Zeeman levels with exotic field dependence in the high field phase of a S=1 Heisenberg antiferromagnetic chain

We have performed electron spin resonance measurements over a wide frequency and magnetic field range on a single crystal of the S=1 quasi-one-dimensional Heisenberg antiferromagnet $\rm Ni(C_5H_{14}N_2)_2N_3(PF_6)$. We observed gapped excitation branches above the critical field ($H_{\rm c}$) where the Haldane gap closes. These branches are analyzed by a phenomenological field-theory using complex-field $\phi^{4}$ model. A satisfactory agreement between experiment and theory is obtained.