Kibble-Zurek dynamics in the transverse-field Ising chain under nontrivial Markovian noise

The Kibble Zurek (KZ) mechanism is a quintessential result in the study of universal dynamics near a quantum phase transition, with many applications to quantum processors and simulators. However, in the current NISQ era, coupling between a many-body system and its noisy environment can never be neglected. Here we study the KZ mechanism in the transverse-field Ising chain subject to local, Markovian noise. Previous studies have largely been restricted to limited kinds of noise (e.g. noise in the transverse field) that yield simple dissipative dynamics (e.g. free fermion Lindblad master equations). Here, we leverage a recently developed numerical technique [1] to simulate more nontrivial dissipation, such as T1 relaxation or depolarizing noise, which necessarily map to interacting fermionic master equations. Our approach allows us to characterize the resulting competition of dissipation and criticality for a wide range of physically relevant settings.

[1] Pocklington and Clerk. PRX Quantum 6 (2025)