# Integrable Matrix Models in Discrete Space-Time

### Submission summary

 As Contributors: Enej Ilievski Arxiv Link: https://arxiv.org/abs/2003.05957v2 (pdf) Date submitted: 2020-07-23 14:40 Submitted by: Ilievski, Enej Submitted to: SciPost Physics Discipline: Physics Subject area: Mathematical Physics Approaches: Theoretical, Computational

### 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.

###### Current status:
Editor-in-charge assigned

Revised version.

### List of changes

- We have addressed the points by one of the referees
(short notational clarifications added when appropriate, fixed misprints).
- We have resolved and a number misprints throughout the text.