First-order Quantum Phase Transitions and Localization in the 2D Haldane Model with Non-Hermitian Quasicrystal Boundaries

TL;DR

This paper investigates the complex phase diagram and quantum phase transitions in a 2D non-Hermitian Haldane model with quasicrystal boundaries, revealing a new critical phase and a first-order transition driven by imaginary zeros.

Contribution

It introduces a novel phase diagram for the 2D Haldane model with quasicrystal boundaries, identifying a critical phase and a first-order transition mechanism involving imaginary zeros.

Findings

Discovery of a new critical phase with multifunctional wave functions.

Identification of a first-order quantum phase transition induced by imaginary zeros.

Observation of phase splitting proportional to the number of potential zeros.

Abstract

The non-Hermitian extension of quasicrystals (QC) are highly tunable system for exploring novel material phases. While extended-localized phase transitions have been observed in one dimension, quantum phase transition in higher dimensions and various system sizes remain unexplored. Here, we show the discovery of a new critical phase and imaginary zeros induced first-order quantum phase transition within the two-dimensional (2D) 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 quasiperiodic potential, which is divided into three distinct phases by two critical boundaries: phase (I) with extended wave functions, PT-restore phase (II) with localized wave functions, and a critical phase (III) with multifunctional wave functions. To describe the wavefunctions in these distinct phases, we introduce a low-energy approximation theory and an effective two-chain model. Additionally, we uncover a first-order structural phase transition induced (FOSPT) by imaginary zeros. As we increase the size of the potential boundary, we observe the critical phase splitting into regions in proportion to the growing number of potential zeros. Importantly, these observations are consistent with groundstate fidelity and energy gap calculations. Our research enhances the comprehension of phase diagrams associated with high-dimensional quasicrystal potentials, offering valuable contributions to the exploration of unique phases and quantum phase transition.