Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging Different Concepts of Nonequilibrium Criticality

TLDR

The authors investigate the dynamics of a transverse‑field Ising chain with power‑law decaying interactions, aiming to relate two distinct nonequilibrium critical phenomena and provide a symmetry‑based interpretation. They analyze quenches from a ferromagnetic state in this model, identifying a critical transverse field where the time‑averaged order parameter vanishes, and a second class of dynamical criticality manifested as time‑periodic singularities in the Loschmidt echo that appears for all interaction exponents. They find that the order‑parameter transition occurs only for long‑range interactions with exponent α ≤ 2, while the Loschmidt‑echo singularities arise for all α and coincide with the order‑parameter transition in the long‑range regime.

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.