Gapless Non-Hermitian Criticality via Fidelity Susceptibility

Zhang et al. (2024) used fidelity susceptibility to map phase transitions between gapless topological phases, while Zhou et al. (2021) linked non-Hermitian topology to dynamical quantum phase transitions (DQPTs). This idea merges both: apply fidelity susceptibility to non-Hermitian gapless systems (e.g., nonreciprocal SSH chains) to detect criticality where bulk gaps vanish but topology changes. Unlike Zhou's focus on quenches from trivial to topological phases, we'd probe intrinsic transitions between distinct non-Hermitian gapless phases, testing whether DQPTs still correlate with topological invariants. This challenges Zhang et al.'s assumption of Hermiticity and could reveal whether their stable critical line persists under gain/loss asymmetry. The approach leverages unsupervised ML (Käming et al. 2021) to analyze noisy DQPT data from ultracold-atom simulators, offering a pathway to discover exotic non-Hermitian universality.

References:

1. Quantum phase transition and critical behavior between the gapless topological phases. Hao-Long Zhang, Han-Ze Li, Sheng Yang, Xue-Jia Yu (2024). Physical Review A.
2. Non-Hermitian topological phases and dynamical quantum phase transitions: a generic connection. Longwen Zhou, Qianqian Du (2021).
3. Unsupervised machine learning of topological phase transitions from experimental data. Niklas Käming, Anna Dawid, Korbinian Kottmann, M. Lewenstein, K. Sengstock, A. Dauphin, C. Weitenberg (2021). Machine Learning: Science and Technology.