Modular Hamiltonian for Excited States in Conformal Field Theory

Area of Science:

• Theoretical Physics
• Quantum Information Theory
• Conformal Field Theory

Background:

• Relative entropy quantifies distinguishability between quantum states.
• Conformal field theories (CFTs) are crucial in quantum field theory and statistical mechanics.
• Calculating relative entropy for excited states is computationally challenging.

Purpose of the Study:

• To introduce a novel replica trick for computing relative entropy.
• To provide a method for calculating modular Hamiltonian matrix elements.
• To connect quantum Fisher information to replica geometry.

Main Methods:

• Analytic continuation of partition functions that break Z_n replica symmetry.
• Utilizing correlation functions on the replica geometry.
• Applying the method to two-dimensional conformal field theories.

Main Results:

• A novel replica trick for relative entropy calculation in CFT.
• Computation of arbitrary matrix elements of the modular Hamiltonian for excited states.
• Expression of quantum Fisher information in vacuum via two-point functions on replica geometry.

Conclusions:

• The developed replica trick offers a powerful tool for studying quantum information measures in CFT.
• The method simplifies calculations of complex quantum properties.
• This work opens new avenues for investigating quantum correlations in diverse physical systems.