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Frustration in quantum spin systems promote a variety of novel quantumphases. An important example is the frustrated spin-$1$ model on the squarelattice with the nearest-neighbor bilinear ($J_1$) and biquadratic ($K_1$)interactions. We provide strong evidence for a nematic spin liquid phase in arange of $K_1/J_1$ near the SU(3)-symmetric point ($J_1 = K_1$), based on thelinear flavor-wave theory and extensive density matrix renormalization groupcalculation. This phase displays no spin dipolar or quadrupolar order,preserves translational symmetry but spontaneously breaks $C_4$ latticerotational symmetry, and possesses fluctuations peaked at the wavevector $(\pi,2\pi/3)$. The spin excitation gap drops rapidly with system size and appears tobe gapless, and the nematic order is attributed to the dominant $(\pi, 2\pi/3)$fluctuations. Our results provide a novel mechanism for electronic nematicorder and, more generally, open up a new avenue to explore frustration-inducedexotic ground states.

Nematic Spin Liquid Phase in a Frustrated Spin-1 System on the Square Lattice