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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

Renormalization group approach to a Bose system and irrelevance of quantum features

Attilio L. Stella, Flavio Toigo

Published Jul 1, 1976• 16 citations
Publisher
DOI
10.1007/bf02723351

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The renormalization group transformation near four space-dimensions is extended to irreversible processes of a quantum Bose system in terms of a coherent-state formalism. Recursion relations for a kinetic equation are obtained explicitly up to O(ε2), where ε≡4-d and d denotes the space dimensionality. It is shown that terms representing the quantum effects become “irrelevant” by renormalization group scale transformation which can be carried out in the case of quantum fields due to coherent-state formalism. The complex parameter S introduced by Abrahams and Tsuneto phenomenologically is obtained from the microscopic point of view by eliminating microscopic (non-critical) fluctuations. It is also shown that S is driven to the TDGL type at the fixed point, so that the dynamical critical exponent z agrees with that obtained by Halperin, Hohenberg and Ma in the TDGL model.
The ability of entanglement renormalization (ER) to generate a proper real-space renormalization group (RG) flow in extended quantum systems is analyzed in the setting of harmonic lattice systems in D =1 and 2 spatial dimensions. A conceptual overview of the steps involved in momentum-space RG is provided and contrasted against the equivalent steps in the real-space setting. The real-space RG flow, as generated by ER, is compared against the exact results from momentum-space RG, including an investigation of a critical fixed point and the effect of relevant and irrelevant perturbations.