Competing Orders and Anomalies

Abstract

A conservation law is one of the most fundamental properties in nature, but a certain class of conservation "laws"' could be spoiled by intrinsic quantum mechanical effects, so-called quantum anomalies. Profound properties of the anomalies have deepened our understanding in quantum many body systems. Here, we investigate quantum anomaly effects in quantum phase transitions between competing orders and striking consequences of their presence. We explicitly calculate topological nature of anomalies of non-linear sigma models (NLSMs) with the Wess-Zumino-Witten (WZW) terms. The non-perturbative nature is directly related with the 't Hooft anomaly matching condition : anomalies are conserved in renormalization group flow. By applying the matching condition, we show massless excitations are enforced by the anomalies in a whole phase diagram in sharp contrast to the case of the Landau-Ginzburg-Wilson theory which only has massive excitations in symmetric phases. Furthermore, we find non-perturbative criteria to characterize quantum phase transitions between competing orders. For example, in 4D, we show the two competing order parameter theories, CP(1) and the NLSM with WZW, describe different universality class. Physical realizations and experimental implication of the anomalies are also discussed.

Published version

References in corpus (15)

• "Deconfined" quantum critical points
• Quantum Criticality in Heavy Fermion Metals
• Theory of Intertwined Orders in High Temperature Superconductors
• Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
• Anomalies of discrete symmetries in three dimensions and group cohomology
• Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• Competition between spin density wave order and superconductivity in the underdoped cuprates
• Torsion, Parity-odd Response and Anomalies in Topological States
• Quantum critical point shifts under superconductivity: the pnictides and the cuprates
• The Origin of Families and $SO(18)$ Grand Unification
• Geometric phases and competing orders in two dimensions
• Charge-Density-Wave and Superconductor Competition in Stripe Phases of High Temperature Superconductors
• Charge-$2e$ Skyrmion condensate in a hidden order state
• Topological Orders with Global Gauge Anomalies

Cited by in corpus (3)

• Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions
• Definition and Classification of Fermi Surface Anomalies
• Decorated defect condensate, a window to unconventional quantum phase transitions in Weyl semimetals