Dynamical Phase Transition in Droplet Dynamics

Xiao Wang (Cornell, Eun-Ah Kim group) introduces droplet dynamics — a compact spatial block of local excitations or defect insertions embedded in a much larger quantum background — and shows how it realizes a universal class of unconventional dynamical transitions, identified as dynamical Gross–Witten–Wadia transitions, in both the XX/free-fermion and transverse-field Ising chains.

Abstract

In this talk, I will introduce the droplet dynamics, where a quantum droplet is a compact spatial block of local excitations or defect insertions embedded in a much larger quantum background. Specifically, I will talk about the droplet dynamics in both XX/free-fermion chain and transverse field Ising chain. I will show that these dynamics can realize a universal class of unconventional dynamical transitions, which we identify as dynamical Gross-Witten-Wadia transitions. In the large-droplet limit, the dynamical free energy associated with the Loschmidt echo develops two universal regimes: a pre-critical quadratic regime and a post-critical logarithmic regime. These regimes meet at a rescaled critical time, where the third time derivative is discontinuous. Then in the transverse field Ising chain, I will further show that the same universal dynamical transitions can also be accessed through spin droplet dynamics, whose Loschmidt echoes are given by the squared magnitudes of compact multipoint space-time spin autocorrelators. In the large-field paramagnetic phase, the longitudinal-spin droplet echo converges to the Loschmidt echo of free-fermion droplet dynamics as the transverse field is increased. In the small-field ferromagnetic phase, Kramers–Wannier duality identifies the transverse-spin droplet as the corresponding dual realization. Our results establish droplet dynamics as a unifying framework for a new class of universal dynamical transitions, and connect these dynamics to space-time spin correlators in quantum many-body systems.

Lecture notes will be posted here after the talk.