Freed by interaction kinetic states in the Harper model

TL;DR

This paper investigates how interactions induce delocalized pairs in a quasiperiodic lattice, revealing a new class of states called FIKS that could impact understanding of electron transport and be observed experimentally.

Contribution

It introduces and analyzes Freed by Interaction Kinetic States (FIKS) in the Harper model, demonstrating their emergence and properties through numerical methods.

Findings

FIKS pairs become fully delocalized at large system sizes

Number of sites occupied by FIKS grows algebraically with system size

Potential experimental detection in cold atom setups

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.