# Response of macroscopic and microscopic dynamical quantifiers to the quantum critical region

## TL;DR

This paper investigates how certain dynamical physical quantities in the transverse field quantum XY model respond to the quantum critical region at finite temperatures, demonstrating their effectiveness in detecting quantum criticality through non-equilibrium dynamics.

## Contribution

It introduces a class of dynamical quantifiers based on energy absorption, entanglement, and mutual information that effectively identify the quantum critical region during non-equilibrium evolution.

## Key findings

- Maximum energy absorption decreases faster with temperature within QCR.
- Nearest neighbor entanglement shows a sharper fall-off in QCR.
- Quantum mutual information effectively signals the QCR during dynamics.

## Abstract

At finite temperatures, the quantum critical region (QCR) emerges as a consequence of the interplay between thermal and quantum fluctuations. We seek for suitable physical quantities, which during dynamics can give prominent response to QCR in the transverse field quantum $XY$ model. We report that the maximum energy absorbed, the nearest neighbor entanglement and the quantum mutual information of the time evolved state after a quench of the transverse magnetic field exhibits a faster fall off with temperature when the initial magnetic field is taken from within the QCR, compared to the choice of the initial point from different phases. We propose a class of dynamical quantifiers, originated from the response of these physical quantities and show that they can faithfully mimic the equilibrium physics, namely detection of the QCR at finite temperatures.