Fidelity susceptibility of the anisotropic 
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 model: The exact solution

Luo, Qiang; Zhao, Jize; Wang, Xiaoqun

doi:10.1103/physreve.98.022106

Cited by 29 publications

(22 citation statements)

References 54 publications

(69 reference statements)

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“…On the other hand, in the usual setting considered in the literature, the transverse field g is varied across the value g = 1, and the longitudinal field is kept fixed at h = 0 [11,14,15,[17][18][19]. In such case, an analogous FSS follows [17], where the scaling variable of Eq.…”

Section: A Fss At the Continuous Transitionmentioning

confidence: 99%

“…Let us finally consider equal fixed boundary conditions (EFBC) favoring one of the two magnetized phases. This is obtained by adding equal fixed spin states | ↓ at the ends x = 0 and x = L + 1 of the chain (18). In such case, the interplay between the size L and the bulk field h gives rise to a more complex finite-size behavior with respect to that of neutral boundary conditions, such as PBC and ABC [53].…”

Section: Equal and Fixed Boundary Conditionsmentioning

confidence: 99%

“…In quantum many-body systems, the establishment of a non-analytic behavior has been exploited to evidence CQTs in several different contexts, which have been deeply scrutinized both analytically and numerically. We quote, for example, free-fermion models [14][15][16][17][18], interacting spin [19][20][21][22][23][24][25] and particle models [26][27][28][29][30][31][32], as well as systems presenting peculiar topological [33][34][35] and nonequilibrium steady-state transitions [36,37]. However a characterization of first-order QTs (FOQTs) in this context is still missing, despite the fact that they are of great phenomenological interest.…”

Section: Introductionmentioning

confidence: 99%

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Ground-state fidelity at first-order quantum transitions

Rossini

Vicari

2018

Phys. Rev. E

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We analyze the scaling behavior of the fidelity, and the corresponding susceptibility, emerging in finite-size many-body systems whenever a given control parameter λ is varied across a quantum phase transition. For this purpose we consider a finite-size scaling (FSS) framework. Our working hypothesis is based on a scaling assumption of the fidelity in terms of the FSS variables associated to λ and to its variation δλ. This framework entails the FSS predictions for continuous transitions, and meanwhile enables to extend them to first-order transitions, where the FSS becomes qualitatively different. The latter is supported by analytical and numerical analyses of the quantum Ising chain along its first-order quantum transition line, driven by an external longitudinal field. arXiv:1807.01674v2 [cond-mat.stat-mech] 30 Nov 2018

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Section: A Fss At the Continuous Transitionmentioning

confidence: 99%

Section: Equal and Fixed Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Ground-state fidelity at first-order quantum transitions

Rossini

Vicari

2018

Phys. Rev. E

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“…The XY chain with the transverse field is attracting much attention [1,2,3] in the context of the quantum information theory [4,5,6]. A key ingredient is that the model covers both the XX-and XY -symmetric cases, and a variety of phase transitions occur, as the transverse field and the XY -anisotropy change.…”

Section: Introductionmentioning

confidence: 99%

Fidelity-mediated analysis of the transverse-field $XY$ chain with the long-range interactions: Anisotropy-driven multi-criticality

Nishiyama

2021

Preprint

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The transverse-field XY chain with the long-range interactions was investigated by means of the exact-diagonalization method. The algebraic decay rate σ of the long-range interaction is related to the effective dimensionality D(σ), which governs the criticality of the transverse-field-driven phase transition at H = H c . According to the large-N analysis, the phase boundary H c (η) exhibits a reentrant behavior within 2 < D < 3.065 . . ., as the XY -anisotropy η changes. On the one hand, as for the D = (2 + 1) and (1 + 1) short-range XY magnets, the singularities have been determined as H c (η) − H c (0) ∼ |η| and 0, respectively, and the transient behavior around D ≈ 2.5 remains unclear. As a preliminary survey, setting (σ, η) = (1, 0.5), we investigate the phase transition by the agency of the fidelity, which seems to detect the singularity at H = H c rather sensitively. Thereby, under the setting σ = 4/3 (D = 2.5), we cast the fidelity data into the crossover-scaling formula with the properly scaled η, aiming to determine the multi-criticality around η = 0. Our result indicates that the multi-criticality is identical to that of the D = (2 + 1) magnet, and H c (η)'s linearity might be retained down to D > 2.

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“…The one-dimensional XY model subjected to the transverse field H and anisotropy η with the Hamiltonian H XY = − i [(1 + η)σ x i σ x i+1 + (1 − η)σ y i σ y i+1 + Hσ z i ] (σ i : Pauli matrices at site i) is attracting much attention [1,2,3,4] in the context of the quantum information theory [5,6]. A key ingredient is that the model covers both XX-(η = 0) and Ising-symmetric (η = 1) cases, and there appear rich characters as to the transversefield-driven order-disorder phase transition.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional easy-plane SU$(3)$ magnet with the transverse field: Anisotropy-driven multicriticality

Nishiyama

2021

Preprint

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The two-dimensional easy-plane SU(3) magnet subjected to the transverse field was investigated with the exact-diagonalization method. So far, as to the XY model (namely, the easy-plane SU(2) magnet), the transverse-field-driven order-disorder phase boundary has been investigated with the exact-diagonalization method, and it was claimed that the end-point singularity (multicriticality) at the XXsymmetric point does not accord with large-N -theory's prediction. Aiming to reconcile the discrepancy, we extend the internal symmetry to the easy-plane SU(3) with the anisotropy parameter η, which interpolates the isotropic (η = 0) and fully anisotropic (η = 1) cases smoothly. As a preliminary survey, setting η = 1, we analyze the orderdisorder phase transition through resorting to the fidelity susceptibility χ F , which exhibits a pronounced signature for the criticality. Thereby, with η scaled carefully, the χ F data are cast into the crossover-scaling formula so as to determine the crossover exponent φ, which seems to reflect the extension of the internal symmetry group to SU(3).

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Fidelity susceptibility of the anisotropic XY model: The exact solution

Cited by 29 publications

References 54 publications

Ground-state fidelity at first-order quantum transitions

Ground-state fidelity at first-order quantum transitions

Fidelity-mediated analysis of the transverse-field $XY$ chain with the long-range interactions: Anisotropy-driven multi-criticality

Two-dimensional easy-plane SU$(3)$ magnet with the transverse field: Anisotropy-driven multicriticality

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