Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model

Yang, Shuming; Gu, Shi-Jian; Sun, C. P.; Lin, Hai–Qing

doi:10.1103/physreva.78.012304

Cited by 149 publications

(174 citation statements)

References 41 publications

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“…We expect that the same mechanism as described above should be able to explain oscillations of fidelity (peaks in fidelity susceptibility) observed in the gapless phase of the Kitaev model [41].…”

Section: B Across γ=0 Critical Linementioning

confidence: 99%

Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond

Rams

Damski

2011

Phys. Rev. A

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We study ground state fidelity defined as the overlap between two ground states of the same quantum system obtained for slightly different values of the parameters of its Hamiltonian. We focus on the thermodynamic regime of the XY model and the neighborhood of its critical points. We describe in detail cases when fidelity is dominated by the universal contribution reflecting quantum criticality of the phase transition. We show that proximity to the multicritical point leads to anomalous scaling of fidelity. We also discuss fidelity in a regime characterized by pronounced oscillations resulting from the change of either the system size or the parameters of the Hamiltonian. Moreover, we show when fidelity is dominated by non-universal contributions, study fidelity in the extended Ising model, and illustrate how our results provide additional insight into dynamics of quantum phase transitions. Special attention is put to studies of fidelity from the momentum space perspective. All our main results are obtained analytically. They are in excellent agreement with numerics.

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Section: B Across γ=0 Critical Linementioning

confidence: 99%

Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond

Rams

Damski

2011

Phys. Rev. A

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“…[2][3][4][5] Because the ground states in some topological quantum systems (e.g., the Kitaev spin models on honeycomb 3 and triangle-honeycomb 5 lattices) are exactly solvable, QPTs in these systems can be analytically investigated. In these topological systems, the discovered QPTs include the transition between a gapped Abelian phase and a gapless phase, 4,6 the transition between Abelian and non-Abelian phases, 5,[7][8][9][10] and the transition between two non-Abelian phases with different Chern numbers. 3 Also, an unconventional QPT between two non-Abelian phases was found 11 in the Kitaev spin model on a trianglehoneycomb lattice by a fermionization method.…”

Section: Introductionmentioning

confidence: 99%

“…(A20), we can define an analytical function F c (1) k , c (2) k , c (3) k , c (4) k , c (5) k , c (6) k by |g(Λ 1 ,…”

mentioning

confidence: 99%

Exotic phase diagram of a topological quantum system

2010

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We study the quantum phase transitions (QPTs) in the Kitaev spin model on a trianglehoneycomb lattice. In addition to the ordinary topological QPTs between Abelian and non-Abelian phases, we find new QPTs which can occur between two phases belonging to the same topological class, namely, either two non-Abelian phases with the same Chern number or two Abelian phases with the same Chern number. Such QPTs result from the singular behaviors of the nonlocal spin-spin correlation functions at the critical points.

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“…It is obvious that QFI is only constituted by the nonzero eigenvalues and the corresponding eigenstates of the density matrix (23), namely, QFI is only determined by the support of (23).…”

Section: Application To X Statesmentioning

confidence: 99%

“…FS is a more effective tool than fidelity itself in quantum physics, especially in detecting the quantum phase transitions [19,22,23]. Interestingly, the above two seemingly irrelevant concepts are in fact closely related to each other.…”

Section: Introductionmentioning

confidence: 99%

Fidelity susceptibility and quantum Fisher information for density operators with arbitrary ranks

Liu

Xiong

Song

et al. 2014

Physica A: Statistical Mechanics and its Applications

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Abstract. Taking into account the density matrices with non-full ranks, we show that the fidelity susceptibility is determined by the support of the density matrix. Combining with the corresponding expression of the quantum Fisher information, we rigorously prove that the fidelity susceptibility is proportional to the quantum Fisher information. As this proof can be naturally extended to the full rank case, this proportional relation is generally established for density matrices with arbitrary ranks. Furthermore, we give an analytical expression of the quantum Fisher information matrix, and show that the quantum Fisher information matrix can also be represented in the density matrix's support.

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Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model

Cited by 149 publications

References 41 publications

Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond

Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond

Exotic phase diagram of a topological quantum system

Fidelity susceptibility and quantum Fisher information for density operators with arbitrary ranks

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