Maximal Entanglement and Frozen Information: A Unified Framework for Dynamical Quantum Phase Transitions

TL;DR

This paper introduces a unified information-theoretic framework for dynamical quantum phase transitions, linking maximal entanglement, Loschmidt echo zeros, and suppressed information scrambling in free quantum systems.

Contribution

It establishes that critical momentum modes at DQPTs exhibit maximal entanglement and vanishing OTOC, unifying these signatures across different models.

Findings

Critical modes saturate entanglement to ln(2).

Vanishing OTOC at critical modes indicates halted information flow.

Fisher zeros, maximal entanglement, and OTOC suppression are equivalent signatures.

Abstract

Dynamical quantum phase transitions (DQPTs) are temporal singularities marked by zeros of the Loschmidt echo, yet their underlying quantum-information structure remains elusive. Here, we introduce a momentum-resolved entanglement entropy as a direct probe of DQPTs in translation-invariant free systems. We analytically establish that every critical momentum mode $k^{*}$ associated with a DQPT saturates its entanglement to the maximal value $\ln{2}$, coinciding with the vanishing of the Loschmidt echo. Crucially, we demonstrate that this maximal entanglement universally suppresses information scrambling: a momentum-resolved out-of-time-ordered correlator (OTOC) vanishes identically for all times at $k^{*}$. These three signatures -- Fisher zeros, maximal entanglement, and vanished OTOC -- are proved to be equivalent in both the transverse-field Ising and Su-Schrieffer-Heeger models, despite their distinct bipartitions (momentum-pair vs. sublattice). Our results establish a unified, information-theoretic framework for DQPTs, revealing them a points where quantum correlations saturate and information flow halts. This work elevates entanglement and scrambling to central dynamical order parameters, offering a universal perspective on nonequilibrium quantum critically.