The Ising and anisotropy phase transitions of the periodic XY model in a transverse field

Zhong, Ming; Tong, Peiqing

doi:10.1088/1751-8113/43/50/505302

Cited by 23 publications

(26 citation statements)

References 35 publications

(49 reference statements)

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“…As is well-known the XY model undergoes a second-order QPT (Ising transition [36]) at the CP λ c = 1 [10], that separates a ferromagnetic ordered phase from a quantum paramagnetic phase. For λ > 1 one can observe another second-order QPT at the CP γ c = 0 called anisotropy transition [35,37]. Differently from the Ising transition, that is due to the action of the external field, this transition is driven by the anisotropy parameter γ and separates a ferromagnet ordered along the x direction and a ferromagnet ordered along the y direction.…”

Section: B the Xy Modelmentioning

confidence: 99%

Spotlighting quantum critical points via quantum correlations at finite temperatures

2011

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We extend the program initiated in [T. Werlang et al., Phys. Rev. Lett. 105, 095702 (2010)] in several directions. Firstly, we investigate how useful quantum correlations, such as entanglement and quantum discord, are in the detection of critical points of quantum phase transitions when the system is at finite temperatures. For that purpose we study several thermalized spin models in the thermodynamic limit, namely, the XXZ model, the XY model, and the Ising model, all of which with an external magnetic field. We compare the ability of quantum discord, entanglement, and some thermodynamic quantities to spotlight the quantum critical points for several different temperatures. Secondly, for some models we go beyond nearest-neighbors and also study the behavior of entanglement and quantum discord for second nearest-neighbors around the critical point at finite temperature. Finally, we furnish a more quantitative description of how good all these quantities are in spotlighting critical points of quantum phase transitions at finite T , bridging the gap between experimental data and those theoretical descriptions solely based on the unattainable absolute zero assumption.

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Section: B the Xy Modelmentioning

confidence: 99%

Spotlighting quantum critical points via quantum correlations at finite temperatures

2011

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“…To be more precise, modes with positive and negative velocity follow different KMS conditions. (See equation (27) of [31] for the XY chain. See also equation (54) in [30] for the XX chain, where a more explicit expression in terms of the Fermi distribution is provided in equation (65).…”

Section: Nqpt In the Xy Spin 1/2 Model: The C ã Algebra Approachmentioning

confidence: 99%

“…In this paper we use the * C algebra approach, the Lindblad formalism with mesoreservoirs, and the modified Redfield master equation to study the XY spin 1/2 chain-a paradigmatic model exhibiting quantum phase transitions (QPTs) [25][26][27]. The Hamiltonian of the transverse-field XY spin 1/2 chain is where γ denotes the anisotropy, h denotes the magnetic field, and σ m x,y,z are the Pauli spin operators at the mth site.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium quantum phase transitions in the XY model: comparison of unitary time evolution and reduced density operator approaches

Ajisaka¹,

Barra²,

Žunkovič³

2014

New J. Phys.

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We study nonequilibrium quantum phase transitions in the XY spin 1/2 chain using the * C algebra. We show that the well-known quantum phase transition at a magnetic field of h = 1 also persists in the nonequilibrium setting as long as one of the reservoirs is set to absolute zero temperature. In addition, we find nonequilibrium phase transitions associated with an imaginary part of the correlation matrix for any two different reservoir temperatures at h = 1 and γ = ≡ − h h 1 c 2 , where γ is the anisotropy and h the magnetic field strength. In particular, two nonequilibrium quantum phase transitions coexist at h = 1. In addition, we study the quantum mutual information in all regimes and find a logarithmic correction of the area law in the nonequilibrium steady state independent of the system parameters. We use these nonequilibrium phase transitions to test the utility of two models of a reduced density operator, namely the Lindblad mesoreservoir and the modified Redfield equation. We show that the nonequilibrium quantum phase transition at h = 1, related to the divergence of magnetic susceptibility, is recovered in the mesoreservoir approach, whereas it is not recovered using the Redfield master equation formalism. However, none of the reduced density operator approaches could recover all the transitions observed by the * C algebra. We also study the thermalization properties of the mesoreservoir approach.Keywords: nonequilibrium quantum phase transition, XY model, quantum spin chain, exact solution New J. Phys. 16 (2014) 033028 S Ajisaka et al New J. Phys. 16 (2014) 033028 S Ajisaka et al c 2. We also discuss the phase transition at the critical point γ = 0 and h = 1. These results are contrasted with two reduced density operator approaches, which will be discussed in section 3. New J. Phys. 16 (2014) 033028 S Ajisaka et al 4 New J. Phys. 16 (2014) 033028 S Ajisaka et al 6 New J. Phys. 16 (2014) 033028 S Ajisaka et al 9 New J. Phys. 16 (2014) 033028 S Ajisaka et al 17 New J. Phys. 16 (2014) 033028 S Ajisaka et al 18

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“…The study of quantum correlations in the spin systems through the QRG reflects both quantum information properties as well as critical properties of the system [5,6,10,29,[31][32][33]. The ground-state spin entanglement in ddimensional bipartite lattice of the XXZ moel is studied [34], where bipartite concurrence shows similar qualitative behavior.…”

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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The Ising and anisotropy phase transitions of the periodic XY model in a transverse field

Cited by 23 publications

References 35 publications

Spotlighting quantum critical points via quantum correlations at finite temperatures

Spotlighting quantum critical points via quantum correlations at finite temperatures

Nonequilibrium quantum phase transitions in the XY model: comparison of unitary time evolution and reduced density operator approaches

Spatial dependence of entanglement renormalization in XY model

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