2021/11/01 by Yoshihiro Nishiyama
Mathematics · Physics and Astronomy · #Anisotropy #Condensed matter physics #Field (mathematics) #Mathematics #Phase (matter) #Phase boundary #Phase diagram #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Quantum mechanics #Sigma #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1140/epjb/s10051-021-00245-1
openalex publication_date 2021/11/01 · arxiv created 2021/11/21 · arxiv updated 2021/11/23 · openalex created_date 2021/12/06 · openalex updated_date 2026/08/05
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=Hc. According to the large-N analysis, the phase boundary Hc(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 Hc(η) -Hc(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=Hc 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 Hc(η)'s linearity might be retained down to D>2.