QM3 Quantum Matter meets Maths   RSS

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Steve Simon 25/01/2021, 17:00 — 18:00 Europe/Lisbon — Instituto Superior Técnico
, University of Oxford

Lattice Geometry Dependence and Independence: Important Applications of a Simple Law

The ability to create and manipulate optical lattices for cold atoms, with a view towards studying topological matter, has brought renewed focus to the physics of Bloch waves and the role of the lattice in governing their properties. We consider generic tight binding models where particle motion is described in terms of hopping amplitudes between orbitals. The physical attributes of the orbitals, including their locations in space, are independent pieces of information. We identify a notion of geometry-independence: any physical quantity that depends only on the tight-binding parameters (and not on the explicit information about the orbital geometry) is said to be "geometry-independent." Identification of geometry-dependent vs. independent quantities can be used as a novel principle for constraining a variety of results in both non-interacting and interacting systems. We show, e.g., how Hall measurements based on accelerated lattices or tilted potentials, and those based on applying a chemical potential imbalance between reservoirs, give different results due to the fact that one is geometry-dependent, while the other is geometry-independent. Similar considerations apply for thermal Hall responses in electronic, cold atomic, and spin systems.


Steven H. Simon and Mark S. Rudner, Phys. Rev. B 102, 165148, 2020.

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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.