Competing Orders and Anomalies

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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
Publisher
NATURE PUBLISHING GROUP
Issue Date
2016-08
Language
English
Article Type
Article
Keywords

QUANTUM CRITICALITY; WEYL SEMIMETALS; GAUGE-THEORIES; FERMIONS

Citation

SCIENTIFIC REPORTS, v.6, pp.31051

ISSN
2045-2322
DOI
10.1038/srep31051
URI
http://hdl.handle.net/10203/213239
Appears in Collection
PH-Journal Papers(저널논문)
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