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

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.