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 \sigmaσ-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.
We introduce a deterministic SO(3) invariant dynamics of classical spins on a discrete space-time lattice and prove its complete integrability by explicitly finding a related non-constant (baxterized) solution of the set-theoretic quantum Yang-Baxter equation over the 2-sphere. Equipping the algebraic structure with the corresponding Lax operator we derive an infinite sequence of conserved quantities with local densities. The dynamics depend on a single continuous spectral parameter and reduce to a (lattice) Landau-Lifshitz model in the limit of a small parameter which corresponds to the continuous time limit. Using quasiexact numerical simulations of deterministic dynamics and Monte Carlo sampling of initial conditions corresponding to a maximum entropy equilibrium state we determine spin-spin spatio-temporal (dynamical) correlation functions with relative accuracy of three orders of magnitude. We demonstrate that in the equilibrium state with a vanishing total magnetization the correlation function precisely follow Kardar-Parisi-Zhang scaling hence the spin transport belongs to the universality class with dynamical exponent z = 3/2, in accordance to recent related simulations in discrete and continuous time quantum Heisenberg spin 1/2 chains.
We perform energy spectrum analysis of the active turbulence in 3D bulk active nematic using continuum numerical modelling. Specifically, we calculate the spectra of two main energy contributions---kinetic energy and...
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