We design a Bell inequality that is violated by correlations obtained from the ground states of an $XXZ$ spin-1 chain with on-site anisotropies at the region of phase transition. In order to detect such correlations in spin-1 systems we exploit the formalism of the generalized Bell inequality via the use of multipartite and high-order correlations. We observe a sharp violation in the vicinity of the quantum phase transition between the so-called large- $D$ and AFM phase. Interestingly, the violation of our Bell inequality is manifested by the change in the $XXZ$ spin-1 chain ground state to a Greenberger-Horne-Zeilinger-like state in the critical region. Our results provide a characterization of quantum phase transition via the violation of Bell-type constraint by correlations in the $XXZ$ spin-1 chain with multibody correlations and high-order measurements.We design a Bell inequality that is violated by correlations obtained from the ground states of an $XXZ$ spin-1 chain with on-site anisotropies at the region of phase transition. In order to detect such correlations in spin-1 systems we exploit the formalism of the generalized Bell inequality via the use of multipartite and high-order correlations. We observe a sharp violation in the vicinity of the quantum phase transition between the so-called large-$D$ and AFM phase. Interestingly, the violation of our Bell inequality is manifested by the change in the $XXZ$ spin-1 chain ground state to a Greenberger-Horne-Zeilinger-like state in the critical region. Our results provide a characterization of quantum phase transition via the violation of Bell-type constraint by correlations in the $XXZ$ spin-1 chain with multibody correlations and high-order measurements.

arXiv:2105.12391Physical Review AOct 20, 20226 citations

Detecting non-equilibrium quantum phase transitions by violations of Leggett-Garg inequalities

Fernando J. Gómez-Ruiz, Juan José Mendoza-Arenas, Ferney J. Rodríguez +1 more

Bulletin of the American Physical SocietyMar 9, 20180 citations

Detecting Quantum Phase Transitions using Classical Noises

Yan Chen, Yinchen He

Bulletin of the American Physical SocietyMar 1, 20120 citations

Bell inequality and nonlocality in a two-dimensional mixed spin systems

Zheng‐Hang Sun, Ya-Jie Wu, Hailin Huang +1 more

In this paper, we use Bell inequality and nonlocality to study the bipartite correlation in an exactly soluble two-dimensional mixed spin system. Bell inequality turns out to be a valuable detector for phase transitions in this model. It can detect not only the quantum phase transition, but also the thermal phase transitions, of the system. The property of bipartite correlation in the system is also analyzed. In the quantum anti-ferromagnetic phase, the Bell inequality is violated thus nonlocality is present. It is interesting that the nonlocality is enhanced by thermal fluctuation, and similar results have not been observed in anti-ferromagnetic phase. In the ferromagnetic phase, the quantum correlation turns out to be very novel, which cannot be captured by entanglement or nonlocality.In this paper, we use Bell inequality and nonlocality to study the bipartite correlation in an exactly soluble two-dimensional mixed spin system. Bell inequality turns out to be a valuable detector for phase transitions in this model. It can detect not only the quantum phase transition, but also the thermal phase transitions, of the system. The property of bipartite correlation in the system is also analyzed. In the quantum anti-ferromagnetic phase, the Bell inequality is violated thus nonlocality is present. It is interesting that the nonlocality is enhanced by thermal fluctuation, and similar results have not been observed in anti-ferromagnetic phase. In the ferromagnetic phase, the quantum correlation turns out to be very novel, which cannot be captured by entanglement or nonlocality.

arXiv:1307.6680Jul 25, 20130 citations

Emaranhamento e Desigualdade de Bell no Modelo XXZ

Pereira Ls

For many years it was believed that entanglement and violation of the Bell inequalities were the same peculiar aspect of Quantum Mechanics: non-locality. Nowadays, it is known that this equivalence is not complete, being true only for pure states; in other words, there are entangled mixed states that do not violate the Bell inequalities. Thus it is interesting to analyze properties of states which exhibit such difference, in order to better understand it. Here we present such a study of the connection between entanglement and violation of the Bell inequalities in Quantum Phase Transitions. More pecifically, we analyze this relation for two particles in an infinity one-dimensional spin-12 chain described by the XXZ model. We show that the two particles do not violate the Bell-CHSH inequality for any value of anisotropy, even in regions where they are entangled. Therefore, the entanglement that is relevant in Quantum Phase Transitions is not a trivial one , since it is not revealed by the Bell-CHSH inequality. We also demonstrate that the study of the Bell-CHSH inequality can indicate not only the first order phase transition as the infinity order one, while the fundamental energy per particle and the concurrence can only indicate the first order phase transition.For many years it was believed that entanglement and violation of the Bell inequalities were the same peculiar aspect of Quantum Mechanics: non-locality. Nowadays, it is known that this equivalence is not complete, being true only for pure states; in other words, there are entangled mixed states that do not violate the Bell inequalities. Thus it is interesting to analyze properties of states which exhibit such difference, in order to better understand it. Here we present such a study of the connection between entanglement and violation of the Bell inequalities in Quantum Phase Transitions. More pecifically, we analyze this relation for two particles in an infinity one-dimensional spin-12 chain described by the XXZ model. We show that the two particles do not violate the Bell-CHSH inequality for any value of anisotropy, even in regions where they are entangled. Therefore, the entanglement that is relevant in Quantum Phase Transitions is not a trivial one , since it is not revealed by the Bell-CHSH inequality. We also demonstrate that the study of the Bell-CHSH inequality can indicate not only the first order phase transition as the infinity order one, while the fundamental energy per particle and the concurrence can only indicate the first order phase transition.

Jan 1, 20120 citations

We design a Bell inequality that is violated by correlations obtained from the ground states of an

XXZ

spin-1 chain with on-site anisotropies at the region of phase transition. In order to detect such correlations in spin-1 systems we exploit the formalism of the generalized Bell inequality via the use of multipartite and high-order correlations. We observe a sharp violation in the vicinity of the quantum phase transition between the so-called large-

D

and AFM phase. Interestingly, the violation of our Bell inequality is manifested by the change in the

XXZ

spin-1 chain ground state to a Greenberger-Horne-Zeilinger-like state in the critical region. Our results provide a characterization of quantum phase transition via the violation of Bell-type constraint by correlations in the

XXZ

spin-1 chain with multibody correlations and high-order measurements.