Multipartite quantum nonlocality and Bell-type inequalities in a spin-1/2 model with topological quantum phase transitions

Sun, Zhao‐Yu; Wen, Hui-Xin; Li, Meng; Li, Yuebin

doi:10.1103/physreva.104.052202

Cited by 10 publications

(5 citation statements)

References 72 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Particularly, it should be mentioned that the non-violation of the inequality S ⩽ 1 does not mean that there are no quantum correlations in the state. It just implies that we cannot observe any quantum nonlocalities by the current Bell-type experiment [37]. It is of note that we use the twosite quantum nonlocality based on the theory of multipartite nonlocality to identify the TQPTs of the extended Ising model in this work, avoiding the cumbersome numerical calculation of handling the three-body operator of the model.…”

Section: Multipartite Nonlocalitymentioning

confidence: 99%

“…Thus, using multipartite correlations to characterize the QPTs becomes crucial and necessary. In recent years, multipartite nonlocality has been extensively analyzed and employed to identify the QPTs in many lowdimensional quantum many-body systems [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Multipartite nonlocality is an important measure of multipartite correlation, which can be described by violating the Bell-type inequality.…”

Section: Introductionmentioning

confidence: 99%

“…Quantum nonlocality is not the exception. For example, multipartite quantum nonlocality is examined and used to characterize TQPTs in a bond-alternation spin-1/2 Heisenberg model [37] and Kitaev model [36]. The results show that TQPTs can be successfully accompanied by a dramatic change in the hierarchy of multipartite nonlocality.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantum nonlocality and topological quantum phase transitions in the extended Ising chain

Dong

Bao²,

Guo³

et al. 2022

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

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, for example, the anisotropies of the nearest-neighbor and the next-nearest-neighbor spin pairs, the transverse magnetic field, and the three-spin interaction, affect the properties of nonlocality and its first derivative. We find that the nonlocality cannot mark any TQPTs while its first derivative can correctly 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 characteristics of nonlocality and its first derivative. In addition, we also present the energy spectra and the trajectories of the winding vectors of the extended Ising model to further illustrate that nonlocality can be adopted to successfully signalize the TQPTs.

show abstract

Section: Multipartite Nonlocalitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum nonlocality and topological quantum phase transitions in the extended Ising chain

Dong

Bao²,

Guo³

et al. 2022

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

show abstract

“…Among these indicators, entanglement is the first one to be considered and it is found that the QPTs in many spin-chain systems can be signaled by the divergence in its first derivative with respect to the driving parameters [4][5][6][7][8][9][10][11][12][13]. Likewise, Bell nonlocality can also signal QPTs in some spin systems [14][15][16][17]. The feasibility of other quantum correlations, including quantum discord [18,19] and measurementinduced nonlocality [20][21][22], in signaling QPTs of the spinchain systems has also been validated in the past few years [23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Average coherence and average correlated coherence as indicators of quantum phase transitions in the XY model with staggered Dzyaloshinskii-Moriya interaction

Li,

Xie

2024

Laser Phys. Lett.

View full text Add to dashboard Cite

The performance of average coherence (AC) and average correlated coherence (ACC) in detecting quantum phase transitions (QPTs) has been explored by considering the XY model with staggered Dzyaloshinskii-Moriya interaction. By using the quantum renormalization group method, it is shown that the ground-state AC and ACC show either a maximum or a minimum at the QPT point. Moreover, the AC and ACC susceptibilities (i.e. their derivatives with respect to the driving parameter) have two extreme points near the two sides of the QPT point. A finite-scaling analysis reveals that these extreme points tend to the QPT point after several iterations of the renormalization and the susceptibilities at the QPT point become divergent in the thermodynamic limit.

show abstract

“…Coherence is one of the important bases for generating quantum correlations; even conceptually, coherence is more fundamental than quantum correlations, including BN. One can detect the BN of a system by violating some Bell-type inequalities, [22][23][24][25][26][27][28][29][30][31][32] especially the Clauser-Horne-Shimony-Holt (CHSH) inequality. [30][31][32][33][34] It deserves to be emphasized that not all entangled states can possess BN.…”

Section: Introductionmentioning

confidence: 99%

Visualizing and witnessing first-order coherence, Bell nonlocality and purity by using a quantum steering ellipsoid in the non-inertial frame

Yang

Xing

Du³

et al. 2023

Chinese Phys. B

View full text Add to dashboard Cite

Quantum steering ellipsoid (QSE) is a visual characterization for bipartite-qubit systems, and it is also a novel avenue for describing and detecting quantum correlations. Herein, by using the QSE, we visualize and witness the first-order coherence (FOC), the Bell nonlocality (BN), and the purity under the non-inertial frames. Also, the collective influences of the depolarizing channel and the non-coherence-generating channel (NCGC) on the FOC, the BN, and the purity are investigated in the QSE formalism. The results reveal that the distance from the center of QSE to the center of the Bloch sphere visualizes the FOC of bipartite system, the lengths of QSE semiaxis visualize the BN, and the QSE’s shape and position dominant the purity of system. One can capture the FOC, the BN, and the purity via the shape and position of the QSE in the non-inertial frames. The depolarizing channel (The NCGC) gives rise to the shrinking and degrading (the periodical oscillation) of the QSE. One can use these traits to visually characterize and detect the FOC, the BN, and the purity under the influences of external noises. Of particular note is that the condition for the QSE achieving the Bloch sphere’s center cannot be influenced by the depolarizing channel and the NCGC. The characteristics visualize that the conditions of the FOC disappearance are invariant under the additional influences of depolarizing channel and the NCGC, respectively.

show abstract

Multipartite quantum nonlocality and Bell-type inequalities in a spin-1/2 model with topological quantum phase transitions

Cited by 10 publications

References 72 publications

Quantum nonlocality and topological quantum phase transitions in the extended Ising chain

Quantum nonlocality and topological quantum phase transitions in the extended Ising chain

Average coherence and average correlated coherence as indicators of quantum phase transitions in the XY model with staggered Dzyaloshinskii-Moriya interaction

Visualizing and witnessing first-order coherence, Bell nonlocality and purity by using a quantum steering ellipsoid in the non-inertial frame

Contact Info

Product

Resources

About