Entanglement Entropy for 2D Gauge Theories with Matters

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We investigate the entanglement entropy in 1+1-dimensional $SU(N)$ gauge theories with various matter fields using the lattice regularization.

• Here we use extended Hilbert space definition for entanglement entropy, which contains three contributions; (1) classical Shannon entropy associated with superselection sector distribution, where sectors are labelled by irreducible representations of boundary penetrating fluxes, (2) logarithm of the dimensions of their representations, which is associated with "color entanglement", and (3) EPR Bell pairs, which give "genuine" entanglement.
• We explicitly show that entanglement entropies (1) and (2) above indeed appear for various multiple "meson" states in gauge theories with matter fields.
• Furthermore, we employ transfer matrix formalism for gauge theory with fundamental matter field and analyze its ground state using hopping parameter expansion (HPE), where the hopping parameter $K$ is roughly the inverse square of the mass for the matter.