Topological Quantum Criticality in Quasiperiodic Ising Chain

TL;DR

This paper uncovers a new class of topological fixed points in quasiperiodic quantum critical systems, revealing unique topological properties and phase boundaries distinct from known universality classes.

Contribution

It introduces a novel topological fixed point class in quasiperiodic systems, demonstrated through exact solutions and lattice simulations, expanding the understanding of topological quantum criticality.

Findings

Discovery of topological quasiperiodic fixed points

Existence of robust topological edge degeneracies

Phase boundaries governed by new fixed points

Abstract

Topological classifications of quantum critical systems have recently attracted growing interest, as they go beyond the traditional paradigms of condensed matter and statistical physics. However, such classifications remain largely unexplored at critical points in aperiodic environments, particularly under quasiperiodic modulations. In this Letter, we uncover a novel class of topological quasiperiodic fixed points that are intermediate between the clean and infinite-randomness limits. By exactly solving the quasiperiodic cluster-Ising chain, we unambiguously demonstrate that all phase boundaries separating quasiperiodically modulated phases are governed by a new family of topological Ising-like fixed points unique to strongly modulated quasiperiodic systems: Despite exhibiting indistinguishable bulk critical properties, these fixed points host robust topological edge degeneracies and are therefore topologically distinct from previously recognized quasiperiodic universality classes, as further supported by complementary lattice simulations.