Fractons and Luttinger liquids

Details Fractons and Luttinger liquids Fractons and Luttinger liquids

2000-06-30

arxiv.org/abs/cond-mat/0006503v3

J.Phys.Condens.Matter 12 (2000) L673-L675

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Latex, 5 pages, references added (To appear in J. of Physics: Cond. Mat.)

Scientific paper

10.1088/0953-8984/12/44/101

We consider the concept of fractons as particles or quasiparticles which obey a specific fractal statistics in connection with a one-dimensional Luttinger liquid theory. We obtain a dual statistics parameter ${\tilde{\nu}}=\nu+1$ which is identified with the controlling parameter $e^{-2\phi}$ of the Luttinger model. In this way, a bosonic system characterized by a fractal index $i_{f}[h]=i_{f}[2]=1$ is considered as a conformal field theory with central charge $c[\nu=0]=1=i_{f}[2]$ with a compactified radius $R=\frac{1}{\sqrt{\tilde{\nu}}}=1$. Thus, we have a mapping of a bosonic theory to a fermionic one and vice-versa, i.e., the duality symmetry ${{\tilde{h}} =3-h}$ of the universal class $h$ of fractons defined in the interval 1< h <2 is satisfied.

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