Signature of a continuous quantum phase transition in non-equilibrium energy absorption: Footprints of criticality on higher excited states.

Sirshendu Bhattacharyya,Arnab Das,Subinay Dasgupta

doi:10.1038/srep16490

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 (λI) to a final value (λF) 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 λF at critical-points (i.e., at values of λF corresponding to static critical-points of the system). As one excites higher and higher eigenstates of the final Hamiltonian H(λF) by increasing the pulse height , 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.

Highlights

Microscopic details of the system tend to dominate most of the physical properties of the system, and the signature of the ground-state singularity gets obscured
From the point of view of equilibrium physics, a faint positive indication follows from the existence of the so-called quantum critical region in the finite temperature phase diagram of a quantum system, where the behaviors of the system is strongly affected by the existence of an underlying quantum critical point even at T ≠ 03
Similar indication is obtained from non-equilibrium response mechanism of a system driven at a finite rate across a quantum critical point, largely known as the Kibble-Zurek mechanism[15,16], which predicts universal scaling behaviour of defect density with respect to the drive rate

Summary

Introduction

Microscopic details of the system tend to dominate most of the physical properties of the system, and the signature of the ground-state singularity gets obscured. This does not rule out existence of such a signature lying hidden in those excited states in some form. A clear signature of quantum criticality on high-lying states has remained elusive so far We bridge this gap by demonstrating a case where the fingerprints of the QPT on the higher-excited states play an essential role in the occurrence of a non-analyticity in the non-equilibrium response of the system. Though a non-analyticity does not necessarily imply a phase transition (see, e.g.25, where non-analytic behaviour of correlation length is observed at a point with no phase transition), in our case the signature always and exclusively occurs at the critical points

Methods

Results

Conclusion