Nonordinary edge criticaliy of two-dimensional quantum critical magnets

TL;DR

This study uses large-scale quantum Monte Carlo simulations to explore edge correlations in two-dimensional quantum critical magnets, revealing unique edge criticality behaviors that challenge existing theories linking edge states to topological phases.

Contribution

It provides new insights into edge critical phenomena in 2D quantum magnets, showing the impact of edge alignment and perturbations on scaling behaviors, and questions the connection to symmetry-protected topological phases.

Findings

Edge spin correlations depend strongly on edge alignment.

Scaling exponents are similar across different quantum spin-dimer systems.

Perturbations reveal the quantum nature of edge states.

Abstract

Based on large-scale quantum Monte Carlo simulations, we examine the correlations along the edges of two-dimensional semi-infinite quantum critical Heisenberg spin-$1/2$ systems. In particular, we consider coupled quantum spin-dimer systems at their bulk quantum critical points, including the columnar-dimer model and the plaquette-square lattice. The alignment of the edge spins strongly affects these correlations and the corresponding scaling exponents, with remarkably similar values obtained for various quantum spin-dimer systems. We furthermore observe subtle effects on the scaling behavior from perturbing the edge spins that exhibit the genuine quantum nature of these edge states. Our observations furthermore challenge recent attempts that relate the edge spin criticality to the presence of symmetry-protected topological phases in such quantum spin systems.