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 -