Thouless theorem

Collective modes can be viewed as superpositions of Iph configurations. It is convenient to define this relation by using the Thouless theorem which establishes the connection between two arbitrary Slater determinants [25]. Then, the perturbed many-body wave function reads... 

Any ocan be obtained from 4>o via the action of exp(Ti), provided oand are not orthogonal. This is known as the Thouless theorem.] Because the relaxed and unrelaxed orbitals are related by such an orbital rotation, we have (for CCSD),... 

The use of the cue basis in the CCSD method for calculating the energy of the unperturbed (i.e. zero-field case) system is justified by the Thouless theorem [78] which states that the transformation between two non-orthogonal determinants can... 

The impact of this is tremendous. No long-range order (LRO) can exist at finite temperature in one dimension no crystals, no magnets, no superconductors. Only special transitions are possible in two dimensions. The Ising model (n = 1 component) is an example [7]. The Kosterlitz-Thouless transition [8], without LRO, is another case for d = 2 and n = 2, discussed in Section V.C. The thermal fluctuations are very destructive in lower dimensions. Quantum fluctuations (i.e., those associated with the dynamics of a system) also tend to suppress LRO and can sometimes destroy it even at 0 K when the Mermin-Wagner theorem does not apply. Such is the case of the quantum spin- antiferromagnetic models [9] in one dimension. 

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See also in sourсe #XX -- [ ]

See also in sourсe #XX -- [ ]

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