Global Quantum Discord in Transverse‐Field Ising Models on <i>N</i> × <i>N</i> Square Lattices

Sun, Zhao‐Yu; Zhou, Mu; Wang, Mei; Fu, Jin

doi:10.1002/pssb.201800666

Cited by 3 publications

(3 citation statements)

References 43 publications

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“…Taking into account all the quantum correlations of the many-body quantum systems, the idea of the global quantum discord (GQD) is introduced [71,72]. There has been great interest in employing GQD to characterize the quantum phase transitions in low-dimensional spin systems [73][74][75][76]. However, to our best knowledge, multiqubit quantum correlations have rarely been examined and how the multipartite quantum correlations behave is not clear in an MBL system.…”

Section: Introductionmentioning

confidence: 99%

Identifying many-body localization transition through global quantum discord

Shen¹,

Bao²,

Guo³

et al. 2023

J. Phys.: Condens. Matter

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We investigate the many-body localization (MBL) transitions in a spin-1/2 Heisenberg chain with an on-site random magnetic field by employing global quantum discord (GQD). We use the disorder-averaged GQD to estimate the MBL critical point, which is found to be around at W c = 3.8 by making a finite-size scaling analysis. We further compare our results of GQD with those of half-chain entanglement entropy (EE) that is promising in the study of MBL. We show that GQD can exclude the finite-size interference under the same condition, which implies that GQD is more robust than the half-chain EE in characterizing MBL.

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Section: Introductionmentioning

confidence: 99%

Identifying many-body localization transition through global quantum discord

Shen¹,

Bao²,

Guo³

et al. 2023

J. Phys.: Condens. Matter

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“…Fortunately, Sun and his collaborators have proposed an efficient method to study GQD in the framework of tensor networks algorithm [33]. Combined with the MPSs and matrix product density operators (MPDOs) algorithms, the properties of GQD, both for pure states and mixed states in low-dimension quantum systems, have been widely investigated [33][34][35][36][37][38]. These studies mainly focus on the low-dimension quantum spin systems where are suitable for expressing the true materials.…”

Section: Introductionmentioning

confidence: 99%

Global quantum discord in the Lipkin–Meshkov–Glick model at zero and finite temperatures

Bao¹,

Liu²,

Guo³

2021

J. Phys.: Condens. Matter

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We study the global quantum discord (GQD) in the Lipkin-Meshkov-Glick (LMG) model at zero and finite temperatures, in which all spins are mutually interacted and introduced in an external magnetic field (denoted by h). We confirm that the high coordinate number is one of the most distinguishing features of the LMG model, which directly results in the nontrivial behaviors of quantum correlations. We compare the GQD with other quantum correlations measures (such as concurrence, quantum discord, and global entanglement) and find the remarkable difference between them. For instance, we find that GQD spreads in the entire system and captures more information on quantum correlations when comparing with concurrence and quantum (pairwise) discord. We discover that GQD can characterize multipartite correlations in the both broken phase (h < 1) and the symmetric phase (h 1), while global entanglement and its generalized fail. Moreover, we show that the ground-state GQD can identify second-order quantum phase transitions of the LMG model in the thermodynamic limit. By making the scaling behavior of the GQD in the LMG model analysis, we show that GQD (denoted by G) scales as G ∼ k • N + c with k > 0 in the anisotropic cases for any fixed magnetic field. We further show that GQD behaves as G| s n ∼ k • 1 N + c with k < 0 in the isotropic cases for any Dicke state |s n . Herein k and c are the fitting parameters. We also find that the thermal stability of the GQD at low temperatures depends on the energy gap. We further reveal that the extraordinary behaviors of the thermal-state GQD in the isotropic LMG model are explained by the contribution theory of the energy levels.

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“…[ 19,20 ] Second, quantum entanglement can also be applied to characterize the quantum phase transitions (QPTs), [ 2–7,21 ] which help us to expand our understanding of condensed matter physics. Many quantities are developed to identify the quantum entanglement, [ 8,22 ] which one of the simplest forms of quantum entanglement is bipartite entanglement that describes the entanglement between two parts of the system, such as entanglement concurrence and entanglement entropy. [ 23–25 ] They both have been found to exhibit maximum values, singularities, or scaling behaviors near the QPT point.…”

Section: Introductionmentioning

confidence: 99%

Multipartite Nonlocality of Finite and Infinite Transverse‐Field Ising Model

Liu

Bao

Guo

et al. 2021

Physica Status Solidi (b)

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The multipartite nonlocality of finite and infinite transverse‐field Ising model is investigated. For the finite chain, the exact diagonalization method is used to study the multipartite nonlocality at zero and finite temperatures. It is found that the logarithm of nonlocality S presents the linear relationship with the chain length of N at zero temperature. The multipartite nonlocality S shows a peak value near the phase transition point, which can be used to characterize the quantum phase transition of the Ising model. The inherent physical mechanics is that the nonlocality S captures the effect of low‐lying states with a small energy gap. The nonlocality S at the finite temperature is also observed to be scaled as log2 S ≈ aN + b at any fixed magnetic field B, where a and b are fitting parameters. For the infinite chain, the thermal tensor network algorithm is used to examine the multipartite nonlocality. The behaviors of nonlocality S of the infinite chain at the finite temperature are similar to those of finite chain. Compared with the finite chain, the positions of the peak values of the multipartite nonlocality shift to the larger magnetic field, and the peak values are smaller than those of finite chain.

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Global Quantum Discord in Transverse‐Field Ising Models on N × N Square Lattices

Cited by 3 publications

References 43 publications

Identifying many-body localization transition through global quantum discord

Identifying many-body localization transition through global quantum discord

Global quantum discord in the Lipkin–Meshkov–Glick model at zero and finite temperatures

Multipartite Nonlocality of Finite and Infinite Transverse‐Field Ising Model

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