Topological triple phase transition in non-Hermitian Floquet quasicrystals

Sebastian Weidemann,Alexander Szameit,Stefano Longhi,Mark Kremer

doi:10.1038/s41586-021-04253-0

Abstract

Phase transitions connect different states of matter and are often concomitant with the spontaneous breaking of symmetries. An important category of phase transitions is mobility transitions, among which is the well known Anderson localization1, where increasing the randomness induces a metal–insulator transition. The introduction of topology in condensed-matter physics2–4 lead to the discovery of topological phase transitions and materials as topological insulators5. Phase transitions in the symmetry of non-Hermitian systems describe the transition to on-average conserved energy6 and new topological phases7–9. Bulk conductivity, topology and non-Hermitian symmetry breaking seemingly emerge from different physics and, thus, may appear as separable phenomena. However, in non-Hermitian quasicrystals, such transitions can be mutually interlinked by forming a triple phase transition10. Here we report the experimental observation of a triple phase transition, where changing a single parameter simultaneously gives rise to a localization (metal–insulator), a topological and parity–time symmetry-breaking (energy) phase transition. The physics is manifested in a temporally driven (Floquet) dissipative quasicrystal. We implement our ideas via photonic quantum walks in coupled optical fibre loops11. Our study highlights the intertwinement of topology, symmetry breaking and mobility phase transitions in non-Hermitian quasicrystalline synthetic matter. Our results may be applied in phase-change devices, in which the bulk and edge transport and the energy or particle exchange with the environment can be predicted and controlled.

Highlights

An important category among phase transitions—which are manifested in a plethora of different systems and phenomena—is mobility transitions[19,20]
Metal–insulator phase transitions have usually been regarded as unrelated to other types of phase transition, such as spontaneous symmetry breaking occurring in dissipative systems or topological phase transitions observed in topological matter
The localization of the wavefunctions and the metal–insulator phase transition are usually associated with a spectral phase transition[28], which can be characterized by the change of a topological number emerging from the closed contours of the eigenvalue spectrum in the complex plane[9]

Summary

Introduction

An important category among phase transitions—which are manifested in a plethora of different systems and phenomena—is mobility transitions[19,20]. A paradigmatic model showing a mobility transition is the Aubry–André–Harper (AAH) model[22] It describes a one-dimensional system in an intermediate phase between perfect periodic order (crystal) and a completely disordered medium, possessing only long-range order without periodicity. Metal–insulator phase transitions have usually been regarded as unrelated to other types of phase transition, such as spontaneous symmetry breaking occurring in dissipative systems or topological phase transitions observed in topological matter This common wisdom has been challenged by recent theoretical studies[9,10], where the intriguing interplay between aperiodic order and dissipation has been unravelled. The triple phase transition is observed by changing a single parameter, which can be purely Hermitian (strength of the nearest-neighbour coupling) or purely non-Hermitian (strength of the non-Hermitian gauge field), both of which we connect in a phase transition equation

Methods

Results

Conclusion