摘要：
In a previous study, we have proposed a procedure to study global quantum discord in 1D chains whose ground states are described by matrix product states [Z.-Y. Sun et al., Ann. Phys. 359, 115 (2015)]. In this paper, we show that with a very simple generalization, the procedure can be used to investigate quantum mixed states described by matrix product density operators, such as quantum chains at finite temperatures and 1D subchains in high-dimensional lattices. As an example, we study the global discord in the ground state of a 2D transverse-field Ising lattice, and pay our attention to the scaling behavior of global discord in 1D sub-chains of the lattice. We find that, for any strength of the magnetic field, global discord always shows a linear scaling behavior as the increase of the length of the sub-chains. In addition, global discord and the so-called “discord density” can be used to indicate the quantum phase transition in the model. Furthermore, based upon our numerical results, we make some reliable predictions about the scaling of global discord defined on the n × n sub-squares in the lattice.
摘要：
In this paper, we characterize the global multipartite nonlocality in one-dimensional infinite-size spin-1/2 chains. For this purpose, we calculate the multipartite nonlocality of n-site subchains, and take the large- n limit. As n increases from 2 to 100, we find that the average revenue and the marginal revenue of nonlocality converge gradually, thus they can be used to characterize the global multipartite nonlocality in infinite-size chains. Furthermore, in the vicinity of the quantum phase transition (QPT) points of the transverse-field Ising model and the XXZ model, in the large- n limit, multipartite nonlocality becomes extremely sensitive to external perturbation, that is, arbitrarily small perturbation away from the QPT points would lead to a drastic change in the global nonlocality. This signal of QPTs is easily distinguishable, and can be used to detect QPTs. We also draw a vivid physical picture of multipartite correlations and QPTs by analogy with magnetic domains in ferromagnets.
作者机构：
[Sun Z.Y.; Huang H.L.] School of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan 430023, China;[Ding L.J.] College of Science, China Three Gorges University, Yichang 443002, China
会议名称：
3rd International Conference on Advanced Structure, Materials and Engineering, ASME 2014
摘要：
<jats:p>The finite-temperature entanglement entropy for an alternating spin-1/2 chain with multi-spin interactions is investigated by means of Green’s function theory combined with Jordan-Wigner transformation, to identify the spin-Peierls (<jats:italic>SP</jats:italic>) transition. It is found that the two-site thermal entanglement entropy is a useful tool to characterize the<jats:italic>SP</jats:italic>transition. In addition, the competition between multi-spin interaction and Peierls-dimerization plays a central role in the critical phenomenon of the system.</jats:p>
摘要：
<jats:p>The effect of arbitrary orientation in the magnetic field on the entanglement and dense coding of a two-qubit <jats:italic>XX</jats:italic> model is investigated. The concurrence and optimal dense coding capacity are calculated for different orientations of the magnetic field. It is found that the entanglement can be maximized by rotating the magnetic field to an optimal direction at given temperature. Furthermore, there exists critical concurrence <jats:italic>C</jats:italic><jats:sub>c</jats:sub>, beyond which the thermal state is unfeasible for optimal dense coding.</jats:p>
期刊：
Solid State Communications,2014年185:30-34 ISSN：0038-1098
通讯作者：
Huang, H. L.
作者机构：
[Huang, H. L.; Wu, Y. Y.; Sun, Z. Y.] Wuhan Polytech Univ, Sch Elect & Elect Engn, Wuhan 430000, Peoples R China.;[Wang, B.] ENN Grp Co Ltd, Langfang 065001, Hebei, Peoples R China.
通讯机构：
[Huang, H. L.] W;Wuhan Polytech Univ, Sch Elect & Elect Engn, Wuhan 430000, Peoples R China.
关键词：
A. Two-dimensional spin model;D. Bell inequality;D. Nonlocality;D. Phase transition
摘要：
In this paper, we use the Bell inequality to study the bipartite correlation in an exactly soluble two-dimensional Ising-Heisenberg spin system. The Bell inequality can detect not only the quantum phase transition, but also the thermal phase transitions, or the system. The property or 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 phases. In the ferromagnetic phase, the quantum correlation turns out to be very novel, which cannot be captured by entanglement or nonlocality. (C) 2014 Elsevier Ltd. All rights reserved.
摘要：
The ground state of interacting spin chains in external magnetic fields can undergo a quantum phase transition (QPT) characterized by dramatic changes at a critical value of the magnetic field. In this paper, we use Bell-type inequalities to study the multipartite correlations (including multipartite entanglement and multipartite nonlocality in an n-spin subsystem) in the QPT of an infinite XY chain. An efficient numerical optimization procedure is proposed to figure out the violation measure Mn of the inequalities. For n≤7, the magnetic-field ( λ) dependence of Mn is studied. We find the derivative of Mn is divergent exactly at the QPT point λc=1 for any n. In addition, with the increase of n, Mn converges quickly for λ<λc and converges very slowly for λ>λc, which can be regarded as another signal for the QPT. Furthermore, in the vicinity of λc, high-order Bell-type inequalities will be violated as long as n is large enough. This indicates that high-level multipartite correlation will be present when the system is in the vicinity of the QPT point. Nevertheless, genuine n-partite entanglement or genuine n-partite nonlocality is not observed in the QPT.
摘要：
In this paper, using the infinite time-evolving block decimation (iTEBD) algorithm and Bell-type inequalities, we investigate multipartite quantum nonlocality in an infinite one-dimensional quantum spin- 12 XXZ system. High hierarchy of multipartite nonlocality can be observed in the gapless phase of the model, while only the lowest hierarchy of multipartite nonlocality is observed in most regions of the gapped antiferromagnetic phase. Thereby, Bell-type inequalities disclose different correlation structures in the two phases of the system. Furthermore, at the infinite-order quantum phase transition (QPT, or Kosterlitz-Thouless QPT) point of the model, the correlation measures always show a local minimum value, regardless of the length of the subchains. It indicates that relatively low hierarchy of multipartite nonlocality would be observed at the infinite-order QPT point in a Bell-type experiment. The result is in contrast to the existing results of the second-order QPT in the one-dimensional XY model, where multipartite nonlocality with the highest hierarchy has been observed. Thus, multipartite nonlocality provides an alternative perspective to distinguish between these two kinds of QPTs. Reliable clues for the existence of tripartite quantum entanglement have also been found.
摘要：
Bell inequalities and nonlocality have been widely studied in one-dimensional quantum systems. As a kind of quantum correlation, it is expected that bipartite nonlocality should be present in quantum systems, just as bipartite entanglement does. Surprisingly, for various models, two-qubit states do not violate Bell inequalities, i.e., they are local. Recently, it is realized that the results are related to the monogamy trade-off obeyed by bipartite Bell correlations, thus it is believed that for general translation invariant systems, two-qubit states should not violate the Bell inequality [Oliveira, Europhys. Lett. 100, 60004 (2012)]. In this Brief Report, we demonstrate that in perfect translation-invariant systems with an even number of sites, the Bell inequality can be violated. A nontrivial model is constructed to confirm the conclusion.
摘要：
The singularity of quantum correlation has been widely regarded as a valuable indicator for quantum phase transition (QPT) in low-dimensional quantum systems. In this paper, in a two-leg spin ladder with ring exchange, the critical points of the system cannot be detected by analyzing the singularity of the quantum discord (a kind of quantum correlation). Instead, the discord exhibits a novel odd-even effect in the symmetry-breaking (SB) regions, which can be used to detect the two critical points between the SB regions and the non-SB regions. The underlying mechanism of the odd-even effect is explained. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
摘要：
The quantum phase crossover in a spin ladder model with four-spin exchange is investigated. Previous studies show that the crossover cannot be detected by the singularity or finite-size analysis of ground-state observables for finite ladders. In this work, we find that the first-excited-state fidelity shows a sudden drop exactly at the crossover point, regardless of the length of the ladder. It suggests that the excited-state fidelity for finite systems is very effective in detecting the crossover in infinite systems. The underlying mechanism is understood through the analysis of re-construction of the low-lying energy levels of the systems.
摘要：
Recently, nonlocality and Bell inequalities have been used to investigate quantum phase transitions (QPTs) in low-dimensional quantum systems. Nonlocality can be detected by the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) function. In this work, we extend the study of the Bell-CHSH function (BCF) to QPTs in matrix product systems (MPSs). In these kinds of QPTs, the ground-state energy remains analytical in the vicinity of the QPT points, and they are usually called MPS-QPTs. For several typical models, our results show that the BCF can signal MPS-QPTs very well. In addition, we find the BCF can capture signal of QPTs in unentangled states and classical states, for which other measures of quantum correlation (quantum entanglement and quantum discord) fail. Furthermore, we find that in these MPSs, there exists some kind of quantum correlation which cannot be characterized by entanglement, or by nonlocality.
