Entanglement and the Phase Transition in Single-Mode Superradiance

Lambert, Neill; Emary, Clive; Brandes, Tobias

doi:10.1103/physrevlett.92.073602

Cited by 459 publications

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“…The entanglement properties of this model have been already discussed through the concurrence, which exhibits a cusp-like behavior at the critical point [19,20,21,22] as well as interesting dynamical properties [23]. Note that similar results have also been obtained in the Dicke model [24,25] which can be mapped onto the LMG model in some cases [26], or in the reduced BCS model [27].In this letter, we analyze the von Neumann entropy computed from the ground state of the LMG model. We show that, at the critical point, it behaves logarithmically with the size of the blocks L used in the bipartite decomposition of the density matrix with a prefactor that depends on the anisotropy parameter tuning the universality class.…”

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confidence: 68%

Entanglement entropy in the Lipkin-Meshkov-Glick model

et al. 2005

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We analyze the entanglement entropy in the Lipkin-Meshkov-Glick model, which describes mutually interacting spins half embedded in a magnetic field. This entropy displays a singularity at the critical point that we study as a function of the interaction anisotropy, the magnetic field, and the system size. Results emerging from our analysis are surprisingly similar to those found for the one-dimensional XY chain.PACS numbers: 03.65. Ud,03.67.Mn,73.43.Nq Within the last few years, entanglement properties of spin systems have attracted much attention. As initially shown in one-dimensional (1D) spin chains [1,2,3,4], observables measuring this genuine quantum mechanical feature are strongly affected by the existence of a quantum phase transition. For instance, the so-called concurrence [5] that quantifies the two-spin entanglement displays some nontrivial universal scaling properties. Similarly, the von Neumann entropy which rather characterizes the bipartite entanglement between any two subsystems scales logarithmically with the typical size L of these subsystems at the quantum critical point, with a prefactor given by the central charge of the corresponding theory [3,4,6,7]. Note that the role played by the boundaries in these conformal invariant systems has been only recently elucidated [8]. Apart from 1D systems, very few models have been studied so far [9,10,11,12,13], either due to the absence of exact solution or to a difficult numerical treatment. In this context, the LipkinMeshkov-Glick (LMG) model [14,15,16] discussed here has drawn much attention since it allows for very efficient numerical treatment as well as analytical calculations. Introduced by Lipkin, Meshkov and Glick in Nuclear Physics, this model has been the subject of intensive studies during the last two decades because of its relevance for quantum tunneling of bosons between two levels. It is thus of prime interest to describe in particular the Josephson effect in two-mode Bose-Einstein condensates [17,18]. The entanglement properties of this model have been already discussed through the concurrence, which exhibits a cusp-like behavior at the critical point [19,20,21,22] as well as interesting dynamical properties [23]. Note that similar results have also been obtained in the Dicke model [24,25] which can be mapped onto the LMG model in some cases [26], or in the reduced BCS model [27].In this letter, we analyze the von Neumann entropy computed from the ground state of the LMG model. We show that, at the critical point, it behaves logarithmically with the size of the blocks L used in the bipartite decomposition of the density matrix with a prefactor that depends on the anisotropy parameter tuning the universality class. We also discuss the dependence of the entropy with the magnetic field and stress the analogy with 1D systems.The LMG model is defined by the Hamiltonianwhere σ k α is the Pauli matrix at position k in the direction α, and N the total number of spins. This Hamiltonian describes a set of spins half located at the vertices of ...

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confidence: 68%

Entanglement entropy in the Lipkin-Meshkov-Glick model

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“…In QO it is mostly known in the so called rotating wave approximation (RWA), and describes the coupling of a monochromatic field of frequency ω with N non-interacting two-level atoms with level separation ǫ. Recently in connection with QC, the model received renewed attention from solid-state community working on 'phonon cavity quantum dynamics' [21,22], Josephson Junctions and quantum dots [23], quantum chaos [24] and quantum phase transitions [25]. These works are interested on the model in the original form conceived by Dicke [26] without the RWA.…”

Section: B Dicke Modelmentioning

confidence: 99%

Semiclassical limit of the entanglement in closed pure systems

Angelo

Furuya

2005

Phys. Rev. A

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We discuss the semiclassical limit of the entanglement for the class of closed pure systems. By means of analytical and numerical calculations we obtain two main results: (i) the short-time entanglement does not depend on Planck's constant and (ii) the long-time entanglement increases as more semiclassical regimes are attained. On one hand, this result is in contrast with the idea that the entanglement should be destroyed when the macroscopic limit is reached. On the other hand, it emphasizes the role played by decoherence in the process of emergence of the classical world. We also found that, for Gaussian initial states, the entanglement dynamics may be described by an entirely classical entropy in the semiclassical limit.

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“…Quantum entanglement, as one of the most fascinating feature of quantum theory, has attracted much attention over the past decade, mostly because its nonlocal connotation [1] is regarded as a valuable resource in quantum communication and information processing [2]. Recently a great deal of effort has been devoted to the understanding of the connection between quantum entanglement and quantum phase transitions (QPTs) [3,4,5,6,7,8,9,10,11,12,13,14,15]. Quantum phase transitions [16] are transitions between qualitatively distinct phases of quantum many-body systems, driven by quantum fluctuations.…”

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Reexamination of entanglement and the quantum phase transition

2005

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We show that, for an exactly solvable quantum spin model, a discontinuity in the first derivative of the ground state concurrence appears in the absence of quantum phase transition. It is opposed to the popular belief that the non-analyticity property of entanglement (ground state concurrence) can be used to determine quantum phase transitions. We further point out that the analyticity property of the ground state concurrence in general can be more intricate than that of the ground state energy. Thus there is no one-to-one correspondence between quantum phase transitions and the non-analyticity property of the concurrence. Moreover, we show that the von Neumann entropy, as another measure of entanglement, can not reveal quantum phase transition in the present model. Therefore, in order to link with quantum phase transitions, some other measures of entanglement are needed. Quantum entanglement, as one of the most fascinating feature of quantum theory, has attracted much attention over the past decade, mostly because its nonlocal connotation [1] is regarded as a valuable resource in quantum communication and information processing [2]. Recently a great deal of effort has been devoted to the understanding of the connection between quantum entanglement and quantum phase transitions (QPTs) [3,4,5,6,7,8,9,10,11,12,13,14,15]. Quantum phase transitions [16] are transitions between qualitatively distinct phases of quantum many-body systems, driven by quantum fluctuations. In view of the connection between entanglement and quantum correlations [17], one anticipates that entanglement will furnish a dramatic signature of the quantum critical point. People hope that, by employing quantum entanglement, the global picture of the quantum many-body systems could be diagnosed, and one may obtain fresh insight into the quantum many-body problem. Hence, in addition to its intrinsic relevance with quantum information applications, entanglement may also play an interesting role in the context of statistical mechanics.The aforementioned studies are based on the analysis of particular many-body models. Recently a theorem of the relation between QPTs and bipartite entanglement is proposed [18]. The authors conclude that, under certain conditions, a discontinuity in or a divergence of the ground state concurrence [the first derivative of the ground state concurrence] is both necessary and sufficient to signal a first-order QPT (1QPT) [second-order QPT (2QPT)]. Most of the previous investigations for specific models support their conclusion. This may strengthen the belief that one can determine QPTs by using quantum entanglement.In this paper, the entanglement properties (the ground state concurrence and the von Neumann entropy) are calculated for an exactly solvable quantum spin model [19]. Contrary to conventional wisdom, we find that there exists a discontinuity in the first derivative of the concurrence, at which there is no quantum critical point. In fact, similar result had already been discovered in Ref. [7] for a quantum spin mode...

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Entanglement and the Phase Transition in Single-Mode Superradiance

Cited by 459 publications

References 21 publications

Entanglement entropy in the Lipkin-Meshkov-Glick model

Entanglement entropy in the Lipkin-Meshkov-Glick model

Semiclassical limit of the entanglement in closed pure systems

Reexamination of entanglement and the quantum phase transition

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