Gapless spin-fluid ground state in a random quantum Heisenberg magnet

We examine the spin-S quantum Heisenberg magnet with Gaussian-random, infinite-range exchange interactions. The quantum-disordered phase is accessed by generalizing to SU (M) symmetry and studying the large M limit. For large S the ground state is a spin glass, while quantum fluctuations produce a spin-fluid state for small S. The spin-fluid phase is found to be generically gapless---the average, zero temperature, local dynamic spin susceptibility obeys () (1/) +i (/2) sgn () at low frequencies.