# Weak measurement in conformal field theory and holography - VIRTUAL

### APA

Jian, S. (2024). Weak measurement in conformal field theory and holography - VIRTUAL. Perimeter Institute. https://pirsa.org/24020095

### MLA

Jian, Shaokai. Weak measurement in conformal field theory and holography - VIRTUAL. Perimeter Institute, Feb. 27, 2024, https://pirsa.org/24020095

### BibTex

@misc{ pirsa_PIRSA:24020095, doi = {10.48660/24020095}, url = {https://pirsa.org/24020095}, author = {Jian, Shaokai}, keywords = {Condensed Matter}, language = {en}, title = {Weak measurement in conformal field theory and holography - VIRTUAL}, publisher = {Perimeter Institute}, year = {2024}, month = {feb}, note = {PIRSA:24020095 see, \url{https://pirsa.org}} }

Shaokai Jian Tulane University

## Abstract

Weak measurements can be viewed as a soft projection that interpolates between an identity operator and a projection operator, and can induce an effective central charge distinct from the unmeasured CFT. In the first part, I will discuss the effect of measurement and postselection on the critical ground state of a Luttinger liquid theory. Depending on the Luttinger parameter K, the effect of measurement is irrelevant, marginal, or relevant, respectively. When the measurement is marginal, and we find a critical state whose entanglement entropy exhibits a logarithmic behavior with a continuous effective central charge as a function of measurement strength. Inspired by this result, in the second part, I will discuss a holographic description of the weak measurement. The weak measurement is modeled by an interface brane, separating different geometries dual to the post-measurement state and the unmeasured CFT. In an infinite system, the weak measurement is related to ICFT via a spacetime rotation. We find that the holographic entanglement entropy with twist operators located on the defect is consistent in both calculations for ICFT and weak measurements. In a finite system, the weak measurement can lead to a rich phase diagram, in which the post-measurement geometry can realize a Python’s lunch.

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