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American Physical Society, Physical review E: Statistical, nonlinear, and soft matter physics, 5(89)

DOI: 10.1103/physreve.89.052133

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Bose-Einstein condensation in diamond hierarchical lattices

Journal article published in 2014 by M. L. Lyra, F. A. B. F. de Moura, I. N. de Oliveira ORCID, M. Serva
This paper is available in a repository.
This paper is available in a repository.

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Abstract

The Bose-Einstein condensation of noninteracting particles restricted to move on the sites of hierarchical diamond lattices is investigated. Using a tight-binding single-particle Hamiltonian with properly rescaled hopping amplitudes, we are able to employ an orthogonal basis transformation to exactly map it on a set of decoupled linear chains with sizes and degeneracies written in terms of the network branching parameter q and generation number n. The integrated density of states is shown to have a fractal structure of gaps and degeneracies with a power-law decay at the band bottom. The spectral dimension d s coincides with the network topological dimension d f = ln (2q)/ ln (2). We perform a finite-size scaling analysis of the fraction of condensed particles and specific heat to characterize the critical behavior of the BEC transition that occurs for q > 2 (d s > 2). The critical exponents are shown to follow those for lattices with a pure power-law spectral density, with non-mean-field values for q < 8 (d s < 4). The transition temperature is shown to grow monotonically with the branching parameter, obeying the relation 1/T c = a + b/(q − 2).