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Interacting fermions in self-similar potentials

J. Vidal·D. Mouhanna·T. Giamarchi
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Abstract

We consider interacting spinless fermions in one dimension embedded in self-similar quasiperiodic potentials. We examine generalizations of the Fibonacci potential known as precious mean potentials. Using a bosonization technique and a renormalization group analysis, we study the low-energy physics of the system. We show that it undergoes a metal-insulator transition for any filling factor, with a critical interaction that strongly depends on the position of the Fermi level in the Fourier spectrum of the potential. For some positions of the Fermi level the metal-insulator transition occurs at the non interacting point. The repulsive side is an insulator with a gapped spectrum whereas in the attractive side the spectrum is gapless and the properties of the system are described by a Luttinger liquid. We compute the transport properties and give the characteristic exponents associated to the frequency and temperature dependence of the conductivity.

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J. Vidal, D. Mouhanna, T. Giamarchi. 2001-07-12. Interacting fermions in self-similar potentials. https://doi.org/10.1103/physrevb.65.014201

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