Effective band-projected description of interacting quasiperiodic systems

TL;DR

This paper develops a second-order band projection method to accurately describe interactions in quasiperiodic systems, successfully capturing phase transitions and dynamical properties that first-order approaches miss.

Contribution

The study introduces a second-order perturbative band projection approach that effectively models correlated quasiperiodic systems, surpassing the limitations of first-order methods.

Findings

Second-order band projection reproduces the phase diagram accurately.

Identification of dynamical signatures for different phases.

Validation of the method with DMRG results.

Abstract

We study the interplay between electronic interactions and quasiperiodicity in a one-dimensional narrow-band system, focusing on ground-state and low-energy excitation properties. Using band projection as low-energy effective approach, we show that a projection restricted to first order in the interaction strength fails to reproduce the correlated phase diagram. This contrasts with the standard success of first-order band projection in translationally invariant flatband systems and highlights the essential role of virtual processes involving remote bands in quasiperiodic settings. By incorporating second-order interband contributions perturbatively, we obtain an effective Hamiltonian that quantitatively reproduces the exact phase iagram previously obtained using density matrix renormalization group calculations, including the transition between a Luttinger liquid and a charge-density-wave phase and the crossover to a quasifractal charge-density-wave regime at strong quasiperiodicity. We further use this controlled framework to investigate low-energy neutral excitations and the optical conductivity, identifying clear dynamical signatures distinguishing the different phases. Our results establish second-order band projection as a reliable tool for correlated quasiperiodic narrow-band systems and suggest a promising route for studying interacting quasiperiodic and moir\'e materials beyond one dimension.