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arXiv · 2003.05957

Integrable Matrix Models in Discrete Space-Time

Žiga Krajnik·Enej Ilievski·Tomaž Prosen
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Abstract

We introduce a class of integrable dynamical systems of interacting classical matrix-valued fields propagating on a discrete space-time lattice, realized as many-body circuits built from elementary symplectic two-body maps. The models provide an efficient integrable Trotterization of non-relativistic $\sigma$-models with complex Grassmannian manifolds as target spaces, including, as special cases, the higher-rank analogues of the Landau-Lifshitz field theory on complex projective spaces. As an application, we study transport of Noether charges in canonical local equilibrium states. We find a clear signature of superdiffusive behavior in the Kardar-Parisi-Zhang universality class, irrespectively of the chosen underlying global unitary symmetry group and the quotient structure of the compact phase space, providing a strong indication of superuniversal physics.

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Žiga Krajnik, Enej Ilievski, Tomaž Prosen. 2020-03-12. Integrable Matrix Models in Discrete Space-Time. https://doi.org/10.21468/scipostphys.9.3.038

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