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arXiv:1504.00654 · Physical Review B

Competing spin-liquid states in the spin- 1 2 Heisenberg model on the triangular lattice

Wen-Jun Hu, Shou-Shu Gong, Wei Kang Zhu, D. N. Sheng

Published Oct 2, 2015• 214 citations
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Abstract

We study the spin-$\frac{1}{2}$ Heisenberg model on the triangular lattice with antiferromagnetic first- $({J}_{1})$ and second- $({J}_{2})$ nearest-neighbor interactions using density matrix renormalization group. By studying the spin correlation function, we find a ${120}^{\ensuremath{\circ}}$ magnetic order phase for ${J}_{2}\ensuremath{\lesssim}0.07{J}_{1}$ and a stripe antiferromagnetic phase for ${J}_{2}\ensuremath{\gtrsim}0.15{J}_{1}$. Between these two phases, we identify a spin-liquid region characterized by exponential decaying spin and dimer correlations, as well as large spin singlet and triplet excitation gaps on finite-size systems. We find two near degenerating ground states with distinct properties in two sectors, which indicates more than one spin-liquid candidate in this region. While the sector with spinons is found to respect time reversal symmetry, the even sector without spinons breaks such a symmetry for finite-size systems. Furthermore, we detect the signature of the fractionalization by following the evolution of different ground states with inserting spin flux into the cylinder system. Moreover, by tuning the anisotropic bond coupling, we explore the nature of the spin-liquid phase and find the optimal parameter region for gapped ${Z}_{2}$ spin liquids.

DOI
10.1103/physrevb.92.140403

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Topological Spin Liquid Phase in the Spin-1/21/21/2 Triangular Heisenberg Model
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We study the interplay of competing interactions in spin-12\frac{1}{2}21​ triangular Heisenberg model through tuning the first- (J1{J}_{1}J1​), second- (J2{J}_{2}J2​), and third-neighbor (J3{J}_{3}J3​) couplings. Based on a large-scale density-matrix renormalization group calculation, we identify a quantum phase diagram of the system and discover a gapless chiral spin-liquid (CSL) phase in the intermediate J2{J}_{2}J2​ and J3{J}_{3}J3​ regime. This CSL state spontaneously breaks time-reversal symmetry with finite scalar chiral order, and it has gapless excitations implied by a vanishing spin triplet gap and a finite central charge on the cylinder. Moreover, the central charge grows rapidly with the cylinder circumference, indicating emergent spinon Fermi surfaces. To understand the numerical results we propose a parton mean-field spin-liquid state, the U(1)U(1)U(1) staggered flux state, which breaks time-reversal symmetry with chiral edge modes by adding a Chern insulator mass to Dirac spinons in the U(1)U(1)U(1) Dirac spin liquid. This state also breaks lattice rotational symmetries and possesses two spinon Fermi surfaces driven by nonzero J2{J}_{2}J2​ and J3{J}_{3}J3​, which naturally explains the numerical results. This realizes an example of a gapless CSL state with coexisting spinon Fermi surfaces and chiral edge states, demonstrating the rich family of interesting quantum phases emergent from competing interactions in triangular-lattice magnets.
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