# Recent seminars

## 21/09/2020, Monday, 17:00–18:00 Europe/Lisbon — Online

Gil Refael, Institute for Quantum Information and Matter.
Floquet higher-order topological insulators: principles and path towards realizations.

The co-existence of spatial and non-spatial symmetries together with appropriate commutation/anticommutation relations between them can give rise to static higher-order topological phases, which host gapless boundary modes of co-dimension higher than one. Alternatively, space-time symmetries in a Floquet system can also lead to anomalous Floquet boundary modes of higher co-dimensions, with different commutation/anticommutation relations with respect to non-spatial symmetries. In my talk I will review how these dynamical analogs of the static HOTI's emerge, and also show how a coherently excited phonon mode can be used to support non-trivial Floquet higher-order topological phases. If time allows, I will also review recent work on Floquet engineering and band flattening of twisted-bilayer graphene.

## 14/09/2020, Monday, 17:00–18:00 Europe/Lisbon — Online

Vincenzo Alba, University of Amsterdam.
Hydrodynamic framework for out-of-equilibrium entangled many-body systems.

Entanglement and entropy are key concepts standing at the foundations of quantum and statistical mechanics, respectively. In the last decade the study of quantum quenches revealed that these two concepts are intricately intertwined. For integrable models, novel hydrodynamic approaches based on a quasiparticle picture emerged as a new platform allowing for a quantitative understanding of quantum information dynamics in quantum many-body systems. Remarkably, this gives fresh insights on how thermodynamics emerges in isolated out-of-equilibrium quantum systems.

I will start by reviewing this new unifying framework. I will then discuss several applications to entanglement-related quantities, such as entanglement entropies, mutual information, logarithmic negativity. I will also show how the framework allows to study the interplay between quantum information dynamics and transport of local conserved quantities. Finally, I will derive some simple bounds on the quantum information scrambling in out-of-equilibrium systems.

## 07/09/2020, Monday, 17:00–18:00 Europe/Lisbon — Online

Svetlana Jitomirskaya, University of California, Irvine.
Anderson localization and local eigenvalue statistics.

Poisson local statistics of eigenvalues is widely accepted as a necessary signature of Anderson localization, but so far has been rigorously established only for random systems. We will argue that this paradigm is wrong, and the reality is a lot more complex and interesting, by presenting both rigorous results for the Harper and Maryland models and numerics for other quasiperiodic and similar models with localization. We will also discuss a conjecture on what the distribution is in the general ergodic situation.

## 27/07/2020, Monday, 17:00–18:00 Europe/Lisbon — Online

Raquel Queiroz, Weizmann Institute of Science.
Boundary Obstructed Topological Phases.

Symmetry protected topological (SPT) phases are gapped phases of matter that cannot be deformed to a trivial phase without breaking the symmetry or closing the bulk gap. Here, we introduce a new notion of a topological obstruction that is not captured by bulk energy gap closings in periodic boundary conditions. More specifically, given a symmetric boundary termination we say two bulk Hamiltonians belong to distinct bound­ary obstructed topological phases (BOTPs) if they can be deformed to each other on a system with periodic boundaries, but cannot be deformed to each other in the open system without closing the gap at at least one high symmetry surface. BOTPs are not topological phases of matter in the standard sense since they are adiabat­ically deformable to each other on a torus but, similar to SPTs, they are associated with boundary signatures in open systems such as surface states or fractional corner charges. In contrast to SPTs, these boundary signatures are not anomalous and can be removed by symmetrically adding lower dimensional SPTs on the boundary, but they are stable as long as the spectral gap at high-symmetry edges/surfaces remains open. We show that the double-mirror quadrupole model of [Science, 357(6346), 2018] is a prototypical example of such phases, and present a detailed analysis of several aspects of boundary obstructions in this model. In addition, we intro­duce several three-dimensional models having boundary obstructions, which are characterized either by surface states or fractional corner charges. We also provide a general framework to study boundary obstructions in free-fermion systems in terms of Wannier band representations (WBR), an extension of the recently-developed band representation formalism to Wannier bands. WBRs capture the notion of topological obstructions in the Wannier bands which can then be used to study topological obstructions in the boundary spectrum by means of the correspondence between the Wannier and boundary spectra. This establishes a form of bulk-boundary correspondence for BOTPs by relating the bulk band representation to the boundary topology.

### Video

Queiroz_slides.pdf

## 20/07/2020, Monday, 17:00–18:00 Europe/Lisbon — Online

Christophe Garban, Université Lyon 1.
A new point of view on topological phase transitions.

Topological phase transitions were discovered by Berezinskii-Kosterlitz-Thouless in the 70's. They describe intriguing phase transitions for classical spins systems such as the plane rotator model (or $XY$ model). I will start by reviewing how this phase transition arises in cases such as:

• the $XY$ model (spins on $\mathbb{Z}^2$ with values in the unit circle)
• the integer-valued Gaussian Free Field (or $\mathbb{Z}$-ferromagnet)
• Abelian Yang-Mills on $\mathbb{Z}^4$

I will then connect topological phase transitions to a statistical reconstruction problem concerning the Gaussian Free Field and will show that the feasibility of the reconstruction undergoes a KT transition.

This is a joint work with Avelio Sepúlveda (Lyon) and the talk will be based mostly on the preprint: https://arxiv.org/abs/2002.12284