PIRSA:23110068

Long-Range Order on Line Defects in Ising Conformal Field Theories

Lanzetta, R. (2023). Long-Range Order on Line Defects in Ising Conformal Field Theories. Perimeter Institute. https://pirsa.org/23110068

Lanzetta, Ryan. Long-Range Order on Line Defects in Ising Conformal Field Theories. Perimeter Institute, Nov. 16, 2023, https://pirsa.org/23110068 

          @misc{ pirsa_PIRSA:23110068,
            doi = {10.48660/23110068},
            url = {https://pirsa.org/23110068},
            author = {Lanzetta, Ryan},
            keywords = {Condensed Matter},
            language = {en},
            title = {Long-Range Order on Line Defects in Ising Conformal Field Theories},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {nov},
            note = {PIRSA:23110068 see, \url{https://pirsa.org}}
          }

Ryan Lanzetta

Perimeter Institute for Theoretical Physics

Talk number
PIRSA:23110068
Collection
Talk Type
Subject
Abstract

It is well-known that one-dimensional systems at finite temperature, such as the classical Ising model, cannot spontaneously break a discrete symmetry due to the proliferation of domain walls. The validity of this statement rests on a few assumptions, including the spatial locality of interactions. In a situation where a one-dimensional system exists as a defect in a critical, higher-dimensional bulk system, the coupling between defect and bulk can induce an effective long-range interaction on the defect. It is thus natural to ask if long-range order can be stabilized on a defect in a critical bulk, which amounts to asking whether domain walls on the defect are relevant or not in the renormalization group sense. I will explore this question in the context of Ising conformal field theory in two and higher dimensions in the presence of a localized symmetry-breaking field. With both perturbative techniques and numerical conformal bootstrap, I will provide evidence that indeed the defect domain wall must be relevant when 2 < d < 4. For the bootstrap calculations, it is essential to include “endpoint” primary fields of the defect, which lead to a rigorous and powerful way to input bulk data. I will additionally give tight estimates of a number of other quantities, including  scaling dimensions of defect operators and the defect entropy, and I will conclude with a discussion of future directions.

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Zoom link https://pitp.zoom.us/j/92671628591?pwd=WjNma3VEV2M4T011dFlLMzM2ZUJiUT09