Solving spin systems, the Babylonian way
2023-11-02 15:30 - 16:30 (America/New_York) | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Probability Seminar
Speaker: Nicola Kistler (Johann Wolfgang Goethe-Universität Frankfurt am Main)
Title: Solving spin systems, the Babylonian way
Abstract: The replica method, together with Parisi’s symmetry breaking mechanism, is an extremely powerful tool to compute the limiting free energy of virtually any mean field disordered system. Unfortunately, the tool is dramatically flawed from a mathematical point of view. I will discuss a truly elementary procedure which allows to rigorously implement two (out of three) steps of the replica method, and conclude with some remarks on the relation between this new point of view and old work by Mezard and Virasoro on the microstructure of ultrametricity, the latter being the fundamental yet unjustified Ansatz in the celebrated Parisi solution. We are still far from a clear understanding of the issues, but quite astonishingly, evidence is mounting that Parisi’s ultrametricity assumption, the onset of scales and the universal hierarchical self-organisation of random systems in the infinite volume limit, is intimately linked to hidden geometrical properties of large random matrices which satisfy rules reminiscent of the popular SUDOKU game.

Landscape of quantum phases in quantum materials
2023-11-02 16:30 - 18:00
Joint Quantum Matter in Mathematics and Physics and Topological Quantum Matter Seminar
Speaker: Liujun Zou (Perimeter Institute)
Title: Landscape of quantum phases in quantum materials

Abstract: A central goal of condensed matter physics is to understand which quantum phases of matter can emerge in a quantum material. For this purpose, one should be able to not only describe the quantum phases using some effective field theories, but also capture the important microscopic information of the material via mathematical formulation. In this talk, I will present a framework to classify quantum phases in quantum materials, where the microscopic information of a material is encoded in its quantum anomaly. I will talk about the application of this framework to classify various exotic quantum phases of matter in different lattice systems. Using our framework, we have obtained many results unexpected from the previous literature.
