Geometry of a two-spin quantum state in evolution

Abstract

We study the quantum evolution of a two-spin system described by the isotropic Heisenberg Hamiltonian in the external magnetic field. It is shown that this evolution happens on a two-parametric closed manifold. The Fubini-Study metric of this manifold is obtained. It is found that this is the metric of the torus. The entanglement of the states which belong to this manifold is investigated.

11 pages, accepted for publication in J. Phys. A

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• Quantum state geometry and entanglement of two spins with anisotropic interaction in evolution
• Geometry and speed of evolution for a spin-s system with long-range zz-type Ising interaction
• Geometric properties of evolutionary graph states and their detection on a quantum computer
• Probing the geometry of two-qubit state space by evolution
• Geometry of quantum state manifolds generated by the Lie algebra operators
• Inter-qubit correlation dynamics driven by mutual interactions