Our paper Mukherjee et al, Phys. Rev. A.**97** 043606 (2018) applies a geometric representation of spin-spin correlations to phenomena in many-body systems. When considered with conventional techniques the correlations in these systems may seem very complicated: For example, plotting the dynamics of the many components of the correlations <S_1^a S_2^b> as a function of time after a quench appears complicated and lacks any apparent structure.

However, this paper showed that underlying the seemingly structureless evolution of the components are motions of geometric shapes that are uncomplicated, easy to remember, and simple to describe. For example, the shapes may simply grow and rotate in a smooth, regular fashion.

Here are movies (from the supplement of that paper), which correspond to the dynamic situations considered in that paper: dynamics of (i) an Ising model evolved from an initial product state with the spins at an angle pi/2, (ii) the same for pi/4, (iii) again an initial angle of pi/2, but now with incoherent spontaneous emission added, and (iv) an initially canted antiferromagnet of lattice fermions under a non-interacting evolution. We also show movies of alternative visualization methods applied to the same dynamics as (ii), such as (v) plotting eigenvalues and eigenvectors of the correlation matrices or (vi) the Wigner functions of the reduced two-spin density matrix. Although there are some differences in details, these alternatives also reveal the hidden simplicity of correlations in many-body dynamics.

Each video should be embedded, and a link is also available for download.

## Ising: initial angle pi/2 (coherent)

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## Ising: initial angle pi/4 (coherent)

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## Ising: initial angle pi/2, spontaneous emission included

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## Fermi-Hubbard: canted antiferromagnet evolved under U=0 dynamics

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## Eigenvectors with length weighted by eigenvalues Ising, initial angle pi/4

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## Wigner functions for Ising, initial angle pi/4

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