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A numerical method for finding the ground states of one-dimensional systems

Authors
Journal
Journal of Computational Physics
0021-9991
Publisher
Elsevier
Publication Date
Volume
89
Issue
1
Identifiers
DOI: 10.1016/0021-9991(90)90122-h
Disciplines
  • Computer Science

Abstract

Abstract Griffiths and Chou introduced a method of effective potentials for finding the ground states of a class of systems that can be described by classical one-dimensional Hamiltonians with nearest neighbor interactions. In practice the effective potentials must be solved numerically by discretization on a grid of N points. Existing algorithms have calculation times that vary as N 2 or worse. We show how this can be reduced to linear in N by means of straightforward optimizations that take advantage of the properties of the effective potentials.

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