QM3 Quantum Matter meets Maths   RSS

Planned sessions

Xiao-Gang Wen 26/04/2021, 17:00 — 18:00 Europe/Lisbon — Instituto Superior Técnico
, Massachusetts Institute of Technology

A holographic view of symmetry -- symmetry as shadow of topological order

Recently, the notion of symmetry has been extended from 0-symmetry described by group to higher symmetry described by higher group. In this talk, we show that the notion of symmetry can be generalized even further to "algebraic higher symmetry". Then we will describe an even more general point of view of symmetry, which puts the (generalized) symmetry charges and topological excitation at equal footing: symmetry can be viewed as gravitational anomaly, or symmetry can be viewed as shadow topological order in one higher dimension. This picture allows us to see many duality relations between seeming unrelated symmetries.

Karyn Le Hur 03/05/2021, 17:00 — 18:00 Europe/Lisbon — Instituto Superior Técnico
, Centre de Physique Theorique, École Polytechnique, CNRS

Geometry, Light Response and Quantum Transport in Topological States of Matter

Topological states of matter are characterized by a gap in the bulk of the system referring to an insulator or a superconductor and topological edge modes as well which find various applications in transport and spintronics. The bulk-edge correspondence is associated to a topological number. The table of topological states include the quantum Hall effect and the quantum anomalous Hall effect, topological insulators and topological superconductors in various dimensions and lattice geometries. Here, we discuss classes of states which can be understood from mapping onto a spin-1/2 particle in the reciprocal space of wave-vectors. We develop a geometrical approach on the associated Poincare-Bloch sphere, developing smooth fields, which shows that the topology can be encoded from the poles only. We show applications for the light-matter coupling when coupling to circular polarizations and develop a relation with quantum transport and the quantum Hall conductivity. The formalism allows to include interaction effects. We show our recent developments on a stochastic approach to englobe these interaction effects and discuss applications for the Mott transition of the Haldane and Kane-Mele models. Then, we develop a model of coupled spheres and show the possibility of fractional topological numbers as a result of interactions between spheres and entanglement allowing a superposition of two geometries, one encircling a topological charge and one revealing a Bell or EPR pair. Then, we show applications of the fractional topological numbers C=1/2 in bilayer honeycomb models describing topological semi-metals characterized by a quantized Berry phase at one Dirac point.

- Joel Hutchinson and Karyn Le Hur, arXiv:2002.11823 (under review)
- Philipp Klein, Adolfo Grushin, Karyn Le Hur, Phys. Rev. B 103, 035114 (2021)

Paul Melotti 10/05/2021, 17:00 — 18:00 Europe/Lisbon — Instituto Superior Técnico
, Fribourg University

The free-fermion eight-vertex model via dimers

The eight-vertex model is an useful description that generalizes several spin systems, as well as the more common six-vertex model, and others. In a special "free-fermion" regime, it is known since the work of Fan, Lin, Wu in the late 60s that the model can be mapped to non-bipartite dimers. However, no general theory is known for dimers in the non-bipartite case, contrary to the extensive rigorous description of Gibbs measures by Kenyon, Okounkov, Sheffield for bipartite dimers. In this talk I will show how to transform these non-bipartite dimers into bipartite ones, on generic planar graphs. I will mention a few consequences: computation of long-range correlations, criticality and critical exponents, and their "exact" application to Z-invariant regimes on isoradial graphs.

David Tong 17/05/2021, 17:00 — 18:00 Europe/Lisbon — Instituto Superior Técnico
, University of Cambridge

Igor Lesanovsky 24/05/2021, 17:00 — 18:00 Europe/Lisbon — Instituto Superior Técnico
, Universität Tübingen

Michael Fleischhauer 07/06/2021, 17:00 — 18:00 Europe/Lisbon — Instituto Superior Técnico
, University of Kaiserslautern

Rubem Mondaini 21/06/2021, 17:00 — 18:00 Europe/Lisbon — Instituto Superior Técnico
, Beijing Computational Science Research Center

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The goal of QM3 is to discuss recent topics in quantum matter from a mathematical perspective while building bridges between the physics and mathematics communities.

Organizers: Bruno Mera, João Pimentel Nunes, José Mourão, Pedro Ribeiro, Roger Picken, Vitor Rocha Vieira
Zoom password: send an email to one of the organizers to ask for the password.