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- W3216987651 abstract "The transverse-field $XY$ chain with the long-range interactions was investigated by means of the exact-diagonalization method. The algebraic decay rate $sigma$ of the long-range interaction is related to the effective dimensionality $D(sigma)$, which governs the criticality of the transverse-field-driven phase transition at $H=H_c$. According to the large-$N$ analysis, the phase boundary $H_c(eta)$ exhibits a reentrant behavior within $2<D < 3.065dots $, as the $XY$-anisotropy $eta$ changes. On the one hand, as for the $D=(2+1)$ and $(1+1)$ short-range $XY$ magnets, the singularities have been determined as $H_c(eta) -H_c(0) sim |eta|$ and $ 0 $, respectively, and the transient behavior around $D approx 2.5$ remains unclear. As a preliminary survey, setting $(sigma,eta)=(1 ,0.5)$, 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 $ sigma=4/3$ ($D=2.5$), we cast the fidelity data into the crossover-scaling formula with the properly scaled $eta$, aiming to determine the multi-criticality around $eta=0$. Our result indicates that the multi-criticality is identical to that of the $D=(2+1)$ magnet, and $H_c(eta)$'s linearity might be retained down to $D>2$." @default.
- W3216987651 created "2021-12-06" @default.
- W3216987651 creator A5065833523 @default.
- W3216987651 date "2021-11-01" @default.
- W3216987651 modified "2023-09-23" @default.
- W3216987651 title "Fidelity-mediated analysis of the transverse-field XY chain with the long-range interactions: anisotropy-driven multi-criticality" @default.
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- W3216987651 doi "https://doi.org/10.1140/epjb/s10051-021-00245-1" @default.
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