Study of the bilinear biquadratic Heisenberg model on a honeycomb lattice via Schwinger bosons

We analyze the biquadratic bilinear Heisenberg magnet on a honeycomb lattice via Schwinger boson formalism. Due to their vulnerability to quantum fluctuations, non conventional lattices (kagome, triangular and honeycomb for example) have been cited as candidates to support spin liquid states. Such states without long range order at zero temperature are known in one-dimensional spin models but their existence in higher dimensional systems is still under debate. Biquadratic interaction is responsible for various possibilities and phases as it is well-founded for one-dimensional systems. Here we have used a bosonic representation to study the properties at zero and finite low temperatures of the biquadratic term in the two-dimensional hexagonal honeycomb lattice. The results show a ordered state at zero temperature but much more fragile than that of a square lattice; the behavior at finite low temperatures is in accordance with expectations.