Bose-Einstein condensation and entanglement in magnetic systems

TL;DR

This paper investigates quantum phase transitions in magnetic systems, focusing on Bose-Einstein condensation of magnons, and explores how entanglement emerges near critical points using magnetic susceptibility as an entanglement witness.

Contribution

It develops a generalized scaling theory for magnetic quantum critical points and links entanglement to magnetic susceptibility in these systems.

Findings

Different universality classes for magnon BEC transitions at $H_{C1}$ and $H_{C2}$

Temperature dependence of physical quantities along the quantum critical trajectory

Magnetic susceptibility as an entanglement witness near quantum critical points

Abstract

We present a study of magnetic field induced quantum phase transitions in insulating systems. A generalized scaling theory is used to obtain the temperature dependence of several physical quantities along the quantum critical trajectory ($H=H_{C}$, $T\to0$) where $H$ is a longitudinal external magnetic field and $H_{C}$ the critical value at which the transition occurs. We consider transitions from a spin liquid at a critical field $H_{C1}$ and from a fully polarized paramagnet, at $H_{C2}$, into phases with long range order in the transverse components. The transitions at $H_{C1}$ and $H_{C2}$ can be viewed as Bose-Einstein condensations of magnons which however belong to different universality classes since they have different values of the dynamic critical exponent $z$. Finally, we use that the magnetic susceptibility is an entanglement witness to discuss how this type of correlation sets in as the system approaches the quantum critical point along the critical trajectory, $H=H_{C2}$, $T\to0$.