Entanglement Entropy of ($2+1$)-Dimensional SU(2) Lattice Gauge Theory

Lukas Ebner, Andreas Schäfer, Clemens Seidl, Berndt Müller, Xiaojun Yao
High Energy Physics - Lattice, High Energy Physics - Lattice (hep-lat), Statistical Mechanics (cond-mat.stat-mech), High Energy Physics - Phenomenology (hep-ph), High Energy Physics - Theory (hep-th), Quantum Physics (quant-ph)
2024-01-26 00:00:00
We study the entanglement entropy of Hamiltonian SU(2) lattice gauge theory in $2+1$ dimensions on linear plaquette chains and show that the entanglement entropies of both ground and excited states follow Page curves. The transition of the subsystem size dependence of the entanglement entropy from the area law for the ground state to the volume law for highly excited states is found to be described by a universal crossover function. Quantum many-body scars in the middle of the spectrum, which are present in the electric flux truncated Hilbert space, where the gauge theory can be mapped onto an Ising model, disappear when higher electric field representations are included in the Hilbert space basis. This suggests the continuum $(2+1)$-dimensional SU(2) gauge theory is a ``fast'' scrambler.
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