Cite as: doi:10.26081/K68K6G

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Quantum spin liquids are known to arise in strongly frustrated spin systems as a
result of competing interactions. Here we consider a spin-1 model on a square
lattice, where despite the absence of geometric frustration, competition between
the nearest neighbor Heisenberg (J) and biquadratic (K) interactions results in
a quantum spin liquid around the J = K point, as evidenced by our density matrix
renormalization group (DMRG) studies. At that point, the model has an emergent
SU(3) symmetry and our calculations based on N = 3 flavor- wave theory indicate
the presence of large quantum fluctuations that destabilize the nearby
antiferromagnetic and quadrupolar orders. What emerges is a quantum spin liquid
with no long-range order in spin or quadrupolar channels, which nevertheless has
fluctuations peaked at the wavevector (π, 2π/3) and spontaneously breaks the C4
rotational symmetry of the square lattice [1]. We demonstrate, by considering an
anisotropic square lattice, that this lattice-nematic spin liquid is distinct
from the limit of weakly coupled Haldane chains. Analysis of the spectral gaps
and entanglement entropy is consistent with the spin liquid being either gapless
or having a very small gap.
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**[1] W.-J. Hu et al, PRB 100, 165142 (2019).
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