Quantum Critical Spectroscopy: New Signature of a Quantum Phase Transition in Non-equilibrium Energy Absorption

We demonstrate existence of a new kind of non-analytic signature of a quantum critical point, observed in the energy absorbed by the concerned system from an externally applied pulse at zero temperature. The pulse is applied by switching a certain coupling parameter $\lambda$ from a value $\lambda_{I}$ to a value $\lambda_{F}$ for a period $\tau$, and then switching it back to $\lambda_{I}$ again. The energy $E_{{\rm abs}}$ absorbed by the system from the pulse is measured as a function of $\lambda_{F}$. We show, if $\lambda_{F} = \lambda_{c}$ is a critical point for the system, then $E_{{\rm abs}}$ vs $\lambda_{F}$ shows a non-analytic behavior right at $\lambda_{F} = \lambda_{c}$, which can be used for accurate detection of a quantum critical point. No non-analyticity is observed for any value of $\lambda_{F}$ that is not critical. This non-analyticity cannot be explained entirely in terms of the ground state properties of the Hamiltonians -- excited states contribute in an essential way. We demonstrate these results analytically for two benchmarking models for studying quantum phase transition, namely, the XY and the Ising chain in transverse field.