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Integrable Matrix Models in Discrete Space-Time

by Žiga Krajnik, Enej Ilievski, Tomaž Prosen

Submission summary

As Contributors: Enej Ilievski
Arxiv Link: (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


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

Author comments upon resubmission

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.

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