# Scaling of decoherence and energy flow in interacting quantum spin systems

## TL;DR

This paper investigates how a qubit coupled to a many-body quantum system behaves out-of-equilibrium, focusing on decoherence, energy flow, and work distribution near quantum phase transitions, using finite-size scaling and numerical simulations.

## Contribution

It introduces a dynamic finite-size scaling framework to analyze out-of-equilibrium quantum dynamics in spin models near phase transitions, validated by numerical results.

## Key findings

- Scaling behaviors match theoretical predictions
- Fast convergence to asymptotic behavior with increasing system size
- Decoherence and energy flow are characterized near critical points

## Abstract

We address the quantum dynamics of a system composed of a qubit globally coupled to a many-body system characterized by short-range interactions. We employ a dynamic finite-size scaling framework to investigate the out-of-equilibrium dynamics arising from the sudden variation (turning on) of the interaction between the qubit and the many-body system, in particular when the latter is in proximity of a quantum first-order or continuous phase transition. Although the approach is quite general, we consider d-dimensional quantum Ising spin models in the presence of transverse and longitudinal fields, as paradigmatic quantum many-body systems. To characterize the out-of-equilibrium dynamics, we focus on a number of quantum-information oriented properties of the model. Namely, we concentrate on the decoherence features of the qubit, the energy interchanges among the qubit and the many-body system during the out-of-equilibrium dynamics, and the work distribution associated with the quench. The scaling behaviors predicted by the dynamic finite-size scaling theory are verified through extensive numerical computations for the one-dimensional Ising model, which reveal a fast convergence to the expected asymptotic behavior with increasing the system size.