Exploring dynamical quantum phase transitions from pure states to mixed states through extended Su-Schrieffer-Heeger models

We investigate dynamical quantum phase transitions (DQPTs) in both pure and mixed states within the extended Su-Schrieffer-Heeger (SSH) model framework, focusing on the SSH-3 and SSH-4 models, which differ in symmetry properties. The SSH-3 model, characterized by a chiral-like point symmetry rather than true chiral symmetry, supports robust localized edge states tied to its topological nature. Our results show that for pure states, DQPTs occur after quenches crossing the topological transition, even when the energy band gap remains open. For mixed states, DQPT behavior aligns with pure states at low temperatures but undergoes significant changes at higher temperatures, including the emergence of multiple critical times. In contrast, the SSH-4 model, which possesses chiral symmetry, features four distinct energy-spectrum configurations. We find that pure-state DQPTs arise only when the quench starts from the initial state, chosen from a band that becomes gapless with another band at a certain critical point, and crosses the critical point. At finite temperature, mixed-state DQPTs persist at low temperatures only if the corresponding pure-state quench induces DQPTs, but they disappear at elevated temperatures. These findings elucidate the interplay between symmetry, band structures, and temperature in governing DQPTs within generalized SSH models.