Title:
Localization and Melting of Interfaces in the Two-Dimensional Quantum Ising Model

Abstract:
 It has been shown that, the quantum-fluctuating interface delimiting a large bubble can be studied as an effective one-dimensional system through a “holographic” mapping. For the considered model, the emergent interface excitations map to an integrable chain of fermionic particles. Thus, we can establish a fascinating bridge between two apparently unrelated dynamical phase transitions. In this article, the authors have studied the nonequilibrium evolution of coexisting ferromagnetic domains in the two-dimensional quantum Ising model—a setup relevant in several contexts, from quantum nucleation dynamics and falsevacuum decay scenarios to recent experiments with Rydberg-atom arrays. 
In this talk, I will focus on the introduction to ​a mapping from the interface of a 2D ferromagnetic quantum Ising model onto a 1D fermionic chain. For concreteness, we will consider the quantum Ising model in a weak external magnetic field, and inspect the nonequilibrium evolution of large domains (or bubbles) of negatively magnetized spins initially prepared in a background of positively magnetized ones. 

Ref:
[1] Federico Balducci, Andrea Gambassi, Alessio Lerose, Antonello Scardicchio, and Carlo Vanoni. Localization and melting of interfaces in the two-dimensional quantum ising model. Phys. Rev. Lett., 129:120601, Sep 2022.
[2] T. Antal, Z. Rácz, A. Rákos, and G. M. Schütz. Transport in the XX chain at zero temperature: Emergence of flat magnetization profiles. Phys. Rev. E, 59:4912–4918, May 1999.
[3] Atsuki Yoshinaga, Hideaki Hakoshima, Takashi Imoto, Yuichiro Matsuzaki, and Ryusuke amazaki. Emergence of hilbert space fragmentation in ising models with a weak transverse field. Physical Review Letters, 129(9), aug 2022.