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Ultrafast entanglement dynamics and spreading of quantum correlations in two-dimensional antiferromagnets

Giammarco Fabiani, Johan H. Mentink

Published Dec 23, 2019• 9 citations
OpenAlex

Abstract

We numerically study the real space-time dynamics of magnon pairs in the two-dimensional antiferromagnetic Heisenberg model after short perturbations of the exchange interaction. Analogous to the dynamics following quantum quenches in one dimension, we find ultrafast light-cone like spreading of quantum spin correlations. Interestingly, the spreading speed is larger than can be expected from the highest magnon or spinon group velocities. Opposed to results in one dimension, the evolution of entanglement is not directly linked to the spreading and dictated by the coherent dynamics of nearest neighbour correlations. We show that this enables coherent control of both phase and amplitude of entanglement oscillations. All results are obtained with the recently proposed neural quantum states.

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We numerically study the real space-time dynamics of magnon pairs in the two-dimensional antiferromagnetic Heisenberg model after short perturbations of the exchange interaction. Analogous to the dynamics following quantum quenches in one dimension, we find ultrafast light-cone like spreading of quantum spin correlations. Interestingly, the spreading speed is larger than can be expected from the highest magnon or spinon group velocities. Opposed to results in one dimension, the evolution of entanglement is not directly linked to the spreading and dictated by the coherent dynamics of nearest neighbour correlations. We show that this enables coherent control of both phase and amplitude of entanglement oscillations. All results are obtained with the recently proposed neural quantum states.
We investigate entanglement dynamics in the antiferromagnetic Heisenberg model in two dimensions following a spatially anisotropic quench of the exchange interactions. Opposed to established results in one dimension, the magnon quasiparticles show an initial growth of entanglement dynamics that does not depend on the system size and is governed by the oscillation period of the exchange interaction. This is much faster than the highest quasiparticle velocity, which we explain by the dominance of the intrinsic entanglement of short wavelength non-propagating magnon-pairs. Furthermore, by adopting the neural quantum states, we provide numerical evidence that this behavior survives even in the presence of strong magnon-magnon interactions, suggesting new avenues for manipulating entanglement dynamics in quantum materials.
We investigate entanglement dynamics in the antiferromagnetic Heisenberg model in two dimensions following a spatially anisotropic quench of the exchange interactions. Opposed to established results in one dimension, the magnon quasiparticles show an initial growth of entanglement dynamics that does not depend on the system size and is governed by the oscillation period of the exchange interaction. We ascribe this to the dominance of the intrinsic entanglement of short wavelength nonpropagating magnon pairs, which also leads to a competition between area-law and volume-law contribution in the entanglement dynamics. Furthermore, by adopting the neural-network quantum states, we provide numerical evidence that this behavior survives even in the presence of strong magnon-magnon interactions, suggesting intriguing avenues for manipulating entanglement dynamics in quantum materials.
We investigate the propagation of magnons after ultrashort perturbations of the exchange interaction in the prototype two-dimensional Heisenberg antiferromagnet. Using the recently proposed neural quantum states, we predict highly anisotropic spreading in space constrained by the symmetry of the perturbation. Interestingly, the propagation speed at the shortest length scale and timescale is up to 40% higher than the highest magnon velocity. We argue that the enhancement stems from extraordinary strong magnon-magnon interactions, suggesting new avenues for manipulating information transfer on ultrashort length scales and timescales.
We investigate the dynamical spreading of spatial correlations after a quantum quench starting from a magnetically disordered state in the transverse-field Ising model at one (1D) and two spatial dimensions (2D). We analyze specifically the longitudinal and transverse spin-spin correlation functions at equal time with use of several methods. From the comparison of the results in 1D obtained by the linear spin-wave approximation (LSWA) and those obtained by the rigorous analytical approach, we show that the LSWA can asymptotically reproduce the exact group velocity in the limit of strong transverse fields while it fails to capture the detailed time dependence of the correlation functions. By applying the LSWA to the 2D case, in which the rigorous analytical approach is unavailable, we estimate the propagation velocity to be $Ja/(2\ensuremath{\hbar})$ at the strong-field limit, where JJJ is the Ising interaction and aaa is the lattice spacing. We also utilize the tensor-network method based on the projected-entangled pair states for 2D and quantitatively compute the time evolution of the correlation functions for a relatively short time. Our findings provide useful benchmarks for quantum simulation experiments of correlation spreading and theoretical refinement of the Lieb-Robinson bound in the future.
The excitations of the Heisenberg antiferromagnetic spin chain in zero field are known as spinons. As pairwise-created fractionalized excitations, spinons are important in the understanding of inelastic neutron scattering experiments in (quasi-)one-dimensional materials. In the present paper, we consider the real space-time dynamics of spinons originating from a local spin flip on the antiferromagnetic ground state of the (an)isotropic Heisenberg spin-1/2 model and the Babujan-Takhtajan spin-1 model. By utilizing algebraic Bethe ansatz methods at finite system size to compute the expectation value of the local magnetization and spin-spin correlations, spinons are visualized as propagating domain walls in the antiferromagnetic spin ordering with anisotropy dependent behavior. The spin-spin correlation after the spin flip displays a light cone, satisfying the Lieb-Robinson bound for the propagation of correlations at the spinon velocity.
We study the spreading of correlations in space and time after a quantum quench in the Bose-Hubbard model. We derive equations of motion for the single-particle Green's function within the contour-time formalism, allowing us to study dynamics in the strong-coupling regime. We discuss the numerical solutions of these equations and calculate the single-particle density matrix for quenches in the Mott phase. We demonstrate light-cone-like spreading of correlations in the Mott phase in one, two, and three dimensions and calculate the propagation velocities in each dimension.