu Zhou(周武), Yan-Fang Zhang(张艳芳), Xiao Lin(林晓), Shixuan Du(杜世萱), and Hong-Jun Gao(高鸿钧) Chin. Phys. B, 2023, 32 (1): 016102.   DOI: 10.1088/1674-1056/aca14a Abstract （91）      PDF （2193KB）（41）       Knowledge map    Two-dimensional honeycomb lattices show great potential in the realization of Dirac nodal line fermions (DNLFs). Here, we successfully synthesized a gold telluride (AuTe) monolayer by direct tellurizing an Au(111) substrate. Low energy electron diffraction measurements reveal that it is (2×2) AuTe layer stacked onto (3×3) Au(111) substrate. Moreover, scanning tunneling microscopy images show that the AuTe layer has a honeycomb structure. Scanning transmission electron microscopy reveals that it is a single-atom layer. In addition, first-principles calculations demonstrate that the honeycomb AuTe monolayer exhibits Dirac nodal line features protected by mirror symmetry, which is validated by angle-resolved photoemission spectra. Our results establish that monolayer AuTe can be a good candidate to investigate 2D DNLFs and provides opportunities to realize high-speed low-dissipation devices.

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Progress and challenges in magnetic skyrmionics Haifeng Du(杜海峰) and Xiangrong Wang(王向荣) Chin. Phys. B, 2022, 31 (8): 087507.   DOI: 10.1088/1674-1056/ac754f Abstract （129）   HTML （4）    PDF （659KB）（120）       Knowledge map    Magnetic skyrmions are two-dimensional localized topological spin-structures characterized by the skyrmion number that measures the number of times of spins wrapping the Bloch sphere. Skyrmions behave like particles under an external stimulus and are promising information carriers. Skyrmions can exist as an isolated object as well as skyrmion condensates in crystal structures, helical/conical states, mazes or irregular stripy states with emergent electromagnetic fields. Thus, skyrmions provide a nice platform for studying fundamental physics, other than its applications in spintronics. In this perspective, we briefly review some recent progress in the field and present an outlook of the fundamental challenges in device applications.

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Advances and challenges in DFT-based energy materials design Jun Kang(康俊), Xie Zhang(张燮), and Su-Huai Wei(魏苏淮) Chin. Phys. B, 2022, 31 (10): 107105.   DOI: 10.1088/1674-1056/ac89d7 Abstract （158）   HTML （0）    PDF （1641KB）（94）       Knowledge map    The growing worldwide energy needs call for developing novel materials for energy applications. Ab initio density functional theory (DFT) calculations allow the understanding and prediction of material properties at the atomic scale, thus, play an important role in energy materials design. Due to the fast progress of computer power and development of calculation methodologies, DFT-based calculations have greatly improved their predictive power, and are now leading to a paradigm shift towards theory-driven materials design. The aim of this perspective is to introduce the advances in DFT calculations which accelerate energy materials design. We first present state-of-the-art DFT methods for accurate simulation of various key properties of energy materials. Then we show examples of how these advances lead to the discovery of new energy materials for photovoltaic, photocatalytic, thermoelectric, and battery applications. The challenges and future research directions in computational design of energy materials are highlighted at the end.

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From microelectronics to spintronics and magnonics Xiu-Feng Han(韩秀峰), Cai-Hua Wan(万蔡华), Hao Wu(吴昊), Chen-Yang Guo(郭晨阳), Ping Tang(唐萍), Zheng-Ren Yan(严政人), Yao-Wen Xing(邢耀文), Wen-Qing He(何文卿), and Guo-Qiang Yu(于国强) Chin. Phys. B, 2022, 31 (11): 117504.   DOI: 10.1088/1674-1056/ac9048 Abstract （137）   HTML （5）    PDF （2474KB）（126）       Knowledge map    In this review, the recent developments in microelectronics, spintronics, and magnonics have been summarized and compared. Firstly, the history of the spintronics has been briefly reviewed. Moreover, the recent development of magnonics such as magnon-mediated current drag effect (MCDE), magnon valve effect (MVE), magnon junction effect (MJE), magnon blocking effect (MBE), magnon-mediated nonlocal spin Hall magnetoresistance (MNSMR), magnon-transfer torque (MTT) effect, and magnon resonant tunneling (MRT) effect, magnon skin effect (MSE), etc., existing in magnon junctions or magnon heterojunctions, have been summarized and their potential applications in memory and logic devices, etc., are prospected, from which we can see a promising future for spintronics and magnonics beyond micro-electronics.