Interplay between multi-spin and chiral spin interactions on triangular lattice

Abstract

We investigate the spin-$\frac{1}{2}$ nearest-neighber Heisenberg model with the four-site ring-exchange $J_4$ and chiral interaction $J_{\chi }$ on the triangular lattice by using the variational Monte Carlo method. The $J_4$ term induces the quadratic band touching (QBT) quantum spin liquid (QSL) with only a $d+id$ spinon pairing (without hopping term), the nodal $d$-wave QSL and U(1) QSL with a finite spinon Fermi surface progressively. The effect of the chiral interaction $J_{\chi }$ can enrich the phase diagram with two interesting chiral QSLs (topological orders) with the same quantized Chern number $\mathcal{C}=\frac{1}{2}$ and ground-state degeneracy GSD = 2, namely the U(1) chiral spin liquid (CSL) and Z${}_2$ $d+id$-wave QSL. The nodal $d$-wave QSL is fragile and will turn to the Z${}_2$ $d+id$ QSL with any finite $J_{\chi }$ within our numerical calculation. However, in the process from QBT to the Z${}_2$ $d+id$ QSL with the increase of $J_{\chi }$, an exotic crossover region is found. In this region, the previous QBT state acquires a small hopping term so that it opens a small gap at the otherwise band touching points, and leads to an energy minimum which is energetically more favorable compared to another competitive local minimum from the Z${}_2$ $d+id$ QSL. We dub this state as the proximate QBT QSL and it gives way to the Z${}_2$ $d+id$ QSL eventually. Therefore, the cooperation of the $J_4$ and $J_{\chi }$ terms favors mostly the Z${}_2$ $d+id$-wave QSL, so that this phase occupies the largest region in the phase diagram.

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Cited by in corpus (4)

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• Recent progress in quantum spin liquids, fractional magnetization plateaus, and unconventional superconductivity in kagome lattices
• Exact diagonalization study of triangular Heisenberg model with four-spin ring-exchange interaction
• Emergent Symmetry-Protected Topological Phases via Polyakov Confinement in Quantum Spin Systems