Interplay of quantum and classical fluctuations near quantum critical points

TL;DR

This paper explores how classical and quantum fluctuations interact near quantum critical points, especially when the system's effective dimension exceeds the upper critical dimension, leading to breakdowns in scaling relations and observable experimental effects.

Contribution

It identifies the breakdown of the scaling relation $ ext{psi}= ext{nu}z$ due to dangerous irrelevant interactions in systems above the upper critical dimension.

Findings

Classical and quantum fluctuations intermingle near the QCP when $d+z>d_C$.

Breakdown of the scaling relation $ ext{psi}= ext{nu}z$ occurs due to dangerous irrelevant interactions.

Experimental consequences include suppression of classical fluctuations near the QCP.

Abstract

For a system near a quantum critical point (QCP), above its lower critical dimension $d_L$, there is in general a critical line of second order phase transitions that separates the broken symmetry phase at finite temperatures from the disordered phase. The phase transitions along this line are governed by thermal critical exponents that are different from those associated with the quantum critical point. We point out that, if the effective dimension of the QCP, $d_{eff}=d+z$ ($d$ is the Euclidean dimension of the system and $z$ the dynamic quantum critical exponent) is above its upper critical dimension $d_C$, there is an intermingle of classical (thermal) and quantum critical fluctuations near the QCP. This is due to the breakdown of the generalized scaling relation $\psi=\nu z$ between the shift exponent $\psi$ of the critical line and the crossover exponent $\nu z$, for $d+z>d_C$ by a \textit{dangerous irrelevant interaction}. This phenomenon has clear experimental consequences, like the suppression of the amplitude of classical critical fluctuations near the line of finite temperature phase transitions as the critical temperature is reduced approaching the QCP.