Quantum entanglement and quantum phase transition for the Ising model on a two-dimension square lattice

Xu, Yu-Liang; Kong, Xiangbin; Liu, Zhongqiang; Wang, Chunyang

doi:10.1016/j.physa.2015.12.002

Cited by 19 publications

(12 citation statements)

References 35 publications

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“…The stable and unstable fixed points h 1 = (0, 1, ∞) of the QRG equations are obtained by solving h 1 h 1 ′ h 1 *, where h 1 = 1 is an unstable fixed point and the QCP of the 1D system. Using the similar QRG method of 1D model [48,49,51,52], now we turn to investigate the related properties of the 2D square lattice. As previously discussed, the values of k and ω are theoretically set to be 0.01 in the rest of this paper.…”

Section: Qrg For the Transverse-field Ising Modelsmentioning

confidence: 99%

“…At zero temperature, the QRG method provides insights into how the block uncertainty and entanglement change as the size of the system becomes large in 1D spin chains. On the basis of the 1D case, some further contributions on two-dimensional (2D) and higher-dimensional systems have been recently made [48][49][50][51][52][53]. In this work, we introduce two different types of the time-dependent magnetic fields into the 2D Ising models, and obtain the effective Hamiltonian of the models by employing the QRG method.…”

Section: Introductionmentioning

confidence: 99%

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Uncertainty Relation and Quantum Phase Transition in the Two-Dimensional Ising Model

Fang

Jiang

2022

Front. Phys.

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By using quantum renormalization group (QRG) approach, we first derive the effective Hamiltonian and QRG equations of the two-dimensional (2D) Ising models with two different time-dependent transverse magnetic fields analytically. Then we examine the nonanalytic and scaling behaviors of the linear-entropy-based uncertainty relation and quantum entanglement of the models near the critical point through numerical analysis. Moreover, we investigate the relation between the quantum critical point and the external magnetic field. Our results show that both the uncertainty relation and the quantum entanglement are feasible to detect the quantum phase transition (QPT), and the uncertainty relation may be a better indicator of QPT than quantum entanglement. Our findings could shed new light on the observable of the QPTs of the solid-state system with the uncertainty relation.

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Section: Qrg For the Transverse-field Ising Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Uncertainty Relation and Quantum Phase Transition in the Two-Dimensional Ising Model

Fang

Jiang

2022

Front. Phys.

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“…Recently, Xu [31] investigated the quantum entanglement around the quantum critical point in the Ising model on a square lattice. Usman [32] gave an analysis of two-dimensional XY systems by using entanglement theory.…”

Section: Introductionmentioning

confidence: 99%

Monogamy quantum correlation near the quantum phase transitions in the two-dimensionalXYspin systems

Qin¹,

Ren²,

Zhang³

2018

Chinese Phys. B

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We investigate the role of quantum correlation around the quantum phase transitions by using quantum renormalization group theory. Numerical analysis indicates that quantum correlation as well as quantum nonlocality can efficiently detect the quantum critical point in the two-dimensional XY systems. The nonanalytic behavior of the first derivative of quantum correlation is observed at the critical point as the size of the model increases. Furthermore, we discuss the quantum correlation distribution in this system based on the square of concurrence (SC) and square of quantum discord (SQD). The monogamous properties of SC and SQD are obtained. Particularly, we prove that the quantum critical point can also be achieved by monogamy score.

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“…In the past, different numerical techniques were used to study such systems [14,15]. Because numerical techniques are suitable to handle the computational complexity in finding the ground states, renormalized control parameters, entanglement and critical properties in higher dimensions [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Spatial dependence of entanglement renormalization in XY model

Usman

Ilyas

Khan

2017

Quantum Inf Process

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In this article a comparative study of the renormalization of entanglement in one, two and three dimensional space and its relation with quantum phase transition (QPT) near the critical point is presented by implementing the Quantum Renormalization Group (QRG) technique. Adopting the Kadanoff's block approach, numerical results for the concurrence are obtained for the spin -1/2 XY model in all the spatial dimensions. The results show similar qualitative behavior as we move from the lower to the higher dimensions in space but the number of iterations reduces for achieving the QPT in the thermodynamic limit. We find that in the two dimensional and three dimensional spin -1/2 XY model, maximum values of the concurrence reduce by the factor of 1/n (n = 2, 3) with reference to the maximum value of one dimensional case. Moreover, we study the scaling behavior and the entanglement exponent. We compare the results for one, two and three dimensional cases and illustrate how the system evolves near the critical point.1 arXiv:1610.00761v1 [quant-ph]

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Quantum entanglement and quantum phase transition for the Ising model on a two-dimension square lattice

Cited by 19 publications

References 35 publications

Uncertainty Relation and Quantum Phase Transition in the Two-Dimensional Ising Model

Uncertainty Relation and Quantum Phase Transition in the Two-Dimensional Ising Model

Monogamy quantum correlation near the quantum phase transitions in the two-dimensionalXYspin systems

Spatial dependence of entanglement renormalization in XY model

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