Relationship between localization-delocalization transition and PT-symmetry breaking.

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Non-Hermitian Systems

Background:

• Parity-time-symmetry (PT-symmetry) breaking and Anderson localization are key phenomena in non-Hermitian systems.
• Previous research suggested universal alignment between PT-symmetry transitions and delocalization.
• Competing Dzyaloshinskii-Moriya (DM) interactions introduce complexity in spin chain dynamics.

Purpose of the Study:

• Investigate the interplay between PT-symmetry breaking and localization in non-Hermitian spin chains.
• Examine the role of next-nearest-neighbor DM couplings on these transitions.
• Establish dynamical metrics for characterizing non-Hermitian phase transitions.

Main Methods:

• Utilized eigenvalue analysis and inverse/normalized participation ratios (IPR/NPR) to identify phases.
• Tracked time-dependent density propagation for dynamical analysis.
• Analyzed long-time survival probability and phase-sensitive Loschmidt echo for phase discrimination.

Main Results:

• Identified three distinct phases: extended, localized, and a novel hybrid phase unique to next-nearest-neighbor DM couplings.
• Demonstrated decoupling of PT-symmetry breaking and localization in specific parameter regimes.
• Showcased distinct dynamical signatures for density evolution, survival probability, and Loschmidt echo across phases.

Conclusions:

• Next-nearest-neighbor DM couplings can decouple PT-symmetry breaking and localization, challenging universal alignment assumptions.
• Dynamical metrics, including Loschmidt echo, are essential for characterizing non-Hermitian phase transitions beyond spectral or localization measures.
• The study highlights the importance of dynamical properties in understanding complex quantum systems.