Topological terms on topological defects: a quantum Monte Carlo study

Abstract

Dirac fermions in $2+1$ dimensions with dynamically generated anticommuting SO(3) antiferromagnetic (AFM) and Z${}_2$ Kekulé valence-bond solid (KVBS) masses map onto a field theory with a topological $\theta$-term. This term provides a mechanism for continuous phase transitions between different symmetry-broken states: topological defects of one phase carry the charge of the other and proliferate at the transition. The $\theta$-term implies that a domain wall of the Z${}_2$ KVBS order parameter harbors a spin-$1/2$ Heisenberg chain, as described by a $1+1$ dimensional SO(3) non-linear sigma model with $\theta$-term at $\theta =\pi$. Using pinning fields to stabilize the domain wall, we show that our auxiliary-field quantum Monte Carlo simulations indeed support the emergence of a spin-$1/2$ chain at the Z${}_2$ topological defect. This concept can be generalized to higher dimensions where $2+1$ dimensional SO(4) or SO(5) theories with topological terms are realized at a domain wall.

5 pages, 3 figures, supplemental material

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• Gross-Neveu Heisenberg criticality: dynamical generation of quantum spin Hall masses
• Non-Hertz-Millis scaling of the antiferromagnetic quantum critical metal via scalable Hybrid Monte Carlo
• Mitigating the fermion sign problem by automatic differentiation
• The ALF (Algorithms for Lattice Fermions) project release 2.4. Documentation for the auxiliary-field quantum Monte Carlo code