Reduced-fidelity approach for quantum phase transitions in spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mstyle scriptlevel="1"><mml:mfrac bevelled="false"><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mstyle></mml:mrow></mml:math>dimerized Heisenberg chains

Xiong, Heng-Na; Ma, Jun; Sun, Zhe; Wang, Xiaoguang

doi:10.1103/physrevb.79.174425

Cited by 12 publications

(6 citation statements)

References 35 publications

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“…Chen et al [33] studied the ground-state fidelity and first-excited-state fidelity of this system. Xiong et al [29] found the reduced fidelity can also be used to indicate the quantum criticalities. In this paper, we will show that the two-site QD of the GS and the first ES is also effective to detect the QPTs.…”

Section: Gmqd For the Heisenberg Model With Nnn Interactionsmentioning

confidence: 99%

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Quantum discord and quantum phase transition in spin-1/2 frustrated Heisenberg chain

Fan¹,

Xiong²,

Huang³

et al. 2013

Preprint

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By using the concept of the quantum discord (QD), we study the spin-1/2 antiferromagnetic Heisenberg chain with next-nearest-neighbor interaction. Due to the SU (2) symmetry and Z2 symmetry in this system, we obtain the analytical result of the QD and its geometric measure (GMQD), which is determined by the two-site correlators. For the 4-site and 6-site cases, the connection between GMQD (QD) and the eigenenergies was revealed. From the analytical and numerical results, we find GMQD (QD) is an effective tool in detecting both the first-order and the infinite-order quantum-phase-transition points for the finite-size systems. Moreover, by using the entanglement excitation energy and a universal frustration measure we consider the frustration properties of the system and find a nonlinear dependence of the GMQD on the frustration.

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Section: Gmqd For the Heisenberg Model With Nnn Interactionsmentioning

confidence: 99%

“…Therefore, one can easily expect that some quantum concepts closely related to the ground states can be used to indicate QPTs. For example, the concepts of quantum entanglement [22][23][24][25][26][27], quantum fidelity [28][29][30][31][32][33] and quantum squeezing [34], have already been widely and successfully employed to study QPTs.…”

Section: Introductionmentioning

confidence: 99%

Quantum discord and quantum phase transition in spin-1/2 frustrated Heisenberg chain

Fan¹,

Xiong²,

Huang³

et al. 2013

Preprint

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“…( 22) and ( 25), we observe that the numerator of χ αα r is proportional to the square of the second derivative of GS energy and the denominator is finite in unpolarized state. The second power in the numerator indicates that the two-site RFS is more effective than the second derivative of the GS energy in measuring QPTs [76]. We compare the RFS of two NN sites with the second derivative of GS energy of N = 18 square lattice (see Fig.…”

Section: Reduced Fidelity Susceptibility In the 2d Compass Modelmentioning

confidence: 99%

Fidelity susceptibility in two-dimensional spin-orbit models

You

Dong

2011

Phys. Rev. B

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We study the quantum phase transitions in the two-dimensional spin-orbit models in terms of fidelity susceptibility and reduced fidelity susceptibility. An order-to-order phase transition is identified by fidelity susceptibility in the two-dimensional Heisenberg XXZ model with Dzyaloshinsky-Moriya interaction on a square lattice. The finite size scaling of fidelity susceptibility shows a power-law divergence at criticality, which indicates the quantum phase transition is of second order. Two distinct types of quantum phase transitions are witnessed by fidelity susceptibility in Kitaev-Heisenberg model on a hexagonal lattice. We exploit the symmetry of two-dimensional quantum compass model, and obtain a simple analytic expression of reduced fidelity susceptibility. Compared with the derivative of ground-state energy, the fidelity susceptibility is a bit more sensitive to phase transition. The violation of power-law behavior for the scaling of reduced fidelity susceptibility at criticality suggests that the quantum phase transition belongs to a first-order transition. We conclude that fidelity susceptibility and reduced fidelity susceptibility show great advantage to characterize diverse quantum phase transitions in spin-orbit models.

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“…Two kinds of QPT were found in this model [33][34][35]; one is the first-order QPT on the energylevel crossing of the GS, and the other is the infinite-order QPT related to the energy-level crossing of the excited states (ESs). Moreover, some quantum concepts have been successfully used to achieve QPT measurement, such as quantum entanglement [36][37][38][39][40], quantum squeezing [41], quantum discord and quantum fidelity [42][43][44][45][46][47]. This motivates us to investigate the relationship between QMA-EUR and QPTs.…”

Section: Introductionmentioning

confidence: 99%

Entropic uncertainty relation and quantum phase transition in spin-1/2 Heisenberg chain

Xiong

Sun

2020

Laser Phys. Lett.

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Based on the quantum-memory-assisted entropic uncertainty relation (QMA-EUR), we study the quantum phase transition (QPT) of a spin-1/2 frustrated Heisenberg chain and show that QMA entropy can be a useful tool to detect QPT. For the six-site case, we choose the reduced two-site as the detecting system and obtain the analytical result of QMA entropy and its bound. We find that the QMA entropy of the ground state is discontinuous at the first-order QPT point. Meanwhile for the excited state, the catastrophe point of QMA entropy approaches the infinite-order QPT point, which is confirmed by the numerical results in the 8-, 10-and 12-site cases. Moreover, we study the behavior of QMA entropy undergoing the dephasing process. Interestingly, two-site QMA entropy can still indicate the QPT point when the state degenerates into a mixed state. In this sense, QMA entropy is more effective than quantum correlation in reflecting the quantum criticality.

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Reduced-fidelity approach for quantum phase transitions in spin-12dimerized Heisenberg chains

Cited by 12 publications

References 35 publications

Quantum discord and quantum phase transition in spin-1/2 frustrated Heisenberg chain

Quantum discord and quantum phase transition in spin-1/2 frustrated Heisenberg chain

Fidelity susceptibility in two-dimensional spin-orbit models

Entropic uncertainty relation and quantum phase transition in spin-1/2 Heisenberg chain

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