Deconfined Boundary Phase Transition of a Quantum Critical Heisenberg Model

TL;DR

This study explores the boundary phase transition in a (2+1)-D quantum critical Heisenberg model with a boundary spin chain, revealing a continuous transition driven by a multispin term and characterized by specific critical exponents.

Contribution

It introduces a boundary multispin $Q$-term to induce and analyze a continuous boundary phase transition in a quantum critical Heisenberg model using quantum Monte Carlo simulations.

Findings

Located the critical point at Q_c=0.310(11)

Measured critical exponents y_s=0.81(4), Δ_s=0.660(15), Δ_v=0.204(14)

Identified weak AF order stabilized by quasi-long-range interactions

Abstract

We investigate the boundary phases of a (2+1)-dimensional quantum critical Heisenberg model with a dangling spin chain. By introducing a multispin $Q$-term along the boundary, we drive a continuous boundary transition from an antiferromagnetic (AF) order to a valence-bond solid (VBS) order. Using large-scale quantum Monte Carlo simulations, we locate the critical point at $Q_{c}=0.310(11)$, and obtain the critical exponents at $Q_{c}$, including $y_{s}=0.81(4)$ and the scaling dimensions of AF and VBS order parameters $\Delta_{s}=0.660(15)$ and $\Delta_{v}=0.204(14)$. The weak long-range AF order for $Q<Q_{c}$ is stabilized by quasi-long-range effective interactions mediated by the critical bulk state, while the VBS phase restores the ordinary critical behavior. Our findings highlight the synergy between topological terms and quasi-long-range interactions in low-dimensional quantum many-body systems.