Quantum Spin Liquid with Broken Unidirectional Symmetry in a Square Lattice Spin-1 Model*

Quantum spin liquids (QSL) 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 (J₁) and biquadratic (K₁) interactions results in a QSL around the J₁=K₁ point, as evidenced by our density matrix renormalization group (DMRG) studies. At that point, the model has an emergent SU(3) symmetry and 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 QSL 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 studying an anisotropic model, that this lattice-nematic spin liquid is distinct from the limit of weakly coupled Haldane chains. Instead, analysis of the spectral gaps and entanglement entropy is consistent with the QSL being either gapless or having a very small gap.
[1] W.-J. Hu et al., arXiv:1711.06523.