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Integrable Matrix Models in Discrete Space-Time
by Žiga Krajnik, Enej Ilievski, Tomaž Prosen
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Submission summary
| Authors (as registered SciPost users): | Enej Ilievski · Žiga Krajnik |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2003.05957v2 (pdf) |
| Date accepted: | 2020-08-20 |
| Date submitted: | 2020-07-23 14:40 |
| Submitted by: | Ilievski, Enej |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| 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.
Author comments upon resubmission
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.
Published as SciPost Phys. 9, 038 (2020)