| Title | Tracy-Widom distribution in the six-vertex model |
|---|---|
| Speaker | Filippo Colomo (University of Florence and INFN) |
| Date&time |
📅 Tuesday, January 21 🕓 11.00 (Rome) |
| Location | |
| Abstract |
The six-vertex model with domain wall boundary conditions exhibits spatial phase separation, with the emergence of regions of order and disorder, sharply separated by a smooth curve, called arctic curve. After reviewing the state of the art the field, including its connection to quantum quenches, we focus on the emptiness formation probability (EFP), a non-local correlation function testing the order-disorder interface, and its fluctuations. While at the free-fermiont point the behaviour of EFP is known in full detail, much less can be said for generic values of $\Delta$. Here we specialize to the ice point, $\Delta=1/2$, where all the Boltzmann weights are equal. We build an explicit and exact, although still conjectural, expression for the EFP as the Fredholm determinant of some linear integral operator. We study the behaviour of the obtained representation in the scaling limit. In particular, as the geometric parameters of the EFP are tuned to the vicinity of the arctic curve, we obtain the GUE Tracy-Widom distribution (just as in the $\Delta=0$ case). In other words, interface fluctuations around the arctic curve fall into the Kardar-Parisi-Zhang universality class.
Joint work with A. Pronko – ArXiv:2405.04358 – Nucl. Phys. B (2024) |
| 🔗 Past seminars | |
| 🔗 Past journal club meetings |
