Quantum dynamics and entanglement of spins on a square lattice

Abstract

Bulk magnetism in solids is fundamentally quantum mechanical in nature. Yet in many situations, including our everyday encounters with magnetic materials, quantum effects are masked, and it often suffices to think of magnetism in terms of the interaction between classical dipole moments. Whereas this intuition generally holds for ferromagnets, even as the size of the magnetic moment is reduced to that of a single electron spin (the quantum limit), it breaks down spectacularly for antiferromagnets, particularly in low dimensions. Considerable theoretical and experimental progress has been made in understanding quantum effects in one-dimensional quantum antiferromagnets, but a complete experimental description of even simple two-dimensional antiferromagnets is lacking. Here we describe a comprehensive set of neutron scattering measurements that reveal a non-spin-wave continuum and strong quantum effects, suggesting entanglement of spins at short distances in the simplest of all two-dimensional quantum antiferromagnets, the square lattice Heisenberg system. antiferromagnetism ͉ entanglement ͉ multimagnons ͉ spin waves O ne of the most fundamental exercises in quantum mechanics is to consider a pair of S ϭ 1/2 spins with an interaction J between them that favors either parallel (ferromagnetic) or antiparallel (antiferromagnetic) alignment. The former results in a spin S tot ϭ 1 ground state, which is a degenerate triplet. Two of the states in this triplet are the possible classical ground states ͉11͘ and ͉22͘, whereas the third is the coherent symmetric superposition ͉12͘ϩ͉21͘, which has no classical analogue. Even more interesting is antiferromagnetic J, for which the ground state is the entirely nonclassical S tot ϭ 0 singlet ͉0͘ ϭ ͉12͘ Ϫ ͉21͘ consisting of the antisymmetric coherent superposition of the two classical ground states of the pair. The state ͉0͘ is an example of maximal entanglement, i.e., a wavefunction for two coupled systems that cannot be written as the product of eigenfunctions for the two separate systems, which in this case are of course the two spins considered individually.

Entanglement in a Quantum Annealing Processor

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Single to Multiquasiparticle Excitations in the Itinerant Helical MagnetCeRhIn5

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