Competing states in the $S=1/2$ triangular-lattice $J_1$-$J_2$ Heisenberg model: a dynamical density-matrix renormalization group study

TL;DR

This study uses an advanced numerical method to explore the intermediate phase of the $S=1/2$ triangular-lattice $J_1$-$J_2$ Heisenberg model, revealing two distinct quantum states, including a Dirac quantum spin liquid.

Contribution

It provides new insights into the nature of the intermediate phase, identifying two variational states with different quantum spin liquid characteristics using improved DMRG techniques.

Findings

Identification of a Dirac QSL state at higher energy.

Evidence of a magnetically ordered or gapped QSL-like state at lower energy.

Dependence of states on initial conditions and boundary setups.

Abstract

Previous studies of the $S=1/2$ triangular-lattice $J_1$--$J_2$ Heisenberg antiferromagnet have inferred the existence of a non-magnetic ground-state phase for an intermediate range of $J_2$, but disagree concerning whether it is a gapped $\mathbb{Z}_2$ quantum spin liquid (QSL), a gapless (Dirac) QSL, or a weakly symmetry-broken phase. Using an improved dynamical density-matrix renormalization group method, we investigate the relevant intermediate $J_2$ regime for cylinders with circumferences from 6 to 9. Depending on the initial state and boundary conditions, we find two {\it distinct} variational states. The higher energy state is consistent with a Dirac QSL. In the lower-energy state, both the static and dynamical properties are qualitatively similar to the magnetically ordered state at $J_2=0$, suggestive of either a weakly magnetically ordered non-QSL or a gapped QSL proximate to a continuous transition to such an ordered state.