Topological terms on topological defects: a quantum Monte Carlo study

TL;DR

This study uses quantum Monte Carlo simulations to explore how topological terms influence phase transitions and defect properties in 2+1D Dirac fermion systems, revealing domain walls host spin-1/2 chains.

Contribution

It demonstrates the emergence of spin-1/2 chains at topological defects in a 2+1D Dirac fermion model with a topological theta-term using quantum Monte Carlo methods.

Findings

Support for spin-1/2 chain emergence at Z2 topological defects

Validation of topological defect properties via quantum Monte Carlo

Potential generalization to higher-dimensional theories with topological terms

Abstract

Dirac fermions in $2+1$ dimensions with dynamically generated anticommuting SO(3) antiferromagnetic (AFM) and Z$_2$ Kekul\'e 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.