On the partial trace over collective spin-degrees of freedom

TL;DR

This paper analyzes the degeneracy structure in collective spin systems and explores the dynamics of two qubits interacting with separate spin baths, including thermodynamic limit considerations.

Contribution

It provides analytical insights into the degeneracy $ u(N,j)$ and studies the dynamics of qubits coupled to spin baths, extending understanding of collective spin systems.

Findings

Analytical properties of degeneracy $ u(N,j)$ derived.

Dynamics of two qubits with Ising interactions analyzed.

Thermodynamic limit behavior studied.

Abstract

We derive analytical properties for the degeneracy $\nu(N,j)$ occurring in the decomposition $\bigoplus\limits_{j}^\frac{N}{2}\nu(N,j)\mathbb C^{2j+1}$ of the state space $\mathbb C^{2\otimes N}$. We also investigate the dynamics of two qubits coupled via Ising interactions to separate spin baths, and we study the thermodynamic limit.