Entanglement and precession in two-dimensional dynamical quantum phase transitions

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.

14 pages, 13 figures

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Cited by in corpus (10)

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• Dynamical bulk boundary correspondence and dynamical quantum phase transitions in higher order topological insulators
• Quantum dynamics in one and two dimensions via recursion method
• Dynamical Quantum Phase Transitions Following Double Quenches: Persistence of the Initial State vs Dynamical Phases
• Scaling and Universality at Ramped Quench Dynamical Quantum Phase Transition
• Fisher zeroes and dynamical quantum phase transitions for two- and three-dimensional models
• Linear-scale simulations of quench dynamics
• Quantum coherence assisted dynamical phase transition
• A Dynamical Bulk-Boundary Correspondence in Two Dimensional Topological Matter
• Dynamical quantum phase transitions in strongly correlated two-dimensional spin lattices following a quench