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Oberseminar Darmstadt
The Heisenberg XXZ chain and the Lorentz mirror model with loop weight 2
Date: 29.01.2026
Time: 16:15–17:45 h
Statistical mechanics models describe how the large scale behaviour of matter changes as parameters such as temperature are varied. Often these models exhibit phase transitions - a drastic change in the behaviour of the system at a critical temperature. The behaviour exactly at the critical temperature is in many models very special, and is expected to be conformally invariant. In particular, two-point correlation functions decay polynomially fast.
Quantum models in d dimensions in their ground state are sometimes describable in terms of classical d+1 dimensional models. In this talk we will discuss a widely studied quantum model, the spin-1/2 Heisenberg XXZ model, in 1 dimension in the ground state. We will explore how it can be described in terms of 2-dimensional classical models. We prove a strong sign of the aforementioned critical behaviour: spin-spin correlation functions decay slowly, and an associated height function delocalises.
Speaker
- Kieran Ryan, TU Wien
Place
- TU Darmstadt S2|15 Raum 401
- Schlossgartenstr. 7, 64289 Darmstadt
Organizers
- Technische Universität Darmstadt
Fachbereich Mathematik - Stochastik
Schlossgartenstraße 7
64289 Darmstadt
Telefon: +49 6151 16-23380
Telefax: +49 6151 16-23381
info(at)stochastik-rhein-mainde
Organizing partners
Goethe-Universität Frankfurt am Main, Johannes Gutenberg-Universität Mainz, Justus-Liebig-Universität Gießen