Revisiting the $J_1$-$J_2$ Heisenberg Model on a Triangular Lattice: Quasi-Degenerate Ground States and Phase Competition

TL;DR

This study uses advanced simulations to compare two nearly degenerate ground states in the $J_1$-$J_2$ Heisenberg model on a triangular lattice, revealing they are not just topological sectors but have distinct physical properties.

Contribution

It provides new insights into the nature of the ground states, challenging the simple topological sector interpretation in the quantum spin liquid regime.

Findings

Differences in static correlations between the two states.

Distinct low-energy excitations in dynamical structure factors.

Evidence against the two states being just topological sectors of a gapped spin liquid.

Abstract

It is generally believed that the spin-$\tfrac{1}{2}$ triangular-lattice $J_1$-$J_2$ Heisenberg model hosts a quantum spin liquid in the intermediate regime between the $120^\circ$ and stripe ordered phases. Density matrix renormalization group studies on cylinders have consistently found two nearly degenerate ground states, commonly interpreted as distinct topological sectors. Using state-of-the-art matrix product state simulations on YC6 cylinders, we compare the static and dynamical properties of these two sectors at $J_2/J_1 = 0.125$. Noticeable differences appear already in static correlations; moreover, high-resolution dynamical structure factors reveal qualitatively distinct low-energy excitations. These results suggest that the two ground states cannot be understood as merely topologically distinct sectors of a gapped $\mathbb{Z}_2$ spin liquid.