Modular Hamiltonian of Excited States in Conformal Field Theory

TL;DR

This paper introduces a new replica trick method for computing the modular Hamiltonian and relative entropy of excited states in conformal field theory, enabling explicit calculations of matrix elements and quantum Fisher information.

Contribution

It develops a novel replica trick that handles symmetry-breaking partition functions, allowing detailed analysis of excited states in conformal field theories.

Findings

Derived a formula for quantum Fisher information in vacuum using two-point functions.

Performed explicit calculations in two-dimensional conformal field theories.

Established a method to compute matrix elements of the modular Hamiltonian for excited states.

Abstract

We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the replica Z_n symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories.