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Competing Orders and Anomalies.

Eun-Gook Moon1,2

  • 1Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637, USA.

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This summary is machine-generated.

Quantum anomalies can disrupt conservation laws. This study reveals how these anomalies enforce massless excitations in quantum phase transitions, offering new criteria for understanding competing orders.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Field Theory
  • High Energy Physics

Background:

  • Conservation laws are fundamental in physics but can be violated by quantum anomalies.
  • Quantum anomalies profoundly impact quantum many-body systems and phase transitions.

Purpose of the Study:

  • To investigate quantum anomaly effects in quantum phase transitions between competing orders.
  • To explore the consequences of these anomalies on the topological nature of non-linear sigma models.

Main Methods:

  • Explicit calculation of topological anomalies in non-linear sigma models (NLSMs) with Wess-Zumino-Witten (WZW) terms.
  • Application of the 't Hooft anomaly matching condition to renormalization group flow.
  • Analysis of competing order parameter theories, including CP(1) and NLSM with WZW in 4D.

Main Results:

  • Anomalies enforce massless excitations across the phase diagram, contrasting with Landau-Ginzburg-Wilson theory.
  • Non-perturbative criteria are established for characterizing quantum phase transitions between competing orders.
  • The CP(1) and NLSM with WZW theories describe distinct universality classes in 4D.

Conclusions:

  • Quantum anomalies play a crucial role in dictating the behavior of quantum phase transitions.
  • The findings provide new theoretical tools for understanding and classifying phases of matter.
  • Physical realizations and experimental implications of quantum anomalies are discussed.