BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Steve Simon (University of Oxford) DTSTART:20210125T170000Z DTEND:20210125T180000Z DTSTAMP:20260423T024726Z UID:QM3/31 DESCRIPTION:Title: Lat tice Geometry Dependence and Independence: Important Applications of a Si mple Law\nby Steve Simon (University of Oxford) as part of Quantum Mat ter meets Maths (IST\, Lisbon)\n\n\nAbstract\nThe ability to create and ma nipulate optical lattices for cold atoms\, with a view towards studying to pological matter\, has brought renewed focus to the physics of Bloch waves and the role of the lattice in governing their properties. We consider ge neric tight binding models where particle motion is described in terms of hopping amplitudes between orbitals. The physical attributes of the orbita ls\, including their locations in space\, are independent pieces of inform ation. We identify a notion of geometry-independence: any physical quantit y that depends only on the tight-binding parameters (and not on the explic it information about the orbital geometry) is said to be "geometry-indepen dent." Identification of geometry-dependent vs. independent quantities can be used as a novel principle for constraining a variety of results in bot h non-interacting and interacting systems. We show\, e.g.\, how Hall measu rements based on accelerated lattices or tilted potentials\, and those bas ed on applying a chemical potential imbalance between reservoirs\, give di fferent results due to the fact that one is geometry-dependent\, while the other is geometry-independent. Similar considerations apply for thermal H all responses in electronic\, cold atomic\, and spin systems.\n\n\nRef:\n\ nSteven H. Simon and Mark S. Rudner\, Phys. Rev. B 102\, 165148\, 2020.\n LOCATION:https://researchseminars.org/talk/QM3/31/ END:VEVENT END:VCALENDAR