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Machine learning methods provide a new perspective on the study of many-body system in condensed matter physics and there is only limited understanding of their representational properties and limitations in quantum spin liquid systems. In this work, we investigate the ability of the machine learning method based on the restricted Boltzmann machine in capturing physical quantities including the ground-state energy, spin-structure factor, magnetization, quantum coherence, and multipartite entanglement in the two-dimensional ferromagnetic spin liquids on a honeycomb lattice. It is found that the restricted Boltzmann machine can encode the many-body wavefunction quite well by reproducing accurate ground-state energy and structure factor. Further investigation on the behavior of multipartite entanglement indicates that the residual entanglement is richer in the gapless phase than the gapped spin-liquid phase, which suggests that the residual entanglement can characterize the spin-liquid phases. Additionally, we confirm the existence of a gapped non-Abelian topological phase in the spin liquids on a honeycomb lattice with a small magnetic field and determine the corresponding phase boundary by recognizing the rapid change of the local magnetization and residual entanglement. [ABSTRACT FROM AUTHOR]

We use multipartite entanglement and trace distance to detect the quantum phase transitions of the extended one-dimensional compass spin-chain model by applying the density matrix renormalization group method which is represented by the matrix product state. It is shown that singular behaviors of the first-order derivative of the multipartite entanglement and trace distance occur at the critical point of the system. The scaling behaviors of trace distance and multipartite entanglement are also discussed, and we show that the universal finite-size scaling law is valid for the multipartite entanglement and trace distance around the critical point. Moreover, we explore the quantum coherence for this model and find that the first-order derivative of the quantum coherence also displays discontinuity and exhibits singular critical behaviors that are the same as the trace distance and multipartite entanglement. [ABSTRACT FROM AUTHOR]

We investigate the quantum phase transition of an atomic ensemble trapped in a single-mode optical cavity via the geometric phase and quantum Fisher information of an extra probe atom which is injected into the optical cavity and interacts with the cavity field. We also find that the geometric quantum correlation between two probe atoms exhibits a double sudden transition phenomenon and show this double sudden transition phenomenon is closely associated with the quantum phase transition of the atomic ensemble. Furthermore, we propose a theoretical scheme to prolong the frozen time during which the geometric quantum correlation remains constant by applying time-dependent electromagnetic field. [ABSTRACT FROM AUTHOR]

We investigate the dynamics of quantum correlations for the Tavis–Comming model in continuous dephasing process. It is shown that quantum discord and entanglement can reach stationary value, and quantum Zeno effect occurs in strong-coupling region. Furthermore, we explore the influence of continuous dephasing process on the trace distance between two marginal states of the two atoms and find that the trace distance also achieve a constant value during time evolution. [ABSTRACT FROM AUTHOR]

We investigate the dynamics of quantum correlation between two separated qubits trapped in one-dimensional plasmonic waveguide. It is found that for a class of initial states, the quantum discord shows a sudden change phenomenon during the dynamical evolution. Furthermore, we demonstrate that the quantum discord can be enhanced if a proper product of the plasmon wave number and two qubits distance is chosen. Finally, we find that the non-zero quantum discord between two qubits can be created for the states without initial quantum discord during the time evolution of the system. [ABSTRACT FROM AUTHOR]

We study the dynamics of quantum correlations of the systems consisting of two non-interacting superconducting qubits interacting with their own data bus and common data bus, where the qubits are driven by a controllable time-dependent electromagnetic field. We investigate how the time-dependent electromagnetic field affects the dynamics of the quantum discord and the three-partite entanglement of the systems. It is found that the quantum discord vanishes only asymptotically although entanglement disappears suddenly during the time evolution and the quantum discord between two qubits can be increased by adjusting the time-dependent electromagnetic field. [ABSTRACT FROM AUTHOR]

We propose a scheme of entanglement transfer through two independent arrays of cavities coupled by optical fibers when each of the cavities contains a single two-level atom. We study the entanglement dynamics of the transferred states and find the explicit expression for the density matrix and concurrence. It is shown that the amount of the transferred entanglement has a direct connection with the target states and the lengths of the arrays of cavities. Moreover, the influence of the initial states and the length of the arrays of cavities on the phenomenon of entanglement sudden death is also investigated. [ABSTRACT FROM AUTHOR]

By investigating the accuracy of the learned energy and structure factor in four phases, we confirmed the validity of the machine learning method in solving the QSL honeycomb lattice." Https://arxiv.org/abs/2003.07280 (2021) In addition, the text in the Conclusion and discussion, "By investigating the accuracy of the learned energy and structure factor, we first confirmed the validity of the machine learning method in solving the QSL honeycomb lattice." now reads: "We note that a previous study SP 52 sp has examined the capability of RBMs to find ground-state energy of the Kitaev honeycomb model. As a result, Reference 52 was omitted and is listed below, Noormandipour, M., Sun, Y. & Haghighat, B. Restricted boltzmann machine representation for the groundstate and excited states of kitaev honeycomb model. [Extracted from the article]

The basic invariants and general form of invariants are discussed for the harmonic oscillator with time-dependent mass. In the case of the damped harmonic oscillator, the explicit expression for the basic invariants is found. The basic invariants are then used to study squeezed states. Finally, the high- n squeezed states are constructed. [ABSTRACT FROM AUTHOR]

It has been shown that the topological term in the O(3) nonlinear δ-model can be removed by a suitable canonical transformation using classical theory. In this paper, the quantum unitary transformation corresponding to the classical canonical transformation is presented. The meaning of the unitary transformation and the removability of the topological term are then discussed. [ABSTRACT FROM AUTHOR]

We study the topological quantum phase transition in the 2-D Kitaev honeycomb model by making use of the square root of the quantum Jensen-Shannon divergence and find that the square root of the quantum Jensen-Shannon divergence exhibits singular behaviors at the critical point of quantum phase transition. The scaling behaviors of the square root of the quantum Jensen-Shannon divergence are also examined from the first-order derivatives, and we demonstrate that the square root of the quantum Jensen-Shannon divergence obeys universal finite-size scaling laws. Furthermore, we explore the performance of quantum discord and the relative entropy coherence of the system. It is shown that quantum discord and relative entropy coherence display similar critical behaviors, and the square root of the quantum Jensen-Shannon divergence and quantum discord can serve as good indicators for quantum phase transitions. [ABSTRACT FROM AUTHOR]