# Dynamical criticality and domain-wall coupling in long-range Hamiltonians

## TL;DR

This paper investigates how bound domain walls influence anomalous dynamical criticality in long-range quantum spin chains, showing that removing domain-wall coupling eliminates certain critical behaviors and revealing complex phase diagrams.

## Contribution

It demonstrates that bound domain walls are essential for anomalous cusps in Loschmidt return rates and explores the rich dynamical phases of long-range Kitaev chains.

## Key findings

- Bound domain walls are necessary for anomalous cusps.
- Removing domain-wall coupling eliminates anomalous criticality.
- Long-range Kitaev chains exhibit complex dynamical phases.

## Abstract

Dynamical quantum phase transitions hold a deep connection to the underlying equilibrium physics of the quench Hamiltonian. In a recent study [J.~C.~Halimeh \textit{et al.}, arXiv:1810.07187], it has been numerically demonstrated that the appearance of anomalous cusps in the Loschmidt return rate coincides with the presence of bound domain walls in the spectrum of the quench Hamiltonian. Here, we consider transverse-field Ising chains with power-law and exponentially decaying interactions, and show that by removing domain-wall coupling via a truncated Jordan-Wigner transformation onto a Kitaev chain with long-range hopping and pairing, anomalous dynamical criticality is no longer present. This indicates that bound domain walls are necessary for anomalous cusps to appear in the Loschmidt return rate. We also calculate the dynamical phase diagram of the Kitaev chain with long-range hopping and pairing, which in the case of power-law couplings is shown to exhibit rich dynamical criticality including a doubly critical dynamical phase.