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The few-body problem on a lattice

Daniel C. Mattis

Daniel C. Mattis

  • Department of Physics, University of Utah, Salt Lake City, Utah 84112

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Rev. Mod. Phys. 58, 361 – Published 1 April, 1986

DOI: https://doi.org/10.1103/RevModPhys.58.361

Abstract

The author explores some of the inherent simplifications of "quantum lattice physics." He distinguishes between fermions and bosons and analyzes the n-body problem for each, with n=1,2,3… typically a small number. With delta-function (zero-range) interactions, the three-body problem on a lattice is manageable, and some results can even be extrapolated to n≥4. Such calculations are not limited to one dimension (where the well-known Bethe ansatz solves a number of n-body problems). On the contrary, studies cited are mainly in three dimensions and actually simplify with increasing dimensionality. For example, it is found that bound states of n≥3 particles in d≥3 dimensions are formed discontinuously as the strength of two-body attractive forces is increased, and are therefore always in the easily analyzed "strong coupling limit." In the Appendix, an exactly solved example from the theory of itinerant-electron magnetism illustrates how a rigorous solution to the few-body problem is capable of yielding information concerning the N-body problem.

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Rev. Mod. Phys. 58, 361– Published 1 April, 1986

    © 1986 American Physical Society

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