Quadratic fermionic interactions yield Hamiltonians with large ground-state energy gaps

作     者：Michael J. O’Hara Dianne P. O’Leary 

作者机构：[]Applied Mathematics Program University of Maryland College Park Maryland 20742 USA 

出 版 物：《Physical Review A》 (物理学评论A辑：原子、分子和光学物理学)

年 卷 期：2009年第79卷第3期

页      面：032331-032331页

核心收录：

学科分类：070207[理学-光学] 07[理学] 08[工学] 0803[工学-光学工程] 0702[理学-物理学] 

基　　金：National Science Foundation, NSF Directorate for Computer and Information Science and Engineering, CISE, (0514213) 

主　　题：Ising model 

摘      要：Polynomially large ground-state energy gaps are rare in many-body quantum systems, but useful in quantum information and an interesting feature of the one-dimensional quantum Ising model. We show analytically that the gap is generically polynomially large not just for the quantum Ising model, but for one-, two-, and three-dimensional interaction lattices and Hamiltonians with certain random interactions. We extend the analysis to Hamiltonian evolutions and we use the Jordan-Wigner transformation and a related transformation for spin-3/2 particles to show that our results can be restated using spin operators in a surprisingly simple manner. These results also yield a new perspective on the one-dimensional cluster state.