A simple analysis of the mixed-state information metric in AdS$_3$/CFT$_2$

TL;DR

This paper calculates the quantum information metrics for thermal CFTs perturbed by scalar operators and confirms the holographic results, enhancing understanding of mixed-state information geometry in AdS3/CFT2.

Contribution

It provides a direct computation of mixed-state information metrics in thermal CFTs and verifies holographic predictions for specific scalar operators.

Findings

Exact agreement between field theory and holographic calculations.

Extension of information metric analysis to mixed states in thermal CFTs.

Validation of holographic methods for mixed-state quantum information measures.

Abstract

We compute the quantum information metrics of a thermal CFT on $\mathbb R^{1,1}$ perturbed by the scalar primary operators of conformal dimension $\Delta=3,4,5,6$. In particular, we assume that the Hamiltonian of the mixed state commutes with each other and the temperature is fixed. Under these conditions, the evaluation is analogous to the pure state case. We also apply the method of [arXiv:1607.06519] to calculate the mixed state information metric for the scalar primary operator with conformal dimension $\Delta=4$ holographically. We find an exact agreement between the two results in our approach.