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

TL;DR

This paper explores unconventional quantum phase transitions in Weyl semimetals, focusing on topological defects and emergent bosonic fields with topological terms, revealing new critical phenomena beyond traditional Landau theory.

Contribution

It introduces a detailed analysis of three types of unconventional quantum critical points involving topological defects and emergent topological terms in Weyl semimetals.

Findings

Identification of critical points beyond Landau's paradigm

Connection between topological defects and phase transitions

Insights into topological order and symmetry breaking

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.