Abstract
We study real-time meson-meson scattering processes in $(1+1)$-dimensional QED by means of Tensor Networks. We prepare initial meson wave packets with given momentum and position introducing an approximation based on the free fermions model. Then, we compute the dynamics of two initially separated colliding mesons, observing a rich phenomenology as the interaction strength and the initial states are varied in the weak and intermediate coupling regimes. Finally, we consider elastic collisions and measure some scattering amplitudes as well as the entanglement generated by the process. Remarkably, we identify two different regimes for the asymptotic entanglement between the outgoing mesons: it is perturbatively small below a threshold coupling, past which its growth as a function of the coupling abruptly accelerates.
Highlights
The investigation of fundamental interactions is one of the more challenging research fields in physics from a theoretical, experimental and computational point of view
We have shown that tensor network (TN) methods are viable numerical techniques for the simulation of the dynamics of (1 þ 1)dimensional lattice quantum electrodynamics (QED2)
We identified a matrix product states (MPS) representation of the stable particle states of the theory, namely meson bound states
Summary
The investigation of fundamental interactions is one of the more challenging research fields in physics from a theoretical, experimental and computational point of view. The most common approach for the numerical simulation of quantum gauge theories relies on lattice gauge theory (LGT) models [3,4], in which quantum fields are defined on a discrete space-time lattice Within this framework, Monte Carlo techniques are the established tool to predict scattering amplitudes [5]. We perform TN simulations by using matrix product states (MPS) to investigate the real-time dynamics of scattering events in a (1 þ 1)-dimensional Abelian lattice gauge theory in the Hamiltonian formulation [49,50].
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