Quantum Integrable Models on 1 + 1 Discrete Space Time

Alexey P. Isaev, С. М. Сергеев

John M. Arnold

The Jaynes-Cummings model of early quantum optics is examined from the point of view of a discrete-space discrete-time formulation of the electromagnetic field (the FDTD formulation) excited by an elementary quantum Hertzian dipole associated to a single edge of the discrete-space lattice. The quantum Hertz dipole is a natural 2-level atomic system, and the quantum dynamics of the electromagnetic field in the discrete space surrounding the dipole, described by functional integrals over field space, is essentially a stochastic (Monte-Carlo) algorithm for solving the FDTD equations by searching for the field distribution about which the field action Lagrangian functional S is stationary.

Anton Vladimirovich Zabrodin

Žiga Krajnik, Enej Ilievski, Tomaž Prosen +1 more

We construct an integrable lattice model of classical interacting spins in discrete space-time, representing a discrete-time analogue of the lattice Landau-Lifshitz ferromagnet with uniaxial anisotropy. As an application we use this explicit discrete symplectic integration scheme to compute the spin Drude weight and diffusion constant as functions of anisotropy and chemical potential. We demonstrate qualitatively different behavior in the easy-axis and the easy-plane regimes in the non-magnetized sector. Upon approaching the isotropic point we also find an algebraic divergence of the diffusion constant, signaling a crossover to spin superdiffusion.

Michael Fowler

Žiga Krajnik, Enej Ilievski, Tomaž Prosen +1 more

We construct an integrable lattice model of classical interacting spins in discrete space-time, representing a discrete-time analogue of the lattice Landau-Lifshitz ferromagnet with uniaxial anisotropy. As an application we use this explicit discrete symplectic integration scheme to compute the spin Drude weight and diffusion constant as functions of anisotropy and chemical potential. We demonstrate qualitatively different behavior in the easy-axis and the easy-plane regimes in the non-magnetized sector. Upon approaching the isotropic point we also find an algebraic divergence of the diffusion constant, signaling a crossover to spin superdiffusion.