Department of Theoretical Physics, University of Trieste, Italy

Computer experiments whose results prompt for novel analytical formulations.

- Light simulations, mostly with model Hamiltonians, run on table-top computers

Investigation of condensed-matter observables at the fundamental level, in simple paradigmatic materials

The research concerns several observables of materials (crystalline and non-crystalline) having a geomrtrical nature. The archetype in this class of observables is the macroscopic electric polarization of solids, for which first-principle understanding dates since 1992 onwards. Such observables have very different experimental meanings, yet they show a common formal structure from a theoretical viewpoint. A list of known geometrical observables includes electrical polarization, orbital magnetization, anomalous Hall conductivity, Drude weight, some conductivity sum rules, and the so called “axion” term in magnetoelectric response.

The research is conducted via analytical techniques, as well as via simulations on selected test cases. Quite often, the computational experiment provides an unexpected result and originates the analytical development.

We have also further developed the modern theory of the insulating state, pioneered by us in 1999, whose basic tenet is that the quantum geometry of the electronic ground state sharply differentiates insulators from metals. The theory deals on a common ground with all kinds of insulators: band insulators, Mott insulators, Anderson insulators, quantum Hall insulators, Chern and topological insulators.

Theoretical and computational research work on physical properties of real materials whose root is in the geometry and/or topology of the electronic ground state.

- ONR 2017, Geometrical Properties, 2017-2020

- STI IMX THEOS, EPFL, Lausanne, Switzerland
- CFM, University of the Basque Country, San Sebastian, Spain

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