We study multipartite entanglement in non-equilibrium quantum phase transition (NEQPT) attainable in a coherently driven atomic ensemble undergoing collective decay. The NEQPT arises in the steady state of the system as the drive field strength is varied in comparison with the decay parameter. A close connection is observed between the critical behavior and the multi-partite entanglement in the system determined via the von Neumann entropy. The derivative of the von Neumann entropy shows Lambda-type behavior typical of the second order phase transitions. We further show that the calculated bi- and tri- partite entropies satisfy the Lieb inequality.
We study multipartite entanglement in non-equilibrium quantum phase transition (NEQPT) attainable in a coherently driven atomic ensemble undergoing collective decay. The NEQPT arises in the steady state of the system as the drive field strength is varied in comparison with the decay parameter. A close connection is observed between the critical behavior and the multi-partite entanglement in the system determined via the von Neumann entropy. The derivative of the von Neumann entropy shows Lambda-type behavior typical of the second order phase transitions. We further show that the calculated bi- and tri- partite entropies satisfy the Lieb inequality.
This paper establishes the theoretical framework of Many-Body Quantum Frequency Synchronization Criticality (MQFSC), investigating how an ensemble of N interacting quantum systems undergoes a sudden non-equilibrium phase transition from an incoherent state to a frequency-locked collective phase. We introduce the quantum order parameter for frequency synchronization, defined as R_omega = | (1/N) sum_{j=1}^N exp(i omega_j t) |, which shifts from zero to unity when the coupling strength exceeds a sharp critical threshold denoted by K > K_c. Utilizing Lindblad master equations and quantum mean-field approximations, we derive the exact critical coupling condition and characterize the underlying critical phenomena, including quantum fluctuations, critical slowing down, and enhanced multipartite entanglement. These findings bridge non-equilibrium statistical mechanics and quantum information science, opening new avenues for advanced quantum metrology and macroscopic coherence engineering.
The ground state of interacting spin chains in external magnetic fields can undergo a quantum phase transition (QPT) characterized by dramatic changes at a critical value of the magnetic field. In this paper, we use Bell-type inequalities to study the multipartite correlations (including multipartite entanglement and multipartite nonlocality in an n-spin subsystem) in the QPT of an infinite XY chain. An efficient numerical optimization procedure is proposed to figure out the violation measure Mn of the inequalities. For $n\ensuremath{\le}7$, the magnetic-field ($\ensuremath{\lambda}$) dependence of Mn is studied. We find the derivative of Mn is divergent exactly at the QPT point ${\ensuremath{\lambda}}_{c}=1$ for any n. In addition, with the increase of n, Mn converges quickly for $\ensuremath{\lambda}<{\ensuremath{\lambda}}_{c}$ and converges very slowly for $\ensuremath{\lambda}>{\ensuremath{\lambda}}_{c}$, which can be regarded as another signal for the QPT. Furthermore, in the vicinity of ${\ensuremath{\lambda}}_{c}$, high-order Bell-type inequalities will be violated as long as n is large enough. This indicates that high-level multipartite correlation will be present when the system is in the vicinity of the QPT point. Nevertheless, genuine n-partite entanglement or genuine n-partite nonlocality is not observed in the QPT.
Measurement-induced phase transition arises from the competition between a deterministic quantum evolution and a repeated measurement process. We explore the measurement-induced phase transition through the Quantum Fisher Information in two different metrological scenarios. We demonstrate through the scaling behavior of the quantum Fisher information the transition of the multi-partite entanglement across the phases. In analogy with standard quantum phase transition, we reveal signature of a measurement-induced phase transition in the non-analytic behaviour of the quantum Fisher information as the measurement strength approaches the critical value. Our results offer novel insights into the features of a quantum systems undergoing measurement-induced phase transition and indicate potential avenues for further exploration in the field of quantum physics.
We consider two different collective spin systems subjected to strong dissipation -- on the same scale as interaction strengths and external fields -- and show that either continuous or discontinuous dissipative quantum phase transitions can occur as the dissipation strength is varied. First, we consider a well known model of cooperative resonance fluorescence that can exhibit a second-order quantum phase transition, and analyze the entanglement properties near the critical point. Next, we examine a dissipative version of the Lipkin-Meshkov-Glick interacting collective spin model, where we find that either first- or second-order quantum phase transitions can occur, depending only on the ratio of the interaction and external field parameters. We give detailed results and interpretation for the steady state entanglement in the vicinity of the critical point, where it reaches a maximum. For the first-order transition we find that the semiclassical steady states exhibit a region of bistability.
Theoretical analysis of a prototypical two-qubit effective non-Hermitian system characterized by asymmetric Heisenberg XY interactions in the absence of external magnetic fields demonstrates that maximal bipartite entanglement and quantum phase transitions can be induced exclusively through non-Hermiticity. At thermal equilibrium as T→0, the system attains maximal entanglement C=1 for values of the non-Hermiticity parameter greater than a critical value γ>γc=J(1−δ2), where J denotes the exchange interaction and δ represents the anisotropy of the system; conversely, for γ<γc, entanglement is nonmaximal and given by C=(1−(γ/J)2). The entanglement undergoes a discontinuous transition to zero precisely at γ=γc. This phase transition originates from the closing of the energy gap at a non-Hermiticity-driven ground state degeneracy, which is fundamentally different from an exceptional point. This work suggests the use of singular-value-decomposition generalized density matrix for the computation of entanglement in bi-orthogonal systems.