Integrable Matrix Models in Discrete Space-Time

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.

arXiv commentv2, 60 pages, 10 figures, 1 table

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Cited by in corpus (35)

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• Dynamics of magnetization at infinite temperature in a Heisenberg spin chain
• Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
• Hydrodynamics in lattice models with continuous non-Abelian symmetries
• Absence of Normal Fluctuations in an Integrable Magnet
• Correlations and commuting transfer matrices in integrable unitary circuits
• Anomalous transport from hot quasiparticles in interacting spin chains
• Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems
• Hydrodynamics of nonintegrable systems from a relaxation-time approximation
• Non-linear fluctuating hydrodynamics for KPZ scaling in isotropic spin chains
• Dynamical criticality of magnetization transfer in integrable spin chains
• Universal anomalous fluctuations in charged single-file systems
• Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability
• Superdiffusion from nonabelian symmetries in nearly integrable systems
• Absence of superdiffusion in certain random spin models
• Kardar-Parisi-Zhang scaling in the Hubbard model
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• The Floquet Baxterisation
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• Integrable fishnet circuits and Brownian solitons