Quantum state texture of dynamical criticality

TL;DR

This paper links quantum state texture, measured by rugosity, to dynamical quantum phase transitions, revealing its role as an order parameter and its universal connection to criticality in nonequilibrium quantum systems.

Contribution

It establishes rugosity as a basis-dependent quantum resource that diagnoses dynamical criticality, connecting it to phase transitions and providing an information-theoretic perspective.

Findings

Rugosity acts as an order parameter for type-I dynamical transitions.

Density of rugosity exactly matches the Loschmidt rate function for type-II transitions.

Rugosity signatures are evident even in physically motivated bases.

Abstract

We investigate the role of quantum state texture in dynamical quantum phase transitions by establishing a direct connection between critical nonequilibrium dynamics and the recently introduced notion of rugosity, a measure of the quantum state texture. Considering a generic quench protocol, we analyze both standard formulations of the dynamical quantum phase transition. For type-I transitions, defined through the long-time behavior of an order parameter, we show that the time averaged rugosity, evaluated in the eigenbasis of the pre-quench Hamiltonian, acts itself as an order parameter, sharply distinguishing the dynamical phases. In the Lipkin-Meshkov-Glick model, this behavior is traced back to the underlying semiclassical structure, where the crossing of the excited-state quantum phase transition separatrix controls the redistribution of the state over the pre-quench energy basis. For type-II transitions, characterized by nonanalyticities in the Loschmidt rate function, we demonstrate that rugosity acquires a universal interpretation. For a suitable choice of basis, the rate function is exactly given by the density of rugosity, establishing a model-independent equivalence. Moreover, we show that even in physically motivated bases, such as the pre-quench energy eigenbasis, rugosity provides clear signatures of dynamical criticality. Our results place rugosity within a broader class of quantities diagnosing dynamical quantum phase transitions, including complexity and entropy production, while highlighting its distinct role as a measure of a basis-dependent quantum resource. This work provides an information-theoretic perspective on dynamical critical phenomena and opens new directions for exploring quantum texture in nonequilibrium many-body systems.