First-order localization and quantum phase transition induced by quasicrystal imaginary domain

The non-Hermitian extension of quasicrystals provides a highly tunable system for exploring novel material phases. While extended-localized phase transitions have been observed in one dimension, quantum phase transitions in higher dimensions and various system sizes remain unexplored. Here, we show the discovery of a new critical phase and first-order structural transition induced by imaginary zeros in the two-dimensional Haldane model with a quasicrystal potential on the upper boundary. Initially, we illustrate a phase diagram that evolves with the amplitude and phase of the quasicrystal potential, which is divided into three distinct phases by two critical boundaries: phase (I) with extended wave functions, parity-time-restore phase (II) with localized wave functions, and a critical phase (III) with multifunctional wave functions. To characterize the wave functions in these distinct phases, we introduce a low-energy approximation theory and an effective two-chain model. Additionally, we uncover a first-order quantum phase transition induced by quasicrystal domains. As we increase the size of the potential boundary, we observe the partitioning of the critical phase into regions in proportion to the growing number of quasicrystal domains. Importantly, these observations are consistent with ground state fidelity and energy gap calculations. Our research advances the understanding of phase diagrams associated with high-dimensional quasicrystal potentials and marks the first discovery of a first-order quantum phase transition induced by quasicrystal domains in non-Hermitian systems.