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.
Highlights
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
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
Topological protection is one of the most fascinating properties of quantum anomalies, and remarkably this protection is independent of interaction strength. ’t Hooft first realized and applied these properties to confinement physics of quantum chromodynamics (QCD), so-called ’t Hooft mathcing, and constrained candidates of low energy degrees of freedom including the Goldstone bosons from the chiral symmetry breaking[3]
Summary
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. ’t Hooft first realized and applied these properties to confinement physics of quantum chromodynamics (QCD), so-called ’t Hooft mathcing, and constrained candidates of low energy degrees of freedom including the Goldstone bosons from the chiral symmetry breaking[3] Such non-perturbative nature has been extensively applied to high energy physics, for example, the standard model, the Skyrme model of hadrons, and black hole physics[1,2,3]. We consider another realization of quantum anomalies in condensed matter systems, non-abelian anomalies in quantum phase transitions between competing orders and investigate consequences of their presence. By using the ’t Hooft anomaly matching condition, we find competing order physics with anomalies must contain massless excitation in sharp contrast to the case of the conventional Landau-Ginzburg-Wilson theory. We provide possible candidate theories of the quantum phase transitions with anomalies
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