Symmetry restoration and quantumness reestablishment

TL;DR

This paper demonstrates that restoring symmetry in mean field theories like BCS reestablishes lost quantum correlations such as discord, revealing new insights into quantum many-body systems and potential technological applications.

Contribution

It introduces a symmetry restoration approach that reestablishes quantumness in mean field theories, highlighting the behavior of quantum discord as an extensive and interaction-independent quantity.

Findings

Quantum discord is extensive with system size.

Restoring symmetry reestablishes quantum discord.

Quantum entanglement remains unchanged with particle number.

Abstract

A realistic quantum many-body system, characterized by a generic microscopic Hamiltonian, is accessible only through approximation methods. The mean field theories, as the simplest practices of approximation methods, commonly serve as a powerful tool, but unfortunately often violate the symmetry of the Hamiltonian. The conventional BCS theory, as an excellent mean field approach, violates the particle number conservation and completely erases quantumness characterized by concurrence and quantum discord between different modes. We restore the symmetry by using the projected BCS theory and the exact numerical solution and find that the lost quantumness is synchronously reestablished. We show that while entanglement remains unchanged with the particle numbers, quantum discord behaves as an extensive quantity with respect to the system size. Surprisingly, discord is hardly dependent on the interaction strengths. The new feature of discord offers promising applications in modern quantum technologies.