Renormalization-group approach to quantum Fisher information in an XY model with staggered Dzyaloshinskii-Moriya interaction

Liu, X. M.; Cheng, Wei‐Wen; Liu, J. M.

doi:10.1038/srep19359

Cited by 30 publications

(12 citation statements)

References 48 publications

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“…(20) where |m and P m are respectively the eigenvectors and eigenvalues of the m th component of the state ρ. Exploiting ( 25) and ( 27) in (24) gives [27]…”

Section: B Quantum Fisher Informationmentioning

confidence: 99%

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Revealing Trade off Relations Among Thermal Coherences and Correlations in Heisenberg XXX Model Under Inhomogeneous Magnetic Eld

Ali¹,

Nadeem²,

Toor³

et al. 2021

Preprint

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We study the validity of quantum Fisher information (QFI) as a faithful quantum coherence and correlation quantier by drawing a comparison with subsystem's coherence measure, rst-order coherence (FOC) and the entanglement measure, Negativity to study the behavior of thermal quantum coherence and correlations in two qubit Heisenberg XXX model, placed in independently controllable magnetic eld by systematically varying the coupling parameter, magnetic eld and bath temperature for ferromagnetic and antiferromagnetic case. After carefully observing the prole of quantum coherence and correlation measures, we propose an inequality relations which shows that there may exist a quantitative relationship between QFI, Negativity and FOC in which, the equality exists at zero temperature. We identify QFI to be a more useful coherence quantier, as it quanties coherence of individual subsystems and correlations among the subsystems. On the other hand, FOC identies coherence present in the individual subsystems only. A reciprocal relationship between Negativity and FOC is also observed in dierent cases. We also observe the existence of entanglement in ferromagnetic case, in contrast to simple Heisenberg XXX model in uniform magnetic eld. We show that in the ferromagnetic case, a very small inhomogeneity in magnetic eld is capable of producing large values of thermal entanglement. This shows that the behavior of entanglement in the ferromagnetic Heisenberg system is highly unstable against inhomogeneity of magnetic elds, which is inevitably present in any solid state realization of qubits.

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“…(20) where |m and P m are respectively the eigenvectors and eigenvalues of the m th component of the state ρ. Exploiting ( 25) and ( 27) in (24) gives [27]…”

Section: B Quantum Fisher Informationmentioning

confidence: 99%

“…Suppose that ρ ij is any bipartite state while A u and B u are respectively arbitrary local orthonormal observable bases for two subsystems in ρ ij . In this case, the QFI encoded in this two-component system with respect to the observables can be evaluated as [27],…”

Section: B Quantum Fisher Informationmentioning

confidence: 99%

Revealing Trade off Relations Among Thermal Coherences and Correlations in Heisenberg XXX Model Under Inhomogeneous Magnetic Eld

Ali¹,

Nadeem²,

Toor³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…QFI also plays a significant role in quantum detection and estimation as it provides a bound on the quantum estimation accuracy. In addition, QFI signaling of quantum phase transitions has received much attention [36].…”

Section: Introductionmentioning

confidence: 99%

Quantum Fisher information and coherence in one-dimensional XY spin models with Dzyaloshinsky-Moriya interactions

Wang

et al. 2018

Sci. China Phys. Mech. Astron.

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We investigate quantum phase transitions in XY spin models using Dzyaloshinsky-Moriya (DM) interactions. We identify the quantum critical points via quantum Fisher information and quantum coherence, finding that higher DM couplings suppress quantum phase transitions. However, quantum coherence (characterized by the l 1 -norm and relative entropy) decreases as the DM coupling increases. Herein, we present both analytical and numerical results.

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“…On the other hand, quantum correlations among the subsystems of a many-body system are closely related to the emergence of the QPT. In recent years, such relationships have been studied from many different perspectives in varies quantum systems 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 . For instance, entanglement has been widely employed to identify QPT with great success 7 8 9 10 11 12 13 14 15 16 17 18 19 20 .…”

mentioning

confidence: 99%

Finite-temperature scaling of trace distance discord near criticality in spin diamond structure

Wang

Sheng

Gong

et al. 2017

Sci Rep

Self Cite

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In this work we explore the quantum correlation quantified by trace distance discord as a measure to analyze the quantum critical behaviors in the Ising-XXZ diamond structure at finite temperatures. It is found that the first-order derivative of the trace distance discord exhibits a maximum around the critical point at finite temperatures. By analyzing the finite-temperature scaling behavior, we show that such a quantum correlation can detect exactly the quantum phase transitions from the entan-gled state in ferrimagnetic phase to an unentangled state in ferrimagnetic phase or to an unentangled state in ferromagnetic phase. The results also indicate that the above two kinds of transitions can be distinguished by the different finite-temperature scaling behaviors. Moreover, we find that the trace distance discord, in contrast to other typical quantum correlations (e.g., concurrence, quantum discord and Hellinger distance), may be more reliable to exactly spotlight the critical points of this model at finite temperatures under certain situations.

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Renormalization-group approach to quantum Fisher information in an XY model with staggered Dzyaloshinskii-Moriya interaction

Cited by 30 publications

References 48 publications

Revealing Trade off Relations Among Thermal Coherences and Correlations in Heisenberg XXX Model Under Inhomogeneous Magnetic Eld

Revealing Trade off Relations Among Thermal Coherences and Correlations in Heisenberg XXX Model Under Inhomogeneous Magnetic Eld

Quantum Fisher information and coherence in one-dimensional XY spin models with Dzyaloshinsky-Moriya interactions

Finite-temperature scaling of trace distance discord near criticality in spin diamond structure

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