费舍尔信息，位于参数估计理论的核心，最近被发现与多体纠缠有密切的关系（Pezzé和Smerzi，Phys. Rev. Lett. 102，100401）。利用Fisher信息对Lipkin-Meskhov-Glick模型的基态行为进行了区分和表征，发现在对称相和破缺相之间存在一个二阶量子相变.我们发现，系统的参数灵敏度在破碎阶段达到海森堡极限，而在对称阶段，它只是在散粒噪声极限附近。基于参数估计的Fisher信息为我们提供了一种研究量子相变的方法。
英文摘要：
Fisher information, lies at the heart of parameter estimation theory, was recently found to have a close relation with multipartite entanglement (Pezzé and Smerzi, Phys. Rev. Lett. 102, 100401). We use Fisher information to distinguish and characterize behaviors of ground state of the Lipkin-Meskhov-Glick model, which displays a second-order quantum phase transition between the broken and symmetric phases. We find that the parameter sensitivity of the system attains the Heisenberg limit in the broken phase, while it is just around the shot-noise limit in the symmetric phase. Based on parameter estimation, Fisher information provides us an approach to the quantum phase transition.
Quantum coherence reflects the origin of quantumness and might be capable of extracting the subtle nature of a system. We investigate the ground-state coherence and steered coherence in the Lipkin-Meshkov-Glick model and show that they detect faithfully the quantum phase transitions of this model. Moreover, we carry out scaling analysis on the coherence and steered coherence by means of the continuous unitary transformation method and it is found that the scaling exponents are uniquely determined by the phase region of this model. These results may provide useful insights into the mechanism un…
The basic Lipkin-Meshkov-Glick model displays a second order ground state quantum phase transition and an excited state quantum phase transition (ESQPT). The inclusion of an anharmonic term in the Hamiltonian implies a second ESQPT of a different nature. We characterize this ESQPT using the mean field limit of the model. The new ESQPT, associated with the changes in the boundary of the finite Hilbert space of the system, can be properly described using the order parameter of the ground state quantum phase transition, the energy gap between adjacent states, the participation ratio, and the quan…
The Variational Quantum Eigensolver (VQE) is a promising algorithm for Noisy Intermediate Scale Quantum (NISQ) computation. Verification and validation of NISQ algorithms' performance on NISQ devices is an important task. We consider the exactly-diagonalizable Lipkin-Meshkov-Glick (LMG) model as a candidate for benchmarking NISQ computers. We use the Bethe ansatz to construct eigenstates of the trigonometric LMG model using quantum circuits inspired by the LMG's underlying algebraic structure. We construct circuits with depth $\mathcal{O}(N)$ and $\mathcal{O}(\log_2N)$ that can prepare any tri…
Correlations play a key role in critical phenomena. Quantities such as the entanglement entropy, for instance, provide key insights into the mechanisms underlying quantum criticality. Almost all of our present knowledge, however, is restricted to bipartite correlations. Some questions still remain unanswered, such as: What parcel of the total correlations are genuinely k-partite? With the goal of shedding light on this difficult question, in this paper we put forth a detailed study of the behavior of genuine multipartite correlations (GMC) of arbitrary orders in the Lipkin-Meshkov-Glick model.…
We study the dynamics of a Lipkin-Meshkov-Glick model in the presence of Markovian dissipation, with a focus on late-time dynamics and the approach to thermal equilibrium. Making use of a vectorized bosonic representation of the corresponding Lindblad master equation, we use degenerate perturbation theory in the weak-dissipation limit to analytically obtain the eigenvalues and eigenvectors of the Liouvillian superoperator, which in turn give access to closed-form analytical expressions for the time evolution of the density operator and observables. Our approach is valid for large systems, but …
Benchmarking Quantum Simulations of the Lipkin-Meshkov-Glick Model Using Large Tensor Networks
The Washington Institute for STEM Entrepreneurship and Research (WISER)（华盛顿STEM创业与研究研究所）；Massachusetts Institute of Technology（麻省理工学院）；Joint Center for Quantum Information and Computer Science, University of Maryland（马里兰大学量子信息与计算科学联合中心）；Naval Nuclear Laboratory（海军核实验室）；IBM Quantum, IBM Research（IBM量子，IBM研究院）；Rensselaer Polytechnic Institute（伦斯勒理工学院）
Investigating Lipkin-Meshkov-Glick Model and Criticality-Enhanced Metrology in a Coherent Ising Machine
Key Laboratory of Multiscale Spin Physics, Ministry of Education, Beijing Normal University（北京师范大学多尺度自旋物理教育部重点实验室）；School of Artificial Intelligence, Beijing Normal University（北京师范大学人工智能学院）
Boosting the performance of a Lipkin-Meshkov-Glick quantum battery via symmetry-breaking quenches or a single-mode bosonic charger
Frontier Research Institute for Interdisciplinary Sciences, Tohoku University（东北大学前沿跨学科研究院）；Department of Applied Physics, Graduate School of Engineering, Tohoku University（东北大学大学院工学研究科应用物理系）；Theoretical Sciences Visiting Program, Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学理论科学访问项目）；Quantum Systems Unit, OIST Graduate University（冲绳科学技术大学院大学量子系统单元）；Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma（俄克拉荷马大学霍默·L·道奇物理与天文学系）；Center for Quantum Research and Technology, The University of Oklahoma（俄克拉荷马大学量子研究与技术中心）
We study the quantum metric tensor and its scalar curvature for a particular version of the Lipkin-Meshkov-Glick model. We build the classical Hamiltonian using Bloch coherent states and find its stationary points. They exhibit the presence of a ground state quantum phase transition, where a bifurcation occurs, showing a change of stability associated with an excited state quantum phase transition. Symmetrically, for a sign change in one Hamiltonian parameter, the same phenomenon is observed in the highest energy state. Employing the Holstein-Primakoff approximation, we derive analytic express…
