FLUX PHASE OF THE HALF-FILLED BAND
FLUX PHASE OF THE HALF-FILLED BAND
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DOI：
10.1103/physrevlett.73.2158
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发表时间：
1994-10-17
影响因子：
8.6
通讯作者：
LIEB, EH
中科院分区：
文献类型：
--
作者：
LIEB, EH
证明了在平面二分图上跳跃的半满电子带的能量最小的最佳磁通量为π/格元。我们只要求图在一个方向上具有周期性，并且结果包括六边形晶格（每个六边形的通量为0）作为特殊情况。该定理在几个方面超越了以前的理论：（1）它不假定所有的斑块都有相同的通量（如在霍夫施塔特模型中）。(2)可以包括任何符号的哈伯德型现场交互，以及某些较长范围的交互。(3)该结论对正温度和基态都成立。(4)如果在D - 1方向上存在周期性（例如，如果在每个正方形面中存在通量P1，则立方晶格具有最低能量）。
The conjecture is verified that the optimum, energy minimizing, magnetic flux for a half-filled band of electrons hopping on a planar, bipartite graph is pi per square plaquette. We require only that the graph has periodicity in one direction and the result includes the hexagonal lattice (with flux 0 per hexagon) as a special case. The theorem goes beyond previous conjectures in several ways: (1) It does not assume, a priori, that all plaquettes have the same flux (as in Hofstadter's model). (2) A Hubbard-type on-site interaction of any sign, as well as certain longer range interactions, can be included. (3) The conclusion holds for positive temperature as well as the ground state. (4) The results hold in D greater than or equal to 2 dimensions if there is periodicity in D - 1 directions (e.g., the cubic lattice has the lowest energy if there is flux pi in each square face).