An itinerant electron model with crystalline or magnetic long range order

Tom Kennedy, Elliott H. Lieb

Research output: Contribution to journalArticlepeer-review

225 Scopus citations


A quantum mechanical lattice model of fermionic electrons interacting with infinitely massive nuclei is considered. (It can be viewed as a modified Hubbard model in which the spin-up electrons are not allowed to hop.) The electron-nucleus potential is "on-site" only. Neither this potential alone nor the kinetic energy alone can produce long range order. Thus, if long range order exists in this model it must come from an exchange mechanism. N, the electron plus nucleus number, is taken to be less than or equal to the number of lattice sites. We prove the following: (i) For all dimensions, d, the ground state has long range order; in fact it is a perfect crystal with spacing √2 times the lattice spacing. A gap in the ground state energy always exists at the half-filled band point (N = number of lattice sites). (ii) For small, positive temperature, T, the ordering persists when d ≥ 2. If T is large there is no long range order and there is exponential clustering of all correlation functions.

Original languageEnglish (US)
Pages (from-to)320-358
Number of pages39
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1-2
StatePublished - Sep 2 1986

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics


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