Quantum Disentanglement in Long-range Orders and Spontaneous Symmetry Breaking

TL;DR

This paper explores how quantum entanglement diminishes in systems with long-range order and spontaneous symmetry breaking, linking disentanglement to phenomena like superconductivity and Bose-Einstein condensation.

Contribution

It demonstrates the role of entanglement reduction in long-range order and proposes methods to characterize entanglement using connected correlation functions.

Findings

Entanglement diminishes between condensate mode and the rest of the system.

Disentanglement underpins long-range order and symmetry breaking.

Connected correlation functions can characterize entanglement in pure states.

Abstract

We investigate the nature of quantum entanglement in long-range orders and spontaneous symmetry breaking. It is shown that diminishing of entanglement between the condensate mode and the rest of the system underlies off-diagonal long-range order, which is the hallmark of superconductivity and Bose-Einstein condensation. It is also revealed that disentanglement underlies various cases of long-range order and spontaneous symmetry breaking. In the course of the discussion, we also present some ideas on characterizing entanglement in many-body systems. Especially, it is shown how the connected correlation functions can be used in characterizing entanglements in a pure state.