Entanglement Entropy for 2D Gauge Theories with Matters

TL;DR

This paper analyzes entanglement entropy in 1+1D SU(N) gauge theories with matter, decomposing it into classical, color, and genuine quantum parts, and explores its behavior using lattice methods and hopping parameter expansion.

Contribution

It provides a detailed decomposition of entanglement entropy in gauge theories with matter and analyzes the ground state using transfer matrix and hopping parameter expansion.

Findings

Entanglement entropy includes classical, color, and Bell pair contributions.

All three entropy components appear in the ground state, with Bell pairs emerging at higher order.

The continuum limit of entanglement entropy can be understood from lattice ground states.

Abstract

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. We evaluate the entanglement entropy for the ground state and show that all (1), (2), (3) above appear in the HPE, though the Bell pair part (3) appears in higher order than (1) and (2) do. With these results, we discuss how the ground state entanglement entropy in the continuum limit can be understood from the lattice ground state obtained in the HPE.