  We investigate the quantum dynamics of Two-Level Systems (TLS) in glasses at
low temperatures (1 K and below). We study an ensemble of TLSs coupled to
phonons. By integrating out the phonons within the framework of the
Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, we derive
analytically the explicit form of the interactions among TLSs, and of the
dissipation terms. We find that the unitary dynamics of the system shows clear
signatures of Many-Body Localization physics. We study numerically the time
behavior of the concurrence, which measures pairwise entanglement also in
non-isolated systems, and show that it presents a power-law decay both in the
absence and in the presence of dissipation, if the latter is not too large.
These features can be ascribed to the strong, long-tailed disorder
characterizing the distributions of the model parameters. Our findings show
that assuming ergodicity when discussing TLS physics might not be justified for
all kinds of experiments on low-temperature glasses.
