Robust thermal quantum correlation and quantum phase transition of spin system on fractal lattices

Xu, Yu-Liang; Zhang, Xin; Liu, Zhongqiang; Kong, Xiangbin; Ren, Tong

doi:10.1140/epjb/e2014-50033-5

Cited by 14 publications

(10 citation statements)

References 46 publications

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“…Initial reports by Osborne and Nielsen [12], and Osterloh et al [13] found the singular and scaling behaviors of pairwise entanglement close to the QCP of the Ising spin chain. Based on these results, the pairwise or block entanglements have been applied to study the QPT in one-dimension (1D) systems by analytic or numerical methods [17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

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

Kong

Liu

et al. 2016

Physica A: Statistical Mechanics and its Applications

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Section: Introductionmentioning

confidence: 99%

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

Kong

Liu

et al. 2016

Physica A: Statistical Mechanics and its Applications

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“…But, it isn't difficult to find that the present studies have focused on the one-dimensional spin chain, the studies of fractal lattices are less [29,35].…”

Section: Introductionmentioning

confidence: 85%

“…As a common representation of quantum correlation, QD captures nonclassical correlation even without entanglement. For a quantum state ρ 12 of the composite system containing subsystems 1 and 2, the QD [29,45] is defined as…”

Section: The Quantum Correlations For the Three Latticesmentioning

confidence: 99%

“…The quantum discord (QD) which captures nonclassical correlation even without entanglement is proved as an effective measure for all aspects of quantum correlation [26,27]. As a wider class of measures than entanglement, QD has become an active research topic over the past few years [28][29][30], which has important application value in quantum information processing, quantum dynamics and even biophysics [31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

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Phase diagrams, quantum correlations and critical phenomena of antiferromagnetic Heisenberg model on diamond-type hierarchical lattices

Zhang¹,

Gao²,

Xu³

et al. 2021

Preprint

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The anisotropic spin-1/2 antiferromagnetic Heisenberg systems are studied on three typical diamond-type hierarchical lattices (systems A, B and C) with fractal dimensions d f = 1.63, 2 and 2.58, respectively. For system A, using the real-space renormalization group approach, we calculate the phase diagram, the critical exponent and quantum discord, and find that there exists a reentrant behavior in the phase diagram. We also find that the quantum discord reaches its maximum at T = 0 and the thermal quantum discord decreases with the increase of L, and it is almost zero at L ≥ 30. No matter how large the size of system is, quantum discord will change to 0 when anisotropic parameter ∆ = 1. For systems B and C, using the equivalent transformation and the real-space renormalization group method, we obtain phase diagrams and find that: the Néel temperature tends to zero in the isotropic Heisenberg limit on d f = 2 system; there exists a phase transition in the isotropic Heisenberg model on system C. By studying quantum discord, we find that there is a certain degree of twist of the relation curve between quantum discord and T when ∆ = 0. Moreover, as an example, we discuss the quantum effect in system A, which can be responsible for the existence of the reentrant behavior in the phase diagram.

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“…Exact calculations on hierarchical lattices are also currently widely used on a variety of statistical mechanics problems [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. On the other hand, this approximation for the cubic lattice is an uncontrolled approximation, as in fact are all renormalization-group theory calculations in d = 3 and all mean-field theory calculations.…”

Section: Renormalization-group Method: Migdal-kadanoff Approximamentioning

confidence: 99%

Devil's staircase continuum in the chiral clock spin glass with competing ferromagnetic-antiferromagnetic and left-right chiral interactions

Çağlar

Berker

2017

Phys. Rev. E

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The chiral clock spin-glass model with q = 5 states, with both competing ferromagnetic-antiferromagnetic and left-right chiral frustrations, is studied in d = 3 spatial dimensions by renormalization-group theory. The global phase diagram is calculated in temperature, antiferromagnetic bond concentration p, random chirality strength, and right-chirality concentration c. The system has a ferromagnetic phase, a multitude of different chiral phases, a chiral spin-glass phase, and a critical (algebraically) ordered phase. The ferromagnetic and chiral phases accumulate at the disordered phase boundary and form a spectrum of devil's staircases, where different ordered phases characteristically intercede at all scales of phase-diagram space. Shallow and deep reentrances of the disordered phase, bordered by fragments of regular and temperature-inverted devil's staircases, are seen. The extremely rich phase diagrams are presented as continuously and qualitatively changing videos.

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Robust thermal quantum correlation and quantum phase transition of spin system on fractal lattices

Cited by 14 publications

References 46 publications

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

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

Phase diagrams, quantum correlations and critical phenomena of antiferromagnetic Heisenberg model on diamond-type hierarchical lattices

Devil's staircase continuum in the chiral clock spin glass with competing ferromagnetic-antiferromagnetic and left-right chiral interactions

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