Quantum phase transitions in bilayer SU(N) anti-ferromagnets

We present a detailed study of the destruction of SU(N) magnetic order in square lattice bilayer anti-ferromagnets using unbiased quantum Monte Carlo numerical simulations and field theoretic techniques. We study phase transitions from an SU(N) Néel state into two distinct quantum disordered "valence-bond" phases: a valence-bond liquid (VBL) with no broken symmetries and a lattice-symmetry breaking valence-bond solid (VBS) state. For finite inter-layer coupling, the cancellation of Berry phases between the layers has dramatic consequences on the two phase transitions: the Néel-VBS transition is first order for all $N\geq5$ accesible in our model, whereas the Néel-VBL transition is continuous for N=2 and first order for N>= 4; for N=3 the Néel-VBL transition show no signs of first-order behavior.

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