Emergent Non-Abelian Gauge Theory in Coupled Spin-Electron Dynamics

Abstract

A clear separation of the time scales governing the dynamics of "slow" and "fast" degrees of freedom often serves as a prerequisite for the emergence of an independent low-energy theory. Here, we consider (slow) classical spins exchange coupled to a tight-binding system of (fast) conduction electrons. The effective equations of motion are derived under the constraint that the quantum state of the electron system at any instant of time $t$ lies in the $n$-dimensional low-energy subspace for the corresponding spin configuration at $t$. The effective low-energy theory unfolds itself straightforwardly and takes the form of a non-abelian gauge theory with the gauge freedom given by the arbitrariness of the basis spanning the instantaneous low-energy sector. The holonomic constraint generates a gauge covariant spin-Berry curvature tensor in the equations of motion for the classical spins. In the non-abelian theory for $n>1$, opposed to the $n=1$ adiabatic spin dynamics theory, the spin-Berry curvature is generically nonzero, even for time-reversal symmetric systems. Its expectation value with the representation of the electron state is gauge invariant and gives rise to an additional {\em geometrical} spin torque. Besides anomalous precession, the $n\ge 2$ theory also captures the spin nutational motion, which is usually considered as a retardation effect. This is demonstrated by proof-of-principle numerical calculations for a minimal model with a single classical spin. Already for $n=2$ and in parameter regimes where the $n=1$ adiabatic theory breaks down, we find good agreement with results obtained from the full (unconstrained) theory.

19 pages, 12 figures, v2 with minor changes

References in corpus (26)

• Berry Phase Effects on Electronic Properties
• Atomistic spin model simulations of magnetic nanomaterials
• Microscopic approach to current-driven domain wall dynamics
• A method for atomistic spin dynamics simulations: implementation and examples
• Adiabatic Theorem without a Gap Condition
• Ab-initio calculation of the Gilbert damping parameter via linear response formalism
• Atomistic spin dynamic method with both damping and moment of inertia effects included from first principles
• Linear dynamics of quantum-classical hybrids
• Magnetization Dynamics, Gyromagnetic Relation, and Inertial Effects
• Spin Dynamics with Inertia in Metallic Ferromagnets
• Time-retarded damping and magnetic inertia in the Landau-Lifshitz-Gilbert equation self-consistently coupled to electronic time-dependent nonequilibrium Green functions
• Consistent classical and quantum mixed dynamics
• Vector Potential and Berry phase-induced Force
• Spin dynamics and relaxation in the classical-spin Kondo-impurity model beyond the Landau-Lifschitz-Gilbert equation
• Spintronics meets nonadiabatic molecular dynamics: Geometric spin torque and damping on noncollinear classical magnetism due to electronic open quantum system
• Anomalous spin precession under a geometrical torque
• Dynamics of localized spins coupled to the conduction electrons with charge/spin currents
• Exploring dynamical magnetism with time-dependent density-functional theory: from spin fluctuations to Gilbert damping
• Relaxation of a classical spin coupled to a strongly correlated electron system
• Inertia effects in the real-time dynamics of a quantum spin coupled to a Fermi sea
• Topological spin torque emerging in classical-spin systems with different time scales
• Accessing long timescales in the relaxation dynamics of spins coupled to a conduction-electron system using absorbing boundary conditions
• Long-time relaxation dynamics of a spin coupled to a Chern insulator
• Magnetic properties of a capped kagome molecule with 60 quantum spins
• Non-Hamiltonian dynamics of indirectly coupled classical impurity spins
• Controlling the real-time dynamics of a spin coupled to the helical edge states of the Kane-Mele model

Cited by in corpus (4)

• Spin Berry curvature of the Haldane model
• Exchangeless braiding of Majorana zero modes in weakly coupled Kitaev chains
• Microscopic theory of spin friction and dissipative spin dynamics
• Geometrical torque on magnetic moments coupled to a correlated antiferromagnet