Thermal entanglement between non-nearest-neighbor spins on fractal lattices

Xu, Yu-Liang; Wang, Lu-Shun; Kong, Xiangbin

doi:10.1103/physreva.87.012312

Cited by 17 publications

(4 citation statements)

References 55 publications

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“…This intuition has been verified for a large number of two-spin systems [18], initially using the concurrence [19][20][21][22][23][24][25][26][27][28][29][30] (for a review, see Ref. 2) and more recently using the negativity [31][32][33]. Generically, there exists a well-defined temperature T c , dubbed the "sudden death temperature," above which the negativity vanishes identically.…”

Section: Introductionmentioning

confidence: 91%

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Entanglement negativity and sudden death in the toric code at finite temperature

Hart¹,

Castelnovo²

2018

Phys. Rev. B

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We study the fate of quantum correlations at finite temperature in the two-dimensional toric code using the logarithmic entanglement negativity. We are able to obtain exact results that give us insight into how thermal excitations affect quantum entanglement. The toric code has two types of elementary excitations (defects) costing different energies. We show that an O(1) density of the lower energy defect is required to degrade the zero-temperature entanglement between two subsystems in contact with one another. However, one type of excitation alone is not sufficient to kill all quantum correlations, and an O(1) density of the higher energy defect is required to cause the so-called sudden death of the negativity. Interestingly, if the energy cost of one of the excitations is taken to infinity, quantum correlations survive up to arbitrarily high temperatures, a feature that is likely shared with other quantum spin liquids and frustrated systems in general, when projected down to their low-energy states. We demonstrate this behaviour both for small subsystems, where we can prove that the negativity is a necessary and sufficient condition for separability, as well as for extended subsystems, where it is only a necessary condition. We further observe that the negativity per boundary degree of freedom at a given temperature increases (parametrically) with the size of the boundary, and that quantum correlations between subsystems with extended boundaries are more robust to thermal fluctuations.

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Section: Introductionmentioning

confidence: 91%

“…2) and more recently using the negativity [31][32][33]. Generically, there exists a well-defined temperature T c , dubbed the "sudden death temperature," above which the negativity vanishes identically.…”

Section: Introductionmentioning

confidence: 99%

Entanglement negativity and sudden death in the toric code at finite temperature

Hart¹,

Castelnovo²

2018

Phys. Rev. B

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“…An important applications of entanglement is to depict quantum phase transition (QPT) [5, 6,7,8,9,10,11,12,13]. The relevant investigation has estab- 10 lished deep links between quantum information theory and condensed matter physics.…”

Section: Introductionmentioning

confidence: 99%

Thermal quantum correlations and quantum phase transitions in Ising-XXZ diamond chain

(高坤)

Kong

et al. 2015

Physica A: Statistical Mechanics and its Applications

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“…Among spin-1/2 chain models, the Heisenberg chain is one of the simplest quantum models which is usually considered as the medium for generating quantum entanglements [2,3,[47][48][49][50][51]. However, spin-1 systems have, naturally, richer phase diagrams and exhibit more complex phenomena and finding their ground state is rather more complicated.…”

Section: Introductionmentioning

confidence: 99%

Generalized concurrence and quantum phase transition in spin-1 Heisenberg model

2020

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In this paper we investigate the ability of the generalized concurrence as a quantum entanglement measure to describe the quantum and thermal phase transitions in the spin-1 Heisenberg model with bilinear and biquadratic interactions and single-ion anisotropy terms, under a magnetic field. Calculations are performed for two and three spin chains based on the exact diagonalization method. We show that in the near vicinity of the zero temperature, the generalized concurrence changes abruptly from a finite non-zero value to zero by changing the parameters of the model. This is signature of a quantum phase transition that is carefully justified by studying the thermodynamic functions such as magnetization, particle number, particle susceptibility and magnetic susceptibility. The critical points are found and various ordered phases are discussed.

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Thermal entanglement between non-nearest-neighbor spins on fractal lattices

Cited by 17 publications

References 55 publications

Entanglement negativity and sudden death in the toric code at finite temperature

Entanglement negativity and sudden death in the toric code at finite temperature

Thermal quantum correlations and quantum phase transitions in Ising-XXZ diamond chain

Generalized concurrence and quantum phase transition in spin-1 Heisenberg model

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