Talks

Motivated by SYK model, there have been a lot of activities to understand quantum dynamics in interacting systems via many-body quantum chaos and describe a variety of quantum phases, e.g., heavy Fermi liquids, marginal and non-Fermi liquid, correlated superconductors, etc., through generalizations of the SYK model. I will first discuss some quantum spin glass models related to the SYK model and the characterization of their dynamics through chaos. I will then discuss some lattice and higher-dimensional generalizations of the SYK model to understand higher-dimensional non-Fermi liquids, such as strange metals and other correlated phases. 

Entanglement in quantum many-body systems is typically fragile to interactions with the environment. Generic unital quantum channels, for example, have the maximally mixed state with no entanglement as their unique steady state. However, we find that for a unital quantum channel that is `strongly symmetric', i.e. it preserves a global on-site symmetry, the maximally mixed steady state in certain symmetry sectors can be highly entangled. For a given symmetry, we analyze the entanglement and correlations of the maximally mixed state in the invariant sector (MMIS), and show that the entanglement of formation and distillation are exactly computable and equal for any bipartition. For all Abelian symmetries, the MMIS is separable, and for all non-Abelian symmetries, the MMIS is entangled. Remarkably, for non-Abelian continuous symmetries described by compact semisimple Lie groups (e.g. SU(2)), the bipartite entanglement of formation for the MMIS scales logarithmically ∼logN with the number of qudits N.