Freed by interaction kinetic states in the Harper model

Abstract

We study the problem of two interacting particles in a one-dimensional quasiperiodic lattice of the Harper model. We show that a short or long range interaction between particles leads to emergence of delocalized pairs in the non-interacting localized phase. The properties of these Freed by Interaction Kinetic States (FIKS) are analyzed numerically including the advanced Arnoldi method. We find that the number of sites populated by FIKS pairs grows algebraically with the system size with the maximal exponent $b=1$, up to a largest lattice size $N=10946$ reached in our numerical simulations, thus corresponding to a complete delocalization of pairs. For delocalized FIKS pairs the spectral properties of such quasiperiodic operators represent a deep mathematical problem. We argue that FIKS pairs can be detected in the framework of recent cold atom experiments [M.~Schreiber {\it et al.} Science {\bf 349}, 842 (2015)] by a simple setup modification. We also discuss possible implications of FIKS pairs for electron transport in the regime of charge-density wave and high $T_c$ superconductivity.

26 pages, 21 pdf and png figures, additional data and high quality figures are available at http://www.quantware.ups-tlse.fr/QWLIB/fikspairs/ , parts of sections 2 and 3 moved to appendices, manuscript accepted for EPJ B

References in corpus (2)

• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Ulam method for the Chirikov standard map

Cited by in corpus (9)

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• Delocalization of two interacting particles in the two-dimensional Harper model
• Localization of Pairs in One-Dimensional Quasicrystals with Power-Law Hopping
• Chaotic delocalization of two interacting particles in the classical Harper model
• Anderson localization for two interacting quasiperiodic particles