Topological Quantum Criticality in Quasiperiodic Ising Chain

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.

💡 Research Summary

In this work the authors investigate quantum criticality in a one‑dimensional spin‑½ cluster‑Ising chain subject to quasiperiodic (QP) modulation of both the Ising coupling J_i and the three‑spin cluster term g_i. The Hamiltonian preserves a Z₂ spin‑flip symmetry and time‑reversal symmetry. The QP modulation is chosen with an irrational wave vector Q = 2π τ_G (τ_G the Golden ratio), leading to couplings of the form J_i = \bar J + h_J cos