Signature of a Continuous Quantum Phase Transition in Nonequilibrium Energy Absorption: Footprints of Criticality on Highly Excited States

TL;DR

This paper demonstrates that quantum critical points leave distinct non-analytic signatures in the energy absorption of highly excited, non-equilibrium states generated by external pulses, revealing criticality beyond ground states.

Contribution

It provides exact analytical evidence that quantum critical points influence energy absorption signatures in highly excited states, extending the understanding of criticality to non-equilibrium conditions.

Findings

Non-analyticities in energy absorption at critical points.

Stronger non-analyticities with higher eigenstate excitation.

Signatures confirmed in Ising and XY chains.

Abstract

Understanding phase transitions in quantum matters constitutes a significant part of present day condensed matter physics. Quantum phase transitions concern ground state properties of many-body systems, and hence their signatures are expected to be pronounced in low-energy states. Here we report signature of a quantum critical point manifested in strongly out-of-equilibrium states with finite energy density with respect to the ground state and extensive (subsystem) entanglement entropy, generated by an external pulse. These non-equilibrium states are evidently completely disordered (e.g., paramagnetic in case of a magnetic ordering transition). The pulse is applied by switching a coupling of the Hamiltonian from an initial value ($\lambda_{I}$) to a final value ($\lambda_{F}$) for sufficiently long time and back again. The signature appears as non-analyticities (kinks) in the energy absorbed by the system from the pulse as a function of $\lambda_{F}$ at critical-points (i.e., at values of $\lambda_{F}$ corresponding to static critical-points of the system). As one excites higher and higher eigenstates of the final Hamiltonian $H(\lambda_{F})$ by increasing the pulse height ($|\lambda_{I} - \lambda_{F}|$), the non-analyticity grows stronger monotonically with it. This implies adding contributions from higher eigenstates help magnifying the non-analyticity, indicating strong imprint of the critical-point on them. Our findings are grounded on exact analytical results derived for Ising and XY chains in transverse field.