Quantum criticality with multiple dynamics

TL;DR

This paper explores how multiple dynamical exponents affect quantum critical scaling, distinguishing between coupled and decoupled cases, and introduces an emergent dynamical exponent in systems with multiple dynamics.

Contribution

It analyzes the impact of multiple dynamics on quantum criticality, proposing conditions for coupled scaling and deriving an emergent dynamical exponent.

Findings

Identification of conditions for coupled multiple dynamic scaling.

Derivation of an emergent dynamical exponent z_e.

Analysis of generalized Phi^4-theories with multiple dynamics.

Abstract

Quantum critical systems with multiple dynamics possess not only one but several time scales, tau_i ~ xi^(z_i), which diverge with the correlation length xi. We investigate how scaling predictions are modified for the simplest case of multiple dynamics characterized by two dynamical critical exponents, z_> and z_<. We argue that one should distinguish the case of coupled and decoupled multiple dynamic scaling depending on whether there exists a scaling exponent which depends on both z_i or not. As an example, we study generalized Phi^4-theories with multiple dynamics below their upper critical dimension, d+z_<<4. We identify under which condition coupled scaling is generated. In this case the interaction of quantum and classical fluctuations leads to an emergent dynamical exponent, z_e=z_>/(nu (z_>-z_<)+1).