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Theoretical and Mathematical Physics

Single-particle Green's function in the anisotropic Heisenberg model II. Allowance for higher correlation functions

Yu. G. Rudoi, Yu. A. Tserkovnikov

Published Jun 1, 1973• 9 citations
Publisher
DOI
10.1007/bf01094568

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Green’s-function theory of the anisotropic Heisenberg model in a transverse field

Edward B. Brown

The S=(1/2 anisotropic Heisenberg model in a transverse field (AHMTF) is studied by means of double-time Green's functions. A new approximation scheme is employed which is based upon the assumption of the statistical independence of the ordering operator. The basic approximations are required to satisfy all relevant operator and correlation identities. Emphasis is placed upon obtaining accurate approximations for those Green's functions which are related to the ordering susceptibility. The scheme is relatively simple to use and applicable to a wide variety of systems. Standard Green's-function techniques are shown to provide results for the critical transverse field for Ising-like systems which violate S=(1/2 identities. They are also shown to be not applicable to the ordered phase of XY-like systems. In contrast, the new approximation provides reasonable results for all temperatures and couplings for the S=(1/2 AHMTF.

Physical review. B, Condensed matter•Jul 1, 1987•14 citations
The S=(1/2 anisotropic Heisenberg model in a transverse field (AHMTF) is studied by means of double-time Green's functions. A new approximation scheme is employed which is based upon the assumption of the statistical independence of the ordering operator. The basic approximations are required to satisfy all relevant operator and correlation identities. Emphasis is placed upon obtaining accurate approximations for those Green's functions which are related to the ordering susceptibility. The scheme is relatively simple to use and applicable to a wide variety of systems. Standard Green's-function techniques are shown to provide results for the critical transverse field for Ising-like systems which violate S=(1/2 identities. They are also shown to be not applicable to the ordered phase of XY-like systems. In contrast, the new approximation provides reasonable results for all temperatures and couplings for the S=(1/2 AHMTF.