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Title
Japanese: 
English:Anomalous behavior of the energy gap in the one-dimensional quantum XY model 
Author
Japanese: 西森秀稔, 奥山真佳, 山中優輝, Marek Rams.  
English: HIDETOSHI NISHIMORI, Manaka Okuyama, Yuuki Yamanaka, Marek Rams.  
Language English 
Journal/Book name
Japanese: 
English:Physical Review E 
Volume, Number, Page Vol. 92        p. 0521126
Published date Nov. 13, 2015 
Publisher
Japanese: 
English:American Physical Society 
Conference name
Japanese: 
English: 
Conference site
Japanese: 
English: 
File
DOI https://doi.org/10.1103/PhysRevE.92.052116
Abstract 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 isotropic XY model, the XX model, the gap behaves very irregularly as a function of the system size at a second order transition point. This is in stark contrast to the usual power-law decay of the gap and is reminiscent of the similar behavior at the first order phase transition in the infinite-range quantum XY model. The gap also shows nontrivial oscillatory behavior for the phase transitions in the anisotropic model in the incommensurate phase. We observe a close relation between this anomalous behavior of the gap and the correlation functions. These results, those for the isotropic case in particular, are important from the viewpoint of quantum annealing where the efficiency of computation is strongly affected by the size dependence of the energy gap

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