Fidelity, Rosen-Zener Dynamics, Entropy and Decoherence in one dimensional hard-core bosonic systems

TL;DR

This paper investigates the non-equilibrium dynamics, quantum phase transitions, entropy, and decoherence in a one-dimensional hard-core boson system subjected to quenches in an alternating potential, revealing how these processes affect coherence and entropy.

Contribution

It introduces a detailed analysis of Rosen-Zener quench schemes in a 1D HCB system, linking quantum criticality with entropy and decoherence phenomena.

Findings

Fidelity shows a sharp dip at the quantum critical point.

Local entropy density is reduced below equilibrium value after HRZ quench.

Decoherence factor dynamics are analytically derived for HRZ and sudden quenches.

Abstract

We study the non-equilibrium dynamics of a one-dimensional system of hard core bosons (HCBs) in the presence of an onsite potential (with an alternating sign between the odd and even sites) which shows a quantum phase transition (QPT) from the superfluid (SF) phase to the so-called "Mott Insulator" (MI) phase. The ground state quantum fidelity shows a sharp dip at the quantum critical point (QCP) while the fidelity susceptibility shows a divergence right there with its scaling given in terms of the correlation length exponent of the QPT. We then study the evolution of this bosonic system following a quench in which the magnitude of the alternating potential is changed starting from zero (the SF phase) to a non-zero value (the MI phase) according to a half Rosen Zener (HRZ) scheme or brought back to the initial value following a full Rosen Zener (FRZ) scheme. The local von Neumann entropy density is calculated in the final MI phase (following the HRZ quench) and is found to be less than the equilibrium value ($\log 2$) due to the defects generated in the final state as a result of the quenching starting from the QCP of the system. We also briefly dwell on the FRZ quenching scheme in which the system is finally in the SF phase through the intermediate MI phase and calculate the reduction in the supercurrent and the non-zero value of the residual local entropy density in the final state. Finally, the loss of coherence of a qubit (globally and weekly coupled to the HCB system) which is initially in a pure state is investigated by calculating the time-dependence of the decoherence factor when the HCB chain evolves under a HRZ scheme starting from the SF phase. This result is compared with that of the sudden quench limit of the half Rosen-Zener scheme where an exact analytical form of the decoherence factor can be derived.