# Anomalous dynamical phase in quantum spin chains with long-range interactions

## TL;DR

This paper explores a newly identified anomalous dynamical phase in long-range quantum spin chains, revealing its connection to symmetry breaking and expanding the understanding of dynamical criticality with potential experimental realizations.

## Contribution

It demonstrates the existence of the anomalous dynamical phase in infinite-range interactions using semiclassical and exact methods, linking it to symmetry breaking and broadening the dynamical phase diagram.

## Key findings

- Anomalous phase characterized by unique non-analytic cusps.
- Transition from regular to anomalous phase coincides with Z2-symmetry breaking.
- Results applicable to experimental setups with long-range interactions.

## Abstract

The existence or absence of non-analytic cusps in the Loschmidt-echo return rate is traditionally employed to distinguish between a regular dynamical phase (regular cusps) and a trivial phase (no cusps) in quantum spin chains after a global quench. However, numerical evidence in a recent study [J. C. Halimeh and V. Zauner-Stauber, arXiv:1610.02019] suggests that instead of the trivial phase a distinct anomalous dynamical phase characterized by a novel type of non-analytic cusps occurs in the one-dimensional transverse-field Ising model when interactions are sufficiently long-range. Using an analytic semiclassical approach and exact diagonalization, we show that this anomalous phase also arises in the fully-connected case of infinite-range interactions, and we discuss its defining signature. Our results show that the transition from the regular to the anomalous dynamical phase coincides with Z2-symmetry breaking in the infinite-time limit, thereby showing a connection between two different concepts of dynamical criticality. Our work further expands the dynamical phase diagram of long-range interacting quantum spin chains, and can be tested experimentally in ion-trap setups and ultracold atoms in optical cavities, where interactions are inherently long-range.