TY - JOUR
T1 - Flux phase of the half-filled band
AU - Lieb, Elliott H.
N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 1994
Y1 - 1994
N2 - 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 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 D2 dimensions if there is periodicity in D-1 directions (e.g., the cubic lattice has the lowest energy if there is flux in each square face).
AB - 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 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 D2 dimensions if there is periodicity in D-1 directions (e.g., the cubic lattice has the lowest energy if there is flux in each square face).
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U2 - 10.1103/PhysRevLett.73.2158
DO - 10.1103/PhysRevLett.73.2158
M3 - Article
C2 - 10056987
AN - SCOPUS:0000376945
VL - 73
SP - 2158
EP - 2161
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 16
ER -