Exotic disordered phases in the quantum $J_1-J_2$ model on the honeycomb lattice

TL;DR

This paper investigates the phase diagram of the frustrated quantum $J_1-J_2$ Heisenberg model on the honeycomb lattice, revealing magnetic orders and novel disordered phases using a Schwinger boson mean field approach.

Contribution

It introduces a detailed phase diagram with identification of two distinct disordered phases, including a spin liquid and a lattice nematic phase, in the $J_1-J_2$ honeycomb model.

Findings

Magnetic long-range order for specific $J_2/J_1$ ratios

Identification of a gapped spin liquid phase

Discovery of a lattice nematic phase

Abstract

We study the ground-state phase diagram of the frustrated quantum $J_1-J_2$ Heisenberg antiferromagnet on the honeycomb lattice using a mean field approach in terms of the Schwinger boson representation of the spin operators. We present results for the ground-state energy, local magnetization, energy gap and spin-spin correlations. The system shows magnetic long range order for $0\leq J_{2}/J_{1}\lesssim 0.2075$ (N\'eel) and $0.398\lesssim J_{2}/J_{1}\leq 0.5$ (spiral). In the intermediate region, we find two magnetically disordered phases: a gapped spin liquid phase which shows short-range N\'eel correlations $(0.2075 \lesssim J_{2}/J_{1} \lesssim 0.3732)$, and a lattice nematic phase $(0.3732 \lesssim J_{2}/J_{1}\lesssim 0.398)$, which is magnetically disordered but breaks lattice rotational symmetry. The errors in the values of the phase boundaries which are implicit in the number of significant figures quoted, correspond purely to the error in the extrapolation of our finite-size results to the thermodynamic limit.