Spin-1/2 sub-dynamics nested in the quantum dynamics of two coupled qutrits

TL;DR

This paper reveals that the complex quantum dynamics of two coupled spin-1 systems can be exactly reduced to simpler, non-interacting spin-1/2 dynamics within a specific subspace, enabling easier analysis of their behavior.

Contribution

It demonstrates a novel exact decomposition of two coupled spin-1 systems into independent spin-1/2 dynamics within a four-dimensional subspace, simplifying their analysis.

Findings

Exact decoupling of 9D dynamics into 4D and 5D subspaces.

In the 4D subspace, the two qutrits behave as non-interacting spin-1/2 pairs.

Potential for applying this reduction to time-dependent Hamiltonians.

Abstract

In this paper we investigate the quantum dynamics of two spin-1 systems, $\vec{\textbf{S}}_1$ and $\vec{\textbf{S}}_2$, adopting a generalized $(\vec{\textbf{S}}_1+\vec{\textbf{S}}_2)^2$-nonconserving Heisenberg model. We show that, due to its symmetry property, the nine-dimensional dynamics of the two qutrits exactly decouples into the direct sum of two sub-dynamics living in two orthogonal four- and five-dimensional subspaces. Such a reduction is further strengthened by our central result consisting in the fact that in the four-dimensional dynamically invariant subspace, the two qutrits quantum dynamics, with no approximations, is equivalent to that of two non interacting spin 1/2's. The interpretative advantages stemming from such a remarkable and non-intuitive nesting are systematically exploited and various intriguing features consequently emerging in the dynamics of the two qutrits are deeply scrutinised. The possibility of exploiting the dynamical reduction brought to light in this paper for exactly treating as well time-dependent versions of our Hamiltonian model is briefly discussed.