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- Title
Fidelity-mediated analysis of the transverse-field XY chain with the long-range interactions: anisotropy-driven multi-criticality.
- Authors
Nishiyama, Yoshihiro
- Abstract
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 .
- Subjects
PHASE transitions; MAGNETS
- Publication
European Physical Journal B: Condensed Matter, 2021, Vol 94, Issue 11, p1
- ISSN
1434-6028
- Publication type
Article
- DOI
10.1140/epjb/s10051-021-00245-1