Abstract
The central theme of this Chapter is the art of terminating a continued fraction [Viswanath and Müller 1990]. The diverse facets of the recursion method which we have developed in previous Chapters are now combined into a new method for the construction of termination functions — a method which transcends the limitations of the calculational schemes portrayed in Chapter 8. Our method surely has its own limitations, and we shall not shy away from pointing them out. But its simplicity and versatility makes it quite powerful, and its enormous flexibility allows for customized fine tuning in individual applications. All this will be demonstrated in extensive tests here in Chapter 9 and then in applications to quantum spin dynamics at high temperature (Chapter 10) and low temperature (Chapter 11).
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References
The Δk-sequence (9.12) was also reported to be relevant for the dynamics of a 2D electron gas [Lee and Hong 1985].
The results of Fig. 9-5 should be compared with Fig. 1 of [Gagliano and Balseiro 1987]. That figure shows the results of attempts to obtain the dynamic structure factor (6.38) by two general methods — a quantum Monte Carlo method and the recursion method with cut-off termination. The data of the former method were quoted from a paper by Schüttler and Scalapino [1986].
The Δk-sequence (9.58) was also reported to be relevant for the dynamics of a 3D electron gas [Hong and Lee 1993].
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© 1994 Springer-Verlag Berlin Heidelberg
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(1994). Reconstruction of Spectral Densities from Incomplete Continued Fractions. In: The Recursion Method. Lecture Notes in Physics Monographs, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48651-0_9
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DOI: https://doi.org/10.1007/978-3-540-48651-0_9
Publisher Name: Springer, Berlin, Heidelberg
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