QM3 Quantum Matter meets Maths   RSS

Planned sessions

Paul A. McClarty 01/04/2020, 11:00 — 12:00 — Instituto Superior Técnico
Paul A. McClarty, Max Planck Institute for the Physics of Complex Systems

Topological Magnons

I give an overview of the insights we and other people have had into the band structure of magnons and discuss in some detail three main topics from our work: (i) the robustness of topological edge states in the presence of magnon interactions (ii) visualization of spin-momentum locking in magnon systems (iii) the non-Hermitian topology of spontaneous magnon decay.

Bruno Mera 08/04/2020, 11:00 — 12:00 — Instituto Superior Técnico
, Security and Quantum Information Group of Instituto de Telecomunicações

Localization anisotropy and complex geometry in two-dimensional insulators

The localization tensor is a measure of distinguishability between insulators and metals. This tensor is related to the quantum metric tensor associated with the occupied bands in momentum space. In two dimensions and in the thermodynamic limit, it defines a flat Riemannian metric over the twist-angle space, topologically a torus, which endows this space with a complex structure, described by a complex parameter τ . It is shown that the latter is a physical observable related to the anisotropy of the system. The quantity τ and the Riemannian volume of the twist-angle space provide an invariant way to parametrize the flat quantum metric obtained in the thermodynamic limit. Moreover, if by changing the couplings of the theory, the system undergoes quantum phase transitions in which the gap closes, the complex structure τ is still well defined, although the metric diverges (metallic state), and it is fixed by the form of the Hamiltonian near the gap closing points. The Riemannian volume is responsible for the divergence of the metric at the phase transition.

[1] Bruno Mera. Localization anisotropy and complex geometry in two-dimensional insulators. Phys. Rev. B, 101:115128, Mar 2020.

Tomaž Prosen 22/04/2020, 11:00 — 12:00 — Instituto Superior Técnico
, University of Ljubljana

Andrea de Luca 06/05/2020, 11:00 — 12:00 — Instituto Superior Técnico
, University of Cergy-Pontoise, CNRS

Achilleas Lazarides 27/05/2020, 11:00 — 12:00 — Instituto Superior Técnico
, Loughborough University

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The goal of $QM^3$ is to discuss recent topics in quantum matter from a mathematical perspective. Build bridges between the physics and mathematics communities.

Organizers: Bruno Mera, João Pimentel Nunes, José Mourão, Pedro Ribeiro, Roger Picken, Vitor Rocha Vieira