Decorated defect condensate, a window to unconventional quantum phase transitions in Weyl semimetals

Abstract

We investigate the unconventional quantum phase transitions in Weyl semimetals. The emergent boson fields, coupling with the Weyl fermion bilinears, contain a Wess-Zumino-Witten term or topological $\Theta$ term inherited from the momentum space monopoles carried by Weyl points. Three types of unconventional quantum critical points will be studied in order: (1) The transition between two distinct symmetry breaking phases whose criticality is beyond Landau's paradigm. (2) The transition between a symmetry breaking state to a topological ordered state. (3) The transition between $3d$ topological order phase to trivial disordered phase whose criticality could be traced back to a $Z_2$ symmetry breaking transition in $4d$. The essence of these unconventional critical points lies in the fact that the topological defect of an order parameter carries either a nontrivial quantum number or a topological term so the condensation of the defects would either break some symmetry or give rise to a topological order phase with nontrivial braiding statistics.

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Cited by in corpus (9)

• Subsystem symmetry protected topological order
• Higher order symmetry-protected topological states for interacting bosons and fermions
• Symmetric Fracton Matter: Twisted and Enriched
• Mixed axial-torsional anomaly in Weyl semimetals
• Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions
• Symmetry breaking and lattice kirigami: finite temperature effects
• On chiral responses to geometric torsion
• Canonical quantization of nonlinear sigma models with theta term, with applications to symmetry-protected topological phases
• Perturbative and global anomalies in bosonic analogues of integer quantum Hall and topological insulator phases