Exact solution of a lattice band problem related to an exactly soluble many-body problem: The missing-states problem

Journal Article · Sat Oct 01 00:00:00 EDT 1988 · Phys. Rev. B: Condens. Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.38.6689· OSTI ID:6826299

Sutherland, B

We introduce and solve a lattice version of an easily soluble one-dimensional continuum quantum system with a periodic potential. The relationship of the one problem to the other is identical to the relationship of the one-dimensional quantum many-body lattice gas recently introduced by Shastry (Phys. Rev. Lett. 60, 639 (1988)) and by Haldane (Phys. Rev. Lett. 60, 635 (1988)) to the one-dimensional quantum many-body continuum gas earlier solved by Sutherland. Thus it is hoped that by understanding the ''missing'' states in this simple case, we might better understand the missing states in the more complicated many-body case, which in many instances comprise all the states. The results are not encouraging.

• Research Organization: Physics Department, University of Utah, Salt Lake City, Utah 84112
• OSTI ID: 6826299
• Journal Information: Phys. Rev. B: Condens. Matter; (United States), Vol. 38:10
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CRYSTAL LATTICES
ANALYTICAL SOLUTION
BAND THEORY
PARTICLE INTERACTIONS
BRILLOUIN ZONES
MANY-BODY PROBLEM
POTENTIALS
CRYSTAL STRUCTURE
INTERACTIONS
ZONES
656000* - Condensed Matter Physics