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arXiv:2105.12391 · Physical Review A

Detection of a quantum phase transition in a spin-1 chain through multipartite high-order correlations

Dongkeun Lee, Adel Sohbi, Wonmin Son

Published Oct 20, 2022• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.106.042432

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We design a Bell inequality that is violated by correlations obtained from the ground states of an XXZXXZXXZ 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-DDD and AFM phase. Interestingly, the violation of our Bell inequality is manifested by the change in the XXZXXZXXZ 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 XXZXXZXXZ spin-1 chain with multibody correlations and high-order measurements.
We find non-localities, violation of local realism, in the many-body ground states of spin-1 XXZ chain with on-site anisotropy. In order to identify the non-localities in higher spin systems, we exploit the generalized version of multipartite Bell-type inequalities which characterize symmetric entangled states under the most general settings via combination of high-order correlations. For a given set of unbiased measurements, we obtain a sharp violation of the multipartite Bell-type inequality at the vicinity of the quantum criticality, a type of the first-order, in the regime of large exchanges and strong on-site anisotropies. It signifies that impossibility of local realistic picture is manifested when a system is subjected to quantum phase transition between weekly entangled states via GHZ-like state. Our results provide the first extendible picture on the relationship between the impossibility of local realistic model and many-body quantum phases in higher-spin system as the observable identifies measurable quantities to detect the non-locality on a particular many-body quantum state.
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 nnn-spin subsystem) in the QPT of an infinite XYXYXY chain. An efficient numerical optimization procedure is proposed to figure out the violation measure Mn{M}_{n}Mn​ of the inequalities. For $n\ensuremath{\le}7$, the magnetic-field ($\ensuremath{\lambda}$) dependence of Mn{M}_{n}Mn​ is studied. We find the derivative of Mn{M}_{n}Mn​ is divergent exactly at the QPT point ${\ensuremath{\lambda}}_{c}=1$ for any nnn. In addition, with the increase of nnn, Mn{M}_{n}Mn​ converges quickly for $\ensuremath{\lambda}<{\ensuremath{\lambda}}_{c}$ and converges very slowly for $\ensuremath{\lambda}>{\ensuremath{\lambda}}_{c}$, which can be regarded as another signal for the QPT. Furthermore, in the vicinity of ${\ensuremath{\lambda}}_{c}$, high-order Bell-type inequalities will be violated as long as nnn 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 nnn-partite entanglement or genuine nnn-partite nonlocality is not observed in the QPT.
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-12XXZ\frac{1}{2} XXZ21​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 XYXYXY 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.
Abstract Here we employ trace distance and bipartite correlations as the detectors for quantum phase transitions (QPTs). Their performances behaving in Ising spin chains with Dzyaloshinskii–Moriya (DM) interaction and an external transverse field are studied, respectively. Exploiting the quantum renormalization group method, all the detectors can effectively characterize the QPTs at the critical points. Moreover, the block–block correlations existing in the multipartite spin systems never violate the Bell inequality with the DM interaction, whereas they are enough to violate this inequality under the transverse field. Finally, we detail the nonanalytic and scaling behavior of the trace distance, which is tightly connected to the critical features of spin systems.
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 nnn-site subchains, and take the large-nnn limit. As nnn 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\mathit{XXZ}XXZ model, in the large-nnn 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.
Multipartite quantum nonlocality and Bell-type inequalities are used to characterize quantum correlations in an infinite-size bond-alternating spin-12\frac{1}{2}21​ Heisenberg chain with next-nearest-neighbor interactions. With the help of powerful tensor-network algorithms, both zero and finite temperatures are considered. First, at zero temperature, both in the even-Haldane phase and in the odd-Haldane phase, a high hierarchy of multipartite nonlocality is observed. Nevertheless, in the two phases, the spread of the multipartite nonlocality among the lattice is different. Thereby, the nonlocality measures are relatively large in one phase and vanish in the other phase, and provide quite sharp signals for the topological quantum phase transitions (QPTs) between these two phases. The influence of the next-nearest-neighbor coupling $\ensuremath{\alpha}$ upon the multipartite nonlocality in the model is also discussed. Second, we find that the footprints of the QPTs survive at low temperatures. Third, based upon the scaling behavior of the finite-temperature nonlocality measure, we propose a quantity K\mathcal{K}K to characterize the finite-temperature nonlocality in the large-nnn limit. We find that in high-temperature regions, K\mathcal{K}K is reduced linearly as the temperature rises.