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arXiv:2306.03478 · Physical review. B./Physical review. B

Interplay between multispin and chiral spin interactions on a triangular lattice

Li-Wei He, Jian‐Xin Li

Published Dec 1, 2023• 5 citations
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Abstract

We investigate the spin-$\frac{1}{2}$ nearest-neighbor Heisenberg model with the four-site ring-exchange ${J}_{4}$ and chiral interaction ${J}_{\ensuremath{\chi}}$ 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 ${J}_{\ensuremath{\chi}}$ can enrich the phase diagram with two interesting chiral QSLs (topological orders) with the same quantized Chern number $C=\frac{1}{2}$ and ground-state degeneracy GSD = 2, namely the $U(1)$ chiral spin liquid (CSL) and ${\mathrm{Z}}_{2}\phantom{\rule{4pt}{0ex}}d+id$-wave QSL. The nodal $d$-wave QSL is fragile and will turn to the ${\mathrm{Z}}_{2}\phantom{\rule{4pt}{0ex}}d+id$ QSL with any finite ${J}_{\ensuremath{\chi}}$ within our numerical calculation. However, in the process from QBT to the ${\mathrm{Z}}_{2}\phantom{\rule{4pt}{0ex}}d+id$ QSL with the increase of ${J}_{\ensuremath{\chi}}$, 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 band touching points, and leads to an energy minimum which is energetically more favorable compared to another competitive local minimum from the ${\mathrm{Z}}_{2}\phantom{\rule{4pt}{0ex}}d+id$ QSL. We dub this state as the proximate QBT QSL and it gives way to the ${\mathrm{Z}}_{2}\phantom{\rule{4pt}{0ex}}d+id$ QSL eventually. Therefore, the cooperation of the ${J}_{4}$ and ${J}_{\ensuremath{\chi}}$ terms favors mostly the ${\mathrm{Z}}_{2}\phantom{\rule{4pt}{0ex}}d+id$-wave QSL, so that this phase occupies the largest region in the phase diagram.

DOI
10.1103/physrevb.108.245102

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