Dynamical Phase Transitions, Caustics, and Quantum Dark Bands

TL;DR

This paper links quantum dynamical phase transitions to caustics in Fock space, revealing their universal nature and proposing an experimental protocol for detection in finite systems.

Contribution

It introduces a novel perspective connecting DPTs with caustics and catastrophe theory, providing analytical insights and an experimental verification protocol.

Findings

DPTs correspond to crossings of Loschmidt echo with caustic switching lines.

Caustics in Fock space explain the universal occurrence of DPTs.

Proposed protocol enables experimental detection of DPTs in finite systems.

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.