Entanglement and precession in two-dimensional dynamical quantum phase transitions

TL;DR

This paper extends the understanding of dynamical quantum phase transitions (DQPTs) to two-dimensional systems, revealing persistent mechanisms and new phenomenologies, with implications for quantum many-body dynamics.

Contribution

It investigates p- and eDQPTs in 2D lattices, showing their persistence and phenomenology, and highlights sensitivity to system details and new behaviors in honeycomb lattices.

Findings

pDQPTs linked to magnetization sign change and entanglement gap

eDQPTs associated with suppressed local observables and avoided crossings

Higher sensitivity of DQPTs to system size and lattice details

Abstract

Non-analytic points in the return probability of a quantum state as a function of time, known as dynamical quantum phase transitions (DQPTs), have received great attention in recent years, but the understanding of their mechanism is still incomplete. In our recent work arXiv:2008.04894, we demonstrated that one-dimensional DQPTs can be produced by two distinct mechanisms, namely semiclassical precession and entanglement generation, leading to the definition of precession (pDQPTs) and entanglement (eDQPTs) dynamical quantum phase transitions. In this manuscript we extend and investigate the notion of p- and eDQPTs in two-dimensional systems by considering semi-infinite ladders of varying width. For square lattices, we find that pDQPTs and eDQPTs persist and are characterized by similar phenomenology as in 1D: pDQPTs are associated with a magnetization sign change and a wide entanglement gap, while eDQPTs correspond to suppressed local observables and avoided crossings in the entanglement spectrum. However, DQPTs show higher sensitivity to the ladder width and other details, challenging the extrapolation to the thermodynamic limit especially for eDQPTs. Moving to honeycomb lattices, we also demonstrate that lattices with odd number of nearest neighbors give rise to phenomenologies beyond the one-dimensional classification.