Evolution of a quantum spin system to its ground state: Role of entanglement and interaction symmetry

TL;DR

This paper investigates how two interacting spins relax to their ground state within a frustrated environment, highlighting the influence of interaction symmetry and coupling conservation on the relaxation process.

Contribution

It reveals the critical role of coupling symmetry and magnetization conservation in the relaxation dynamics of a two-spin quantum system in a frustrated environment.

Findings

Relaxation occurs only within narrow parameter ranges.

Symmetric, magnetization-conserving coupling facilitates relaxation.

Non-conserving coupling inhibits the system from reaching the ground state.

Abstract

We study the decoherence of two ferro- and antiferromagnetically coupled spins that interact with a frustrated spin-bath environment in its ground state. The conditions under which the two-spin system relaxes from the initial spin-up - spin-down state towards its ground state are determined. It is shown that the two-spin system relaxes to its ground state for narrow ranges of the model parameters only. It is demonstrated that the symmetry of the coupling between the two-spin system and the environment has an important effect on the relaxation process. In particular, we show that if this coupling conserves the magnetization, the two-spin system readily relaxes to its ground state whereas a non-conserving coupling prevents the two-spin system from coming close to its ground state.