Plaquette order and deconfined quantum critical point in the spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice

TL;DR

This paper maps the phase diagram of a quantum spin-1 model on a honeycomb lattice, revealing a plaquette order phase induced by quantum fluctuations and analyzing the nature of the phase transition.

Contribution

It provides the first precise determination of the ground state phases and the quantum phase transition characteristics of the spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice.

Findings

Identification of a plaquette order phase breaking lattice symmetry

Quantum fluctuations suppress magnetic orders near the antiferroquadrupolar phase

Phase transition between antiferromagnetic and plaquette phases is either second order or very weak first order

Abstract

We have precisely determined the ground state phase diagram of the quantum spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice using the tensor renormalization group method. We find that the ferromagnetic, ferroquadrupolar, and a large part of the antiferromagnetic phases are stable against quantum fluctuations. However, around the phase where the ground state is antiferroquadrupolar ordered in the classical limit, quantum fluctuations suppress completely all magnetic orders, leading to a plaquette order phase which breaks the lattice symmetry but preserves the spin SU(2) symmetry. On the evidence of our numerical results, the quantum phase transition between the antiferromagnetic phase and the plaquette phase is found to be either a direct second order or a very weak first order transition.