Non-Hermitian quantum many-body scar

Abstract

Ergodicity depicts a thorough exploration of phase space to reach thermal equilibrium for most isolated many-body systems. Recently, the discovery of persistent revivals in the Rydberg-atom quantum simulator has revealed a weakly ergodicity breaking mechanism dubbed as quantum many-body scars, which are a set of nonthermal states storing the initial quantum information through long-time dynamics in the otherwise thermal spectrum. However, until now, the quantum scars have only been studied in closed systems with Hermiticity. Here, we establish the non-Hermitian quantum many-body scars in open systems and characterize their nature from the entanglement entropy, the physical observable and the energy level statistics. Notably, these signatures of the non-Hermitian scarred states switch from the real-energy axis to the imaginary-energy axis after a real-tocomplex spectra transition, where an exceptional point and a quantum tricritical point emerge simultaneously. We further examine their stability against external fields and establish the whole phase diagram. In the realspectrum region, we reveal that the non-Hermitian scars are more fragile than Hermitian counterparts when increasing the strength of non-Hermiticity. Our results may offer insights on ergodicity-breaking and clues for realizing long-lived coherent states in open quantum many-body systems.

General properties of fidelity in non-Hermitian quantum systems with PT symmetry

“…Note that very recently the negative divergence property Eq. ( 22) has been applied to the non-Hermitian quantum many-body scar [25]. On the other hand, fidelity susceptibility without showing positive or negative peaks in the AKLT model provide evidence of Symmetry-Protected-Topological phase does not have either quantum critical point nor EP within small non-Hermitian parameter strength [24].…”

“…Research on higher-order transitions with the fidelity susceptibility is still an ongoing interesting topic [3][4][5][6][7][8][9][10]. On the other hand, since the discovery of the parity-time (PT)-symmetric quantum mechanics [11][12][13], the interest of studying quantum phase transitions has recently extended to non-Hermitian systems [14][15][16][17][18][19][20][21][22][23][24][25].…”