Quantum criticality 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).

8 pages including supplementary material. Minor changes as compared to the previous version

References in corpus (4)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order
• Multiple energy scales at a quantum critical point
• Quantum phase transition in quantum wires controlled by an external gate