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Physical review. B./Physical review. B

Quantum Fisher information in quantum critical systems with topological characterization

Shaoying Yin, Jie Song, Yujun Zhang, Shutian Liu

Published Nov 21, 2019• 39 citations
Publisher

Abstract

We study the relationship between the quantum Fisher information (QFI) of spin pairs and the topological quantum phase transitions (TQPTs) of the extended XY model driven by the anisotropies of the nearest-neighbor and the next-nearest-neighbor spins, the transverse magnetic field, and the three-spin interaction. We find that the first derivative of QFI can correctly characterize the TQPTs at absolute zero temperature. Meanwhile, the impacts of the thermal fluctuations and the site distance of spin pairs on the critical behaviors of the QFI are studied. It is found that the first derivative of QFI for the nearest neighbor or the long-distance spin pairs can only correctly characterize the critical points of the TQPTs at sufficiently low temperature. Remarkably, when the anisotropy of the nearest-neighbor and the next-nearest-neighbor spins are the driven parameters and the site distance $R=5$, the QFI itself can characterize the TQPTs at absolute zero temperature.

DOI
10.1103/physrevb.100.184417

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We study the relationship between the quantum Fisher information (QFI) of spin pairs and the topological quantum phase transitions (TQPTs) of the extended XY model driven by the anisotropies of the nearest-neighbor and the next-nearest-neighbor spins, the transverse magnetic field, and the three-spin interaction. We find that the first derivative of QFI can correctly characterize the TQPTs at absolute zero temperature. Meanwhile, the impacts of the thermal fluctuations and the site distance of spin pairs on the critical behaviors of the QFI are studied. It is found that the first derivative of QFI for the nearest neighbor or the long-distance spin pairs can only correctly characterize the critical points of the TQPTs at sufficiently low temperature. Remarkably, when the anisotropy of the nearest-neighbor and the next-nearest-neighbor spins are the driven parameters and the site distance R=5R=5R=5, the QFI itself can characterize the TQPTs at absolute zero temperature.
We use two-site quantum nonlocality to identify the topological quantum phase transitions (TQPTs) of the extended Ising model driven by varying system parameters. We investigate how the system parameters, including the anisotropies of the nearest-neighbor and the next-nearest-neighbor spin pairs, the transverse magnetic field, and the three-spin interaction, affect the quantum nonlocality. We show that the nonlocality cannot mark any TQPTs while its first derivative can perfectly characterize the TQPTs. By making the influences of the thermal fluctuations and the site distance of spin pairs on the critical behavior of the TQPTs analysis, we show that the sufficiently low temperature has a slight impact on the features of nonlocality and its first derivative while the site distance of spin pairs can significantly alter the properties of nonlocality and its first derivative. We further present the energy spectra and the trajectories of the winding vectors of the model to demonstrate that the quantum nonlocality can be employed to successfully signalize the TQPTs.
We explore quantum speed limit time τQSL of a qubit system coupling to a spin chain environment which is described by an extended Ising model associated with non-trivial topological characterization. For an initial pure state, we find that τQSL exhibits a behavior of local maximum around all critical points when the environment spin chain undergoes a topological quantum phase transition driven by external magnetic field λ or the anisotropy γ of nearest-neighbor interaction. And the value of local maximum would increase by strengthening the coupling between the system and environment around the critical points. However, the behavior of τQSL are both driving parameters and critical points dependent when the topological quantum phase transition is driven by the three-site interaction α or its anisotropy δ. Additionally, we also investigate τQSL for arbitrary time-evolution state in the whole dynamics process and find that τQSL exhibits a behavior of oscillation at non-critical points. However, τQSL will decay rapidly to zero around all critical points, and such trend accompany with oscillation behavior at some critical points.
We investigate the dynamics of entanglement, quantum correlation and classical correlation for the one-dimensional XY model in a transverse magnetic field. With the initial state polarized along the z axis, we find that the first maximum of the classical correlation between the nearest neighbor sites peaks around the critical point for large anisotropy parameter. It may indicate the quantum phase transition. For all kinds of correlation, we find that their behaviors between the nearest neighbor sites are significantly different from those of the next-nearest neighbor sites.
Abstract In recent years, there has been a surge of interest in exploring coherence measures and correlation measures to characterize topological quantum phase transitions (TQPTs). Here, motivated by the continued push in this direction, the steered quantum coherence (SQC) in the extended XY model is studied to analyze its capability in characterizing TQPTs. It is shown that the first derivative of SQC succeeds in signaling different critical points of TQPTs. In particular, it is found that the SQC is a long‐range correlation and the first derivative of SQC can always accurately identify TQPTs for different site distance.
ABSTRACT We investigate the efficiency of quantum teleportation based on a pair of spin‐qubits from two infinite spin chains at temperature T, quantified by the maximum mean fidelity (MMF). For the XY model, we observe a non‐analytic behavior in the first‐order derivative of MMF near the Ising transition point as temperature approaches zero. We conduct a systematic analysis of the key ingredients governing the quantum criticality, including finite‐temperature scaling behavior and critical exponent. Regarding the anisotropy transition, we find that MMF exhibits phase‐dependent extremal behavior: it reaches a maximum in one phase and a minimum in the other. Furthermore, we demonstrate that MMF can also serve as a sensitive probe that accurately characterizes both the Ising transition and the anisotropy one under the long‐range teleportation protocol. For the extended Ising model, the first‐order derivative of MMF displays singular behavior at all critical points associated with topological quantum phase transition (TQPT) driven by different parameter. Through finite‐temperature scaling analysis, we verify the critical behavior and extract the corresponding critical exponent. The results not only confirm the occurrence of two‐type phase transitions simultaneously in a such system but also reveal that all these transitions belong to the Ising‐type transition.