Signatures of Many-Body Localization in the Dynamics of Two-Level Systems in Glasses

TL;DR

This paper explores how many-body localization phenomena manifest in the quantum dynamics of two-level systems in glasses at very low temperatures, revealing non-ergodic behavior and long-tailed disorder effects.

Contribution

It analytically derives TLS interactions and dissipation effects from phonon coupling, demonstrating signatures of many-body localization in their dynamics.

Findings

Concurrence decays as a power law over time.

Long-tailed disorder influences non-ergodic dynamics.

Dissipation does not significantly alter localization signatures.

Abstract

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.