Dynamics, Synchronization and Quantum Phase Transitions of Two Dissipative Spins

TL;DR

This paper studies the static and dynamic behaviors of two dissipative quantum spins coupled via Ising interaction in a common bosonic environment, revealing phase diagrams, synchronization phenomena, and entanglement properties.

Contribution

It provides a comprehensive analysis combining numerical and analytical methods to explore phase transitions and dynamical effects in a two-spin dissipative quantum system.

Findings

Identification of ground state phase diagrams for ohmic and subohmic baths.

Observation of spin synchronization due to non-Markovian bath effects.

Discovery of highly entangled steady states under certain initial conditions.

Abstract

We analyze the static and dynamical properties of two Ising-coupled quantum spins embedded in a common bosonic bath as an archetype of dissipative quantum mechanics. First, we elucidate the ground state phase diagram for an ohmic and a subohmic bath using a combination of bosonic numerical renormalization group (NRG), analytical techniques and intuitive arguments. Second, employing the time-dependent NRG we investigate the system's rich dynamical behavior arising from the complex interplay between spin-spin and spin-bath interactions. Interestingly, spin oscillations can synchronize due to the proximity of the common non-Markovian bath and the system displays highly entangled steady states for certain nonequilibrium initial preparations. We complement our non-perturbative numerical results by exact analytical solutions when available and provide quantitative limits on the applicability of the perturbative Bloch-Redfield approach at weak coupling.