Webinar link: http://bbb2.itp.ac.ru/b/qme-erf-krk
Gaussian Rosenzweig-Porter (GRP) random matrix ensemble is the only one in which the robust multifractal phase have a status of a mathematical theorem. In this paper we suggest an extension of the GRP model, the LN-RP model, by adopting a logarithmically-normal (LN) distribution of off-diagonal matrix elements. We show that large matrix elements from the tail of this distribution give rise to a peculiar weakly-ergodic phase that replaces both the multifractal and the fully-ergodic phases present in GRP ensemble. A new phase is characterized by the broken basis-rotation symmetry which the fully-ergodic phase respects. Thus in addition to the localization and ergodic transitions in LN-RP model there exists also the FWT transition between the two ergodic phases. We formulate the criteria of the localization, ergodic and FWT transitions and obtain the phase diagram of the model. We also suggest a new criteria of stability of the non-ergodic phases and prove that the Anderson transition in LN-RP model is discontinuous, in contrast to its GRP counterpart.

Webinar link: http://bbb2.itp.ac.ru/b/qme-erf-krk
We study SYK_4 model with weak SYK_2 random terms of typical magnitude Γ beyond the simplest perturbative limit considered previously. In the intermediate range J/N << Γ << J/N^{1/2} of the perturbation strength Γ, fluctuations of the Schwarzian soft mode are suppressed and conformal mean-field solution for the Majorana Green function G(τ) is valid much beyond usual timescale t_∗ ∼ N/J characteristic for pure SYK_4 model. However, high momenta of the probability distribution of the Green function are shown to grow as ln([G(τ)]^p) ∝ p^2 at p >> 1, indicating log-normal shape of the distribution P[G(τ)] . Short-time decay of the out-of-time-order correlation function is characterized by the universal exponent 2πT/\hbar, while the pre-factor is much smaller than in pure SYK_4 model, and shows unusual temperature dependence.

Topological insulators combine an insulating bulk with gapless states at their surfaces. This talk introduces "higher-order topological insulators", which are crystalline insulators with a gapped bulk and gapped crystalline boundaries, but topologically protected gapless states at corners or at edges of the crystal. I'll show that such "higher-order boundary states" are a generic boundary manifestation of the nontrivial bulk topology, if the bulk topology relies on a crystalline symmetry for its protection.