Block Lanczos and many‐body theory: Application to the one‐particle Green’s function

It is shown that the spin [Formula: see text] Ising model can be formulated as a spinless fermion many-body problem and that the Green's function technique can be applied to it. The hierarchy of Green's function equations of motion terminates at the (q + 1)-particle Green's function, where q is the coordination number. This finite number of equations yields Fisher's transformation of correlations. The technique discussed in this paper can be used to obtain exact results for the one-dimensional Ising model.

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On the many-body theory of nuclear reactions

Nuclear Physics A ◽

10.1016/s0375-9474(68)91896-4 ◽

1968 ◽

Vol 111 (1) ◽

pp. 392-416 ◽

Cited By ~ 2

Author(s):

K DIETRICH ◽

K HARA

Keyword(s):

Nuclear Reactions ◽

Many Body ◽

Many Body Theory ◽

The Many ◽

Body Theory

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MANY-BODY THEORY FOR HYPERFINE EFFECTS IN ATOMS AND MOLECULES

Le Journal de Physique Colloques ◽

10.1051/jphyscol:1970416 ◽

1970 ◽

Vol 31 (C4) ◽

pp. C4-99-C4-104

Author(s):

T. P. DAS ◽

C. M. DUTTA ◽

N. C. DUTTA

Keyword(s):

Many Body ◽

Atoms And Molecules ◽

Many Body Theory ◽

Body Theory

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Thermodynamic Green’s Functions and Spectral Structure

10.1093/oso/9780198791942.003.0007 ◽

2018 ◽

Author(s):

Norman J. Morgenstern Horing

Keyword(s):

Green’S Function ◽

Green's Function ◽

Green's Functions ◽

Green’S Functions ◽

Spectral Weight ◽

Statistical Thermodynamic ◽

Spectral Structure ◽

Imaginary Time ◽

Translational Invariance ◽

The One

Multiparticle thermodynamic Green’s functions, defined in terms of grand canonical ensemble averages of time-ordered products of creation and annihilation operators, are interpreted as tracing the amplitude for time-developing correlated interacting particle motions taking place in the background of a thermal ensemble. Under equilibrium conditions, time-translational invariance permits the one-particle thermal Green’s function to be represented in terms of a single frequency, leading to a Lehmann spectral representation whose frequency poles describe the energy spectrum. This Green’s function has finite values for both t>t′ and t<t′ (unlike retarded Green’s functions), and the two parts G1> and G1< (respectively) obey a simple proportionality relation that facilitates the introduction of a spectral weight function: It is also interpreted in terms of a periodicity/antiperiodicity property of a modified Green’s function in imaginary time capable of a Fourier series representation with imaginary (Matsubara) frequencies. The analytic continuation from imaginary time to real time is discussed, as are related commutator/anticommutator functions, also retarded/advanced Green’s functions, and the spectral weight sum rule is derived. Statistical thermodynamic information is shown to be embedded in physical features of the one- and two-particle thermodynamic Green’s functions.

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