Particle Statistics, Frustration, and Ground-State Energy
Particle Statistics, Frustration, and Ground-State Energy
复制标题
粒子统计、挫折和基态能量
DOI：
10.1103/physrevb.97.125153
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发表时间：
2014-01
影响因子：
3.7
通讯作者：
Masaki Oshikawa
中科院分区：
文献类型：
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作者：
Wenxing Nie;Hosho Katsura;Masaki Oshikawa
我们研究量子多粒子系统中粒子统计、挫折和基态能量之间的联系。在没有相互作用的情况下，粒子统计对基态能量的影响是微不足道的：由于玻色-爱因斯坦凝聚和泡利不相容原理，非相互作用玻色子的基态能量低于自由费米子的基态能量。然而，在存在核心或其他交互的情况下，这种比较并不是微不足道的。然而，如果所有跳跃幅度都非负，则硬核玻色子的基态能量被证明低于无自旋费米子的基态能量。这种情况可以理解为没有挫折感之间的跳跃。通过将多体哈密顿量映射到虚晶格上的紧束缚模型，我们证明了原始粒子的费米统计在虚晶格中引入了一个有效磁通。后者可以被看作是一种挫折，因为它导致单个粒子传播的沿着不同路径之间的相消干涉。如果我们引入跳跃阻挫，跳跃阻挫有望与“有效阻挫”竞争，导致硬核玻色子的基态能量可能高于费米子的基态能量。我们给出了几个例子，其中硬核玻色子的基态能量被证明是高于费米子的，由于跳跃挫折。这些基本思想在最近的一封信[W. X. Nie，H. Katalina和M. Oshikawa，Phys. Rev. Lett. 111，100402（2013）];更多细节和几个扩展，包括对spinful情况的扩展，在本文中讨论。
We study the connections among particle statistics, frustration, and ground-state energy in quantum many-particle systems. In the absence of interaction, the influence of particle statistics on the ground-state energy is trivial: the ground-state energy of noninteracting bosons is lower than that of free fermions because of Bose-Einstein condensation and Pauli exclusion principle. In the presence of hard-core or other interaction, however, the comparison is not trivial. Nevertheless, the ground-state energy of hard-core bosons is proved to be lower than that of spinless fermions, if all the hopping amplitudes are nonnegative. The condition can be understood as the absence of frustration among hoppings. By mapping the many-body Hamiltonian to a tight-binding model on a fictitious lattice, we show that the Fermi statistics of the original particles introduces an effective magnetic flux in the fictitious lattice. The latter can be regarded as a frustration, since it leads to a destructive interference among different paths along which a single particle is propagating. If we introduce hopping frustration, the hopping frustration is expected to compete with "effective frustration", leading to the possibility that the ground-state energy of hard-core bosons can be higher than that of fermions. We present several examples, in which the ground-state energy of hard-core bosons is proved to be higher than that of fermions due to the hopping frustration. The basic ideas were reported in a recent Letter [W.-X. Nie, H. Katsura, and M. Oshikawa, Phys. Rev. Lett. 111, 100402 (2013)]; more details and several extensions, including one to the spinful case, are discussed in the present paper.
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影响因子：
8.6
作者：
H. Tasaki
通讯作者：
H. Tasaki
影响因子：
3.7
作者：
O. Derzhko;A. Honecker;J. Richter
通讯作者：
O. Derzhko;A. Honecker;J. Richter
影响因子：
2.5
作者：
E. Lieb;M. Loss
通讯作者：
E. Lieb;M. Loss
DOI：
10.1103/physrevb.40.9192
发表时间：
1989-11
期刊：
Physical review. B, Condensed matter
影响因子：
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作者：
H. Tasaki
通讯作者：
H. Tasaki
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