Long-Range Orders in Ground States and Collective Modes in One- and Two-Dimensional Models

概要

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On the basis of Bogoliubov's 1/k^2 theorem the relation between the long-range order in the ground state and the collective mode, namely, the Goldstone particle is investigated. It is pointed out that Bogoliubov's inequality rules out the long-range orders in the ground states of the isotropic Heisenberg model, the half-filled Hubbard model and the interacting Bose system for one dimension while it admits the long-range orders for two dimensions. The present proof is based on the fact that the lowest-excited state that can be regarded as the Goldstone particle has the energy E(k)∝∣k∣ for small k. This energy spectrum is exactly given in the one-dimensional models and is shown to be proven in the ordered state on a reasonable assumption except for the ferromagnetic case.
一般社団法人日本物理学会の論文
1975-10-25