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arXiv · 2603.13548

Effective band-projected description of interacting quasiperiodic systems

Flavio Riche·Raul Liquito·Bruno Amorim·Eduardo V. Castro·Pedro Ribeiro·Miguel Gonçalves
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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.

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Flavio Riche, Raul Liquito, Bruno Amorim, Eduardo V. Castro, Pedro Ribeiro, Miguel Gonçalves. 2026-03-13. Effective band-projected description of interacting quasiperiodic systems. https://arxiv.org/abs/2603.13548

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