Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging different concepts of non-equilibrium criticality

TL;DR

This paper investigates dynamical quantum phase transitions in long-range interacting spin chains, revealing how different non-equilibrium critical phenomena emerge and relate depending on the interaction range, with implications for experimental realizations.

Contribution

It introduces a unified framework connecting order parameter transitions and Loschmidt echo singularities in long-range quantum spin chains after a quench.

Findings

Order parameter transition occurs only for interaction decay exponent $oldsymbol{eta extless 2}$.

Loschmidt echo singularities appear for all interaction ranges $oldsymbol{eta}$.

The two classes of criticality are physically connected through symmetry considerations.

Abstract

We theoretically study the dynamics of a transverse-field Ising chain with power-law decaying interactions characterized by an exponent $\alpha$, which can be experimentally realized in ion traps. We focus on two classes of emergent dynamical critical phenomena following a quantum quench from a ferromagnetic initial state: The first one manifests in the time averaged order parameter, which vanishes at a critical transverse field. We argue that such a transition occurs only for long-range interactions $\alpha \leq 2$ . The second class corresponds to the emergence of time-periodic singularities in the return probability to the ground state manifold (a.k.a. Loschmidt echo) which is obtained for all values of $\alpha$ and agrees with the order parameter transition for $\alpha\leq 2$. We characterize how the two classes of nonequilibrium criticality correspond to each other and give a physical interpretation based on the symmetry of the time-evolved quantum states.