Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1409.7067 · Physical Review Letters

Entanglement and Spin Squeezing in Non-Hermitian Phase Transitions

Tony E. Lee, Florentin Reiter, Nimrod Moiseyev

Published Dec 17, 2014• 152 citations
arXivHTMLPDF

Abstract

We show that non-Hermitian dynamics generate substantial entanglement in many-body systems. We consider the non-Hermitian Lipkin-Meshkov-Glick model and show that its phase transition occurs with maximum multiparticle entanglement: There is full N-particle entanglement at the transition, in contrast to the Hermitian case. The non-Hermitian model also exhibits more spin squeezing than the Hermitian model, showing that non-Hermitian dynamics are useful for quantum metrology. Experimental implementations with trapped ions and cavity QED are discussed.

DOI
10.1103/physrevlett.113.250401

Related papers

Multiparticle entanglement in the Lipkin-Meshkov-Glick model

H. T. Cui

The multiparticle entanglement in the Lipkin-Meshkov-Glick model has been discussed extensively in this paper. Measured by the global entanglement and its generalization, our calculation shows that the multiparticle entanglement can faithfully detect quantum phase transitions. For an antiferromagnetic case the multiparticle entanglement reaches the maximum at the transition point, whereas for ferromagnetic coupling, two different behaviors of multiparticle entanglement can be identified, dependent on the anisotropic parameter in the coupling.

arXiv:0805.0069•Physical Review A•May 6, 2008•34 citations

Probing dynamical phase transitions with a superconducting quantum simulator

Kai Xu, Zheng-Hang Sun, Wuxin Liu +9 more

Nonequilibrium quantum many-body systems, which are difficult to study via classical computation, have attracted wide interest. Quantum simulation can provide insights into these problems. Here, using a programmable quantum simulator with 16 all-to-all connected superconducting qubits, we investigate the dynamical phase transition in the Lipkin-Meshkov-Glick model with a quenched transverse field. Clear signatures of dynamical phase transitions, merging different concepts of dynamical criticality, are observed by measuring the nonequilibrium order parameter, nonlocal correlations, and the Loschmidt echo. Moreover, near the dynamical critical point, we obtain a spin squeezing of -7.0 ± 0.8 dB, showing multipartite entanglement, useful for measurements with precision fivefold beyond the standard quantum limit. On the basis of the capability of entangling qubits simultaneously and the accurate single-shot readout of multiqubit states, this superconducting quantum simulator can be used to study other problems in nonequilibrium quantum many-body systems, such as thermalization, many-body localization, and emergent phenomena in periodically driven systems.

arXiv:1912.05150•Science Advances•Jun 17, 2020•141 citations

Spin squeezing generated by the anisotropic central spin model

Lei Shao, Libin Fu

Spin squeezing, as a crucial quantum resource, plays a pivotal role in quantum metrology, enabling us to achieve high-precision parameter estimation schemes. Here, we investigate the spin squeezing and the quantum phase transition in an anisotropic central spin system. We find that this kind of central spin system can be mapped to the anisotropic Lipkin-Meshkov-Glick model in the limit where the ratio of transition frequencies between the central spin and the spin bath tends towards infinity. This property can induce a one-axis twisting interaction and provides another possibility for generating spin squeezing. We consider the generation of spin-squeezed states through the ground state and the dynamical evolution of the central spin model, respectively. The results show that the dynamical approach is more effective, and the spin-squeezing parameter improves as the anisotropy parameter decreases, while its value scales with system size as ${N}^{\ensuremath{-}2/3}$. Furthermore, we obtain the critical exponent of the quantum Fisher information around the critical point by numerical simulation, and find its value tends to $4/3$ as the frequency ratio and the system size approach infinity. This paper offers a promising scheme for generating spin-squeezed state and paves the way for potential advancements in quantum sensing.

arXiv:2311.11308•Physical Review A•May 13, 2024•7 citations

Collective spin systems in dispersive optical cavity QED: Quantum phase transitions and entanglement

S. Morrison, A. S. Parkins

We propose a cavity QED setup which implements a dissipative Lipkin-Meshkov-Glick model---an interacting collective spin system. By varying the external model parameters the system can be made to undergo both first- and second-order quantum phase transitions, which are signified by dramatic changes in cavity output field properties, such as the probe laser transmission spectrum. The steady-state entanglement between pairs of atoms is shown to peak at the critical points and can be experimentally determined by suitable measurements on the cavity output field. The entanglement dynamics also exhibits pronounced variations in the vicinities of the phase transitions.

arXiv:0711.2325•Physical Review A•Apr 8, 2008•74 citations

Entanglement and U(D)-spin squeezing in symmetric multi-quDit systems and applications to quantum phase transitions in Lipkin–Meshkov–Glick D-level atom models

Manuel Calixto, Alberto Mayorgas, Julio Guerrero

Abstract Collective spin operators for symmetric multi-quDit (namely identical D -level atom) systems generate a U( D ) symmetry. We explore generalizations to arbitrary D of SU(2)-spin coherent states and their adaptation to parity (multi-component Schrödinger cats), together with multi-mode extensions of NOON states. We write level, one- and two-quDit reduced density matrices of symmetric N -quDit states, expressed in the last two cases in terms of collective U( D )-spin operator expectation values. Then, we evaluate level and particle entanglement for symmetric multi-quDit states with linear and von Neumann entropies of the corresponding reduced density matrices. In particular, we analyze the numerical and variational ground state of Lipkin–Meshkov–Glick models of 3-level identical atoms. We also propose an extension of the concept of SU(2)-spin squeezing to SU( D ) and relate it to pairwise D -level atom entanglement. Squeezing parameters and entanglement entropies are good markers that characterize the different quantum phases, and their corresponding critical points, that take place in these interacting D -level atom models.

arXiv:2104.10581•Quantum Information Processing•Sep 1, 2021•22 citations

The role of non-Markovian dissipation in quantum phase transitions: tricriticality, spin squeezing, and directional symmetry breaking

Baptiste Debecker, Lukas Pausch, Jonathan Louvet +3 more

Understanding how to control phase transitions in quantum systems is at the forefront of research for the development of new quantum materials and technologies. Here, we study how the coupling of a quantum system to a non-Markovian environment, i.e., an environment with a frequency-dependent spectral density inducing memory effects, can be used to generate and reshape phase transitions and squeezing in matter phases. Focusing on a Lipkin-Meshkov-Glick model, we demonstrate that non-Markovian dissipation can be leveraged to engineer tricriticality via the fusion of $2^{\mathrm{nd}}$-order and $1^{\mathrm{st}}$-order critical points. We identify phases that arise from different ways of breaking the single weak symmetry of our model, which led us to introduce the concept of \textit{directional spontaneous symmetry breaking} (DSSB) as a general framework to understand this phenomenon. We show that signatures of DSSB can be seen in the emergence of spin squeezing along different directions, and that the latter is controllable via non-Markovian effects, opening up possibilities for applications in quantum metrology. Finally, we propose an experimental implementation of our non-Markovian model in cavity QED. Our work features non-Markovianity as a resource for controlling phase transitions in general systems, and highlights shortcomings of the Markovian limit in this context.

arXiv:2504.11317•Apr 15, 2025•0 citations
We show that non-Hermitian dynamics generate substantial entanglement in many-body systems. We consider the non-Hermitian Lipkin-Meshkov-Glick model and show that its phase transition occurs with maximum multiparticle entanglement: There is full N-particle entanglement at the transition, in contrast to the Hermitian case. The non-Hermitian model also exhibits more spin squeezing than the Hermitian model, showing that non-Hermitian dynamics are useful for quantum metrology. Experimental implementations with trapped ions and cavity QED are discussed.
The multiparticle entanglement in the Lipkin-Meshkov-Glick model has been discussed extensively in this paper. Measured by the global entanglement and its generalization, our calculation shows that the multiparticle entanglement can faithfully detect quantum phase transitions. For an antiferromagnetic case the multiparticle entanglement reaches the maximum at the transition point, whereas for ferromagnetic coupling, two different behaviors of multiparticle entanglement can be identified, dependent on the anisotropic parameter in the coupling.
Nonequilibrium quantum many-body systems, which are difficult to study via classical computation, have attracted wide interest. Quantum simulation can provide insights into these problems. Here, using a programmable quantum simulator with 16 all-to-all connected superconducting qubits, we investigate the dynamical phase transition in the Lipkin-Meshkov-Glick model with a quenched transverse field. Clear signatures of dynamical phase transitions, merging different concepts of dynamical criticality, are observed by measuring the nonequilibrium order parameter, nonlocal correlations, and the Loschmidt echo. Moreover, near the dynamical critical point, we obtain a spin squeezing of -7.0 ± 0.8 dB, showing multipartite entanglement, useful for measurements with precision fivefold beyond the standard quantum limit. On the basis of the capability of entangling qubits simultaneously and the accurate single-shot readout of multiqubit states, this superconducting quantum simulator can be used to study other problems in nonequilibrium quantum many-body systems, such as thermalization, many-body localization, and emergent phenomena in periodically driven systems.
Spin squeezing, as a crucial quantum resource, plays a pivotal role in quantum metrology, enabling us to achieve high-precision parameter estimation schemes. Here, we investigate the spin squeezing and the quantum phase transition in an anisotropic central spin system. We find that this kind of central spin system can be mapped to the anisotropic Lipkin-Meshkov-Glick model in the limit where the ratio of transition frequencies between the central spin and the spin bath tends towards infinity. This property can induce a one-axis twisting interaction and provides another possibility for generating spin squeezing. We consider the generation of spin-squeezed states through the ground state and the dynamical evolution of the central spin model, respectively. The results show that the dynamical approach is more effective, and the spin-squeezing parameter improves as the anisotropy parameter decreases, while its value scales with system size as ${N}^{\ensuremath{-}2/3}$. Furthermore, we obtain the critical exponent of the quantum Fisher information around the critical point by numerical simulation, and find its value tends to 4/34/34/3 as the frequency ratio and the system size approach infinity. This paper offers a promising scheme for generating spin-squeezed state and paves the way for potential advancements in quantum sensing.
We propose a cavity QED setup which implements a dissipative Lipkin-Meshkov-Glick model---an interacting collective spin system. By varying the external model parameters the system can be made to undergo both first- and second-order quantum phase transitions, which are signified by dramatic changes in cavity output field properties, such as the probe laser transmission spectrum. The steady-state entanglement between pairs of atoms is shown to peak at the critical points and can be experimentally determined by suitable measurements on the cavity output field. The entanglement dynamics also exhibits pronounced variations in the vicinities of the phase transitions.
Abstract Collective spin operators for symmetric multi-quDit (namely identical D -level atom) systems generate a U( D ) symmetry. We explore generalizations to arbitrary D of SU(2)-spin coherent states and their adaptation to parity (multi-component Schrödinger cats), together with multi-mode extensions of NOON states. We write level, one- and two-quDit reduced density matrices of symmetric N -quDit states, expressed in the last two cases in terms of collective U( D )-spin operator expectation values. Then, we evaluate level and particle entanglement for symmetric multi-quDit states with linear and von Neumann entropies of the corresponding reduced density matrices. In particular, we analyze the numerical and variational ground state of Lipkin–Meshkov–Glick models of 3-level identical atoms. We also propose an extension of the concept of SU(2)-spin squeezing to SU( D ) and relate it to pairwise D -level atom entanglement. Squeezing parameters and entanglement entropies are good markers that characterize the different quantum phases, and their corresponding critical points, that take place in these interacting D -level atom models.
Understanding how to control phase transitions in quantum systems is at the forefront of research for the development of new quantum materials and technologies. Here, we study how the coupling of a quantum system to a non-Markovian environment, i.e., an environment with a frequency-dependent spectral density inducing memory effects, can be used to generate and reshape phase transitions and squeezing in matter phases. Focusing on a Lipkin-Meshkov-Glick model, we demonstrate that non-Markovian dissipation can be leveraged to engineer tricriticality via the fusion of 2nd2^{\mathrm{nd}}2nd-order and 1st1^{\mathrm{st}}1st-order critical points. We identify phases that arise from different ways of breaking the single weak symmetry of our model, which led us to introduce the concept of \textit{directional spontaneous symmetry breaking} (DSSB) as a general framework to understand this phenomenon. We show that signatures of DSSB can be seen in the emergence of spin squeezing along different directions, and that the latter is controllable via non-Markovian effects, opening up possibilities for applications in quantum metrology. Finally, we propose an experimental implementation of our non-Markovian model in cavity QED. Our work features non-Markovianity as a resource for controlling phase transitions in general systems, and highlights shortcomings of the Markovian limit in this context.