Dynamical Phase Transitions, Caustics, and Quantum Dark Bands

Abstract

We provide a new perspective on quantum dynamical phase transitions (DPTs) by explaining their origin in terms of caustics that form in the Fock space representation of the many-body state over time, using the fully connected transverse field Ising model as an example. In this way we establish a connection between DPTs in a quantum spin system and an everyday natural phenomenon: The dark band between the primary and seconday bows (caustics) in rainbows known as Alexander's dark band. The DPT occurs when the Loschmidt echo crosses the switching line between the evanescent tails of two back-to-back Airy functions that dress neighbouring fold caustics in Fock space and is the time-dependent analogue of what is seen as a function of angle in the sky. The structural stability and universal properties of caustics, as described mathematically by catastrophe theory, explains the generic occurrence of DPTs in the model and suggests that our analysis has wide applicability. Based on our thorough analytical understanding we propose a protocol which can be used to verify the existence of a DPT in a finite system experiment.

References in corpus (13)

• The large deviation approach to statistical mechanics
• Dynamical phase transition in the open Dicke model
• Dynamical Phase Transitions and Instabilities in Open Atomic Many-Body Systems
• Excited state quantum phase transitions in many-body systems
• Coherent Oscillations in an Exciton-Polariton Josephson Junction
• Keldysh approach for non-equilibrium phase transitions in quantum optics: beyond the Dicke model in optical cavities
• Dynamics of a tunable superfluid junction
• Excited-state quantum phase transitions
• Infinite-range Ising ferromagnet in a time-dependent transverse field: quench and ac dynamics near the quantum critical point
• Dynamical phase transitions in dissipative quantum dynamics with quantum optical realization
• Dynamical phase transitions in quantum spin models with antiferromagnetic long-range interactions
• Time-dependent Semiclassics for Ultracold Bosons
• Catastrophes in non-equilibrium many-particle wave functions: universality and critical scaling