TY - JOUR

T1 - Criticality of the excess energy cost due to the unit-flux-quantum external field for the (2 + 1)D superfluid-insulator transition

AU - Nishiyama, Yoshihiro

N1 - Funding Information:
This work was supported by a Grant-in-Aid for Scientific Research (C) from Japan Society for the Promotion of Science (Grant No. 20K03767).
Publisher Copyright:
© 2022 IOP Publishing Ltd and SISSA Medialab srl.

PY - 2022/3

Y1 - 2022/3

N2 - The two-dimensional (2D) spin-S = 1 XY model was investigated numerically as a realization of the (2 + 1)D superfluid-Mott-insulator (SF-MI) transition. The interaction parameters are extended so as to suppress corrections to finite-size scaling. Thereby, the external field of a unit flux quantum (φ = 2π) is applied to the 2D cluster by incorporating the phase factor eiφij (φ ij : gauge angle between the i and j sites) into the hopping amplitudes. Taking the advantage in that the exact-diagonalization method allows us to treat such a complex-valued matrix element, we evaluated the excess energy cost "E(2π) due to the magnetic flux φ = 2π explicitly in the SF (XY) phase. As a result, we found that the amplitude ratio ρ s/ "E(2π) (ρ s: spin stiffness) makes sense in proximity to the critical point, exhibiting a notable plateau in the SF-phase side. The plateau height is estimated, and compared to the related studies.

AB - The two-dimensional (2D) spin-S = 1 XY model was investigated numerically as a realization of the (2 + 1)D superfluid-Mott-insulator (SF-MI) transition. The interaction parameters are extended so as to suppress corrections to finite-size scaling. Thereby, the external field of a unit flux quantum (φ = 2π) is applied to the 2D cluster by incorporating the phase factor eiφij (φ ij : gauge angle between the i and j sites) into the hopping amplitudes. Taking the advantage in that the exact-diagonalization method allows us to treat such a complex-valued matrix element, we evaluated the excess energy cost "E(2π) due to the magnetic flux φ = 2π explicitly in the SF (XY) phase. As a result, we found that the amplitude ratio ρ s/ "E(2π) (ρ s: spin stiffness) makes sense in proximity to the critical point, exhibiting a notable plateau in the SF-phase side. The plateau height is estimated, and compared to the related studies.

KW - quantum criticality

KW - quantum phase transitions

KW - spin chains, ladders and planes

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U2 - 10.1088/1742-5468/ac5cb2

DO - 10.1088/1742-5468/ac5cb2

M3 - Article

AN - SCOPUS:85128295430

VL - 2022

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 3

M1 - 033102

ER -