Effective Luttinger parameter and Kane-Fisher effect in quasiperiodic systems

Abstract

The ground states of interacting one-dimensional metals are generically Luttinger liquids. Luttinger liquid theory is usually considered for translation invariant systems. The Luttinger liquid description remains valid for weak quasiperiodic modulations; however, as the quasiperiodic modulation gets increasingly strong, it is increasingly renormalized and eventually fails, as the system becomes localized. We explore how quasiperiodic modulation renormalizes the Luttinger parameter characterizing this emergent Luttinger liquid, using the renormalization of transmission coefficients across a barrier as a proxy that remains valid for general quasiperiodic modulation. We find, unexpectedly, that quasiperiodic modulation weakens the effects of short-range interactions, but enhances those of long-range interactions. We support the former finding with matrix-product numerics. We also discuss how interactions affect the localization phase boundary.

References in corpus (7)

• The density-matrix renormalization group in the age of matrix product states
• Time-evolving a matrix product state with long-ranged interactions
• The quasi-periodic Bose-Hubbard model and localization in one-dimensional cold atomic gases
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Anderson localization transitions with and without random potentials
• The insulating phases and superfluid-insulator transition of disordered boson chains
• Many-body localization in the interpolating Aubry-André-Fibonacci model