Exceptionally fast dynamics of entanglement in Heisenberg antiferromagnets

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 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.

arXiv:1912.10845Physical review. B./Physical review. BMar 29, 20225 citations

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

Giammarco Fabiani, Johan H. Mentink

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 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.

Dec 23, 20199 citations

Supermagnonic Propagation in Two-Dimensional Antiferromagnets

Giammarco Fabiani, M. D. Bouman, Johan H. Mentink

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 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.

arXiv:2101.10945Physical Review LettersAug 25, 202122 citations

Quench dynamics of entanglement in an open anisotropic spin- 12 Heisenberg chain

Jie Ren, Shiqun Zhu

The quantum entanglement dynamics of a one-dimensional spin- $1/2$ anisotropic $\mathit{XXZ}$ model is studied using the method of the adaptive time-dependent density-matrix renormalization group when two cases of quenches are performed in the system. An anisotropic interaction quench and the maximum number of domain walls of a staggered magnetization quench are considered. The dynamics of the pairwise entanglement between the nearest two qubits in the spin chain is investigated. The entanglement of the two spin qubits can be created and oscillates in both cases of the quench. The anisotropic interaction has a strong influence on the oscillation frequency of the entanglement.The quantum entanglement dynamics of a one-dimensional spin-$1/2$ anisotropic $\mathit{XXZ}$ model is studied using the method of the adaptive time-dependent density-matrix renormalization group when two cases of quenches are performed in the system. An anisotropic interaction quench and the maximum number of domain walls of a staggered magnetization quench are considered. The dynamics of the pairwise entanglement between the nearest two qubits in the spin chain is investigated. The entanglement of the two spin qubits can be created and oscillates in both cases of the quench. The anisotropic interaction has a strong influence on the oscillation frequency of the entanglement.

arXiv:1006.1417Physical Review AJan 21, 201010 citations

Quantum quenches in the anisotropic spin-\frac{1}{2} Heisenberg chain: different approaches to many-body dynamics far from equilibrium

Peter Barmettler, Matthias Punk, Vladimir Gritsev +2 more

Recent experimental achievements in controlling ultracold gases in optical lattices open a new perspective on quantum many-body physics. In these experimental setups, it is possible to study coherent time evolution of isolated quantum systems. These dynamics reveal new physics beyond the low-energy properties that are usually relevant in solid-state many-body systems. In this paper, we study the time evolution of antiferromagnetic order in the Heisenberg chain after a sudden change of the anisotropy parameter, using various numerical and analytical methods. As a generic result, we find that the order parameter, which can show oscillatory or non-oscillatory dynamics, decays exponentially except for the effectively non-interacting case of the XX limit. For weakly ordered initial states, we also find evidence for an algebraic correction to the exponential law. The study is based on numerical simulations using a numerical matrix product method for infinite system sizes (iMPS), for which we provide a detailed description and an error analysis. Additionally, we investigate in detail the exactly solvable XX limit. These results are compared to approximative analytical approaches including an effective description by the XZ model as well as by mean-field, Luttinger-liquid and sine-Gordon theories. The comparison reveals which aspects of non-equilibrium dynamics can, as in equilibrium, be described by low-energy theories and which are the novel phenomena specific to quantum quench dynamics. The relevance of the energetically high part of the spectrum is illustrated by means of a full numerical diagonalization of the Hamiltonian.Recent experimental achievements in controlling ultracold gases in optical lattices open a new perspective on quantum many-body physics. In these experimental setups, it is possible to study coherent time evolution of isolated quantum systems. These dynamics reveal new physics beyond the low-energy properties that are usually relevant in solid-state many-body systems. In this paper, we study the time evolution of antiferromagnetic order in the Heisenberg chain after a sudden change of the anisotropy parameter, using various numerical and analytical methods. As a generic result, we find that the order parameter, which can show oscillatory or non-oscillatory dynamics, decays exponentially except for the effectively non-interacting case of the XX limit. For weakly ordered initial states, we also find evidence for an algebraic correction to the exponential law. The study is based on numerical simulations using a numerical matrix product method for infinite system sizes (iMPS), for which we provide a detailed description and an error analysis. Additionally, we investigate in detail the exactly solvable XX limit. These results are compared to approximative analytical approaches including an effective description by the XZ model as well as by mean-field, Luttinger-liquid and sine-Gordon theories. The comparison reveals which aspects of non-equilibrium dynamics can, as in equilibrium, be described by low-energy theories and which are the novel phenomena specific to quantum quench dynamics. The relevance of the energetically high part of the spectrum is illustrated by means of a full numerical diagonalization of the Hamiltonian.

arXiv:0911.1927New Journal of PhysicsMay 28, 2010128 citations

Quantum dynamics and entanglement of spins on a square lattice

Niels Bech Christensen, Henrik Moodysson Rønnow, MCMORROW Desmond Francis +6 more

Bulk magnetism in solids is fundamentally quantum mechanical in nature. Yet in many situations, including our everyday encounters with magnetic materials, quantum effects are masked, and it often suffices to think of magnetism in terms of the interaction between classical dipole moments. Whereas this intuition generally holds for ferromagnets, even as the size of the magnetic moment is reduced to that of a single electron spin (the quantum limit), it breaks down spectacularly for antiferromagnets, particularly in low dimensions. Considerable theoretical and experimental progress has been made in understanding quantum effects in one-dimensional quantum antiferromagnets, but a complete experimental description of even simple two-dimensional antiferromagnets is lacking. Here we describe a comprehensive set of neutron scattering measurements that reveal a non-spin-wave continuum and strong quantum effects, suggesting entanglement of spins at short distances in the simplest of all two-dimensional quantum antiferromagnets, the square lattice Heisenberg system.Bulk magnetism in solids is fundamentally quantum mechanical in nature. Yet in many situations, including our everyday encounters with magnetic materials, quantum effects are masked, and it often suffices to think of magnetism in terms of the interaction between classical dipole moments. Whereas this intuition generally holds for ferromagnets, even as the size of the magnetic moment is reduced to that of a single electron spin (the quantum limit), it breaks down spectacularly for antiferromagnets, particularly in low dimensions. Considerable theoretical and experimental progress has been made in understanding quantum effects in one-dimensional quantum antiferromagnets, but a complete experimental description of even simple two-dimensional antiferromagnets is lacking. Here we describe a comprehensive set of neutron scattering measurements that reveal a non-spin-wave continuum and strong quantum effects, suggesting entanglement of spins at short distances in the simplest of all two-dimensional quantum antiferromagnets, the square lattice Heisenberg system.

arXiv:0709.3632Proceedings of the National Academy of SciencesSep 20, 2007123 citations

The quantum entanglement dynamics of a one-dimensional spin-

1/2

anisotropic

\mathit{XXZ}

model is studied using the method of the adaptive time-dependent density-matrix renormalization group when two cases of quenches are performed in the system. An anisotropic interaction quench and the maximum number of domain walls of a staggered magnetization quench are considered. The dynamics of the pairwise entanglement between the nearest two qubits in the spin chain is investigated. The entanglement of the two spin qubits can be created and oscillates in both cases of the quench. The anisotropic interaction has a strong influence on the oscillation frequency of the entanglement.