Employing the Holstein–Primakoff transformation, we obtain an approximate description of both the ground state entanglement and the entanglement dynamics in a spin system in terms of spin waves. As an example, we apply the method to a two-dimensional spin system.
Spin-wave theory is a key ingredient in our comprehension of quantum spin systems, and is used successfully for understanding a wide range of magnetic phenomena, including magnon condensation and stability of patterns in dipolar systems. Nevertheless, several decades of research failed to establish the validity of spin-wave theory rigorously, even for the simplest models of quantum spins. A rigorous justification of the method for the three-dimensional quantum Heisenberg ferromagnet at low temperatures is presented here. We derive sharp bounds on its free energy by combining a bosonic formulation of the model introduced by Holstein and Primakoff with probabilistic estimates and operator inequalities.
Applying the functional Schrodinger picture to the Holstein-Primakoff boson theory, we obtain a dispersion energy relation for an antiferromagnetic spin polaron or magnon in two-dimensional systems of strongly correlated electrons. We show that our magnon ground-state wave function is equivalent to that of a retraceable path approximation by Reiter in the long-wavelength limit. Further, we demonstrate that the derived dispersion relation of a quasiparticle leads to the self-consistent Born approximation of the Green's function approach only in the large Heisenberg coupling J limit, showing that this new approach is general enough to contain more physical information than the Green's function approach in dealing with the antiferroinagnetic spin polaron of interest.
There have been numerous studies of entanglement in spin systems. These have usually focused on examining the entanglement between individual spins or determining whether the state of the system is completely separable. Here, we present conditions that allow us to determine whether blocks of spins are entangled. We show that sometimes these conditions can detect entanglement better than conditions involving individual spins. We apply these conditions to study entanglement in spin-wave states, both when there are only a few magnons present and also at finite temperature.