Entanglement of finite cyclic chains at factorizing fields

Rossignoli, R.; Canosa, N.; Matera, Juan Mauricio

doi:10.1103/physreva.77.052322

Cited by 63 publications

(252 citation statements)

References 23 publications

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“…Not only. It is well known that, in the thermodynamic limit, the expectation value of an operator that commutes with the parity is the same if evaluated on |e {γ} or on |o {γ} [25,26,30]. We indicate such expectation value on one of the symmetric ground states as Ô {µi}…”

Section: A Quantitative Approach To the Distinguishabilitymentioning

confidence: 99%

“…In the magnetically ordered phases of a one dimensional system made by spin-1/2, the Hamiltonian admits a twofold degenerated ground states [25,26]. Among all the others, there will be two ground states that are also eigenstates of the parity with opposite eigenvalues.…”

Section: A Quantitative Approach To the Distinguishabilitymentioning

confidence: 99%

“…For example, only some specific ground states, i.e. the ones that maximize the order parameter, present a complete factorization [26,27] and a vanishing mutual information between very far spins [28]. On the other hand, the symmetric ground states, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Quench of a symmetry-broken ground state

Giampaolo¹,

Zonzo

2017

Phys. Rev. A

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We analyze the problem of how different ground states associated to the same set of the Hamiltonian parameters evolve after a sudden quench. To realize our analysis we define a quantitative approach to the local distinguishability between different ground states of a magnetically ordered phase in terms of the trace distance between the reduced density matrices obtained projecting two ground states in the same subset. Before the quench, regardless the particular choice of the subset, any system in a magnetically ordered phase is characterized by ground states that are locally distinguishable. On the other hand, after the quench, the maximum of the distinguishability shows an exponential decay in time. Hence, in the limit of very large time, all the informations about the particular initial ground state are lost even if the systems are integrable. We prove our claims in the framework of the magnetically ordered phases that characterize both the XY model and N -cluster Ising models. The fact that we find similar behavior in models within different classes of symmetry makes us confident about the generality of our results.

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Section: A Quantitative Approach To the Distinguishabilitymentioning

confidence: 99%

Section: A Quantitative Approach To the Distinguishabilitymentioning

confidence: 99%

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Quench of a symmetry-broken ground state

Giampaolo¹,

Zonzo

2017

Phys. Rev. A

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“…The Hamiltonian (46) commutes with the S z spin parity operator P z , irrespective of the coupling range, anisotropy, dimension or geometry of the system [55][56][57],…”

Section: Model and General Expressionsmentioning

confidence: 99%

“…It is first shown that in contrast with the pair entanglement, the quantum discord and the information deficit exhibit, for the exact ground state of these chains, common features, such as an appreciable finite value below the critical field, for all separations. Moreover, they approach a finite common non-zero value [44] at the remarkable factorizing field [49,50,[53][54][55][56][57][58][59][60] that these chains can exhibit in the anisotropic case. On the other hand, we will also show that important differences between the quantum discord on the one side and the standard and generalized information deficit on the other side do arise in the minimizing local spin measurement that defines them.…”

Section: Introductionmentioning

confidence: 99%

Quantum Discord and Information Deficit in Spin Chains

Canosa

Ciliberti

Rossignoli

2015

Entropy

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Abstract:We examine the behavior of quantum correlations of spin pairs in a finite anisotropic XY spin chain immersed in a transverse magnetic field, through the analysis of the quantum discord and the conventional and quadratic one-way information deficits. We first provide a brief review of these measures, showing that the last ones can be obtained as particular cases of a generalized information deficit based on general entropic forms. All of these measures coincide with an entanglement entropy in the case of pure states, but can be non-zero in separable mixed states, vanishing just for classically correlated states. It is then shown that their behavior in the exact ground state of the chain exhibits similar features, deviating significantly from that of the pair entanglement below the critical field. In contrast with entanglement, they reach full range in this region, becoming independent of the pair separation and coupling range in the immediate vicinity of the factorizing field. It is also shown, however, that significant differences between the quantum discord and the information deficits arise in the local minimizing measurement that defines them. Both analytical and numerical results are provided.

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Entanglement and symmetry effects in the transition to the Schrödinger cat regime

Pasquale¹,

Giorgi²,

Zannetti³

2009

Fortschritte der Physik

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We study two-spin entanglement and order parameter fluctuations as a function of the system size in the XY model in a transverse field and in the isotropic XXX model. Both models are characterized by the occurrence of ground state degeneracy also when systems of finite size are considered. This is always true for the XXX model, but only at the factorizing field for the XY model. We study the size dependence of symmetric states, which, in the presence of degeneracy, can be expanded as a linear combination of broken symmetry states. We show that, while the XY model looses its quantum superposition content exponentially with the size N , a decrease of the order of 1/N is observed when the XXX model is considered. The emergence of two qualitatively different regimes is directly related to the difference in the symmetry of the models.

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Entanglement of finite cyclic chains at factorizing fields

Cited by 63 publications

References 23 publications

Quench of a symmetry-broken ground state

Quench of a symmetry-broken ground state

Quantum Discord and Information Deficit in Spin Chains

Entanglement and symmetry effects in the transition to the Schrödinger cat regime

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