Eigenstates of the lattice RS model

Qi Chen, Kaixun Tu, Qing Wang
High Energy Physics - Lattice, High Energy Physics - Lattice (hep-lat)
2023-10-27 16:00:00
For quantum field theories involving interaction between fermion and boson fields, the bare fermionic (bosonic) annihilation operators cannot annihilate the vacuum state, and the bare fermionic (bosonic) creation operators cannot create fermionic (bosonic) one-particle states. The actual bosonic particles contain fermion field components, and fermionic particles contain boson field components, while the vacuum state exhibits entanglement between the fermion and boson fields. We utilize the lattice Rothe-Stamatescu (RS) model to nonperturbatively and directly demonstrate this field mixing. We provide the Hamiltonian of the lattice RS model, calculate its correlation functions, and observe that the correlation functions in the continuum limit recover those of the original continuous RS model. Furthermore, we derive the equations of motion for the lattice RS model and compare them to those of the original RS model. Instead of employing the traditional Fock representation commonly used in discussions of field mixing, we define a special representation to present the vacuum state and one-particle states of the lattice RS model. These eigenstates not only reveal the entanglement between the boson and fermion fields but also allow us to directly observe the spatial entanglement structure.
PDF: Eigenstates of the lattice RS model.pdf
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