Entanglement barrier and its symmetry resolution: theory and experiment

• DOI: 10.48550/arxiv.2209.04393
• Publication Date: 2022-01-01
• Authors: Rath, Aniket; Vitale, Vittorio; Murciano, Sara; Votto, Matteo; Dubail, Jérôme; Kueng, Richard; Branciard, Cyril; Calabrese, Pasquale; Vermersch, Benoît
• Keywords: Quantum Physics; Statistical Mechanics (cond-mat.stat-mech); 0103 physical sciences; FOS: Physical sciences; Quantum Physics (quant-ph); 01 natural sciences; 7. Clean energy; Condensed Matter - Statistical Mechanics

13 + 24 pages with 3 + 7 figures<br/>The operator entanglement (OE) is a key quantifier of the complexity of a reduced density matrix. In out-of-equilibrium situations, e.g. after a quantum quench of a product state, it is expected to exhibit an entanglement barrier. The OE of a reduced density matrix initially grows linearly as entanglement builds up between the local degrees of freedom, it then reaches a maximum, and ultimately decays to a small finite value as the reduced density matrix converges to a simple stationary state through standard thermalization mechanisms. Here, by performing a new data analysis of the published experimental results of [Brydges et al., Science 364, 260 (2019)], we obtain the first experimental measurement of the OE of a subsystem reduced density matrix in a quantum many-body system. We employ the randomized measurements toolbox and we introduce and develop a new efficient method to post-process experimental data in order to extract higher-order density matrix functionals and access the OE. The OE thus obtained displays the expected barrier as long as the experimental system is large enough. For smaller systems, we observe a barrier with a double-peak structure, whose origin can be interpreted in terms of pairs of quasi-particles being reflected at the boundary of the qubit chain. As $U(1)$ symmetry plays a key role in our analysis, we introduce the notion of symmetry resolved operator entanglement (SROE), in addition to the total OE. To gain further insights into the SROE, we provide a thorough theoretical analysis of this new quantity in chains of non-interacting fermions, which, in spite of their simplicity, capture most of the main features of OE and SROE. In particular, we uncover three main physical effects: the presence of a barrier in any charge sector, a time delay for the onset of the growth of SROE, and an effective equipartition between charge sectors.<br/>