Integrable matrix models in discrete space-time
Žiga Krajnik, Enej Ilievski, Tomaž Prosen
SciPost Phys. 9, 038 (2020) · published 14 September 2020
- doi: 10.21468/SciPostPhys.9.3.038
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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.
Cited by 26
Authors / Affiliation: mappings to Contributors and Organizations
See all Organizations.- 1 Žiga Krajnik,
- 1 Enej Ilievski,
- 1 Tomaž Prosen