QUANTUM ROTORS WITH REGULAR FRUSTRATION AND THE QUANTUM LIFSHITZ POINT

We have discussed the zero-temperature quantum phase transition in n-c omponent quantum rotor Hamiltonian in the presence of regular frustrat ion in the interaction. The phase diagram consists of ferromagnetic, h elical and quantum paramagnetic phase, where the ferro-para and the he lical-pars phase boundary meets at a multicritical point called a (d,m ) quantum Lifshitz point where (d; m) indicates that the m of the d sp atial dimensions incorporate frustration. We have studied the Hamilton ian in the vicinity of the quantum Lifshitz point in the spherical lim it and also studied the renormalisation group flow behaviour using sta ndard momentum space renormalisation technique (for finite n). In the spherical limit (n --> infinity) one finds that the helical phase does not exist in the presence of any nonvanishing quantum fluctuation for m = d though the quantum Lifshitz point exists for all d > 1 + m/2, a nd the upper critical dimensionality is given by d(u) = 3+m/2. The sca ling behaviour in the neighbourhood of a quantum Lifshitz point in d d imensions is consistent with the behaviour near the classical Lifshitz point in (d+z) dimensions; The dynamical exponent of the quantum Hami ltonian z is unity in the case of anisotropic Lifshitz point (d > m) w hereas z = 2 in the case of isotropic Lifshitz point (d = m). We have evaluated all the exponents using the renormalisation flow equations a long-with the scaling relations near the quantum Lifshitz point. We ha ve also obtained the exponents in the spherical limit (n -->; co). It has also been shown that the exponents in the spherical model are all related to those of the corresponding Gaussian model by Fisher renorma lisation.