Journal Article Anomalous behavior of the energy gap in the one-dimensional quantum XY model

西森, 秀稔  ,  NISHIMORI, HIDETOSHI  ,  奥山, 真佳  ,  Okuyama, Manaka  ,  山中, 優輝  ,  Yamanaka, Yuuki  ,  Rams, Marek

92p.0521126 , 2015-11 , American Physical Society
We reexamine the well-studied one-dimensional spin-1/2 XY model to reveal its nontrivial energy spectrum,in particular the energy gap between the ground state and the first excited state. In the case of the isotropicXY model, the XX model, the gap behaves very irregularly as a function of the system size at a second ordertransition point. This is in stark contrast to the usual power-law decay of the gap and is reminiscent of the similarbehavior at the first order phase transition in the infinite-range quantum XY model. The gap also shows nontrivialoscillatory behavior for the phase transitions in the anisotropic model in the incommensurate phase. We observea close relation between this anomalous behavior of the gap and the correlation functions. These results, thosefor the isotropic case in particular, are important from the viewpoint of quantum annealing where the efficiencyof computation is strongly affected by the size dependence of the energy gap

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