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 \ensuremath{\chi}\ifmmode\bar\else\textasciimacron\fi{}(\ensuremath{\omega})\ensuremath{\sim}ln(1/\ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert})+i(\ensuremath{\pi}/2)sgn(\ensuremath{\omega}) at low frequencies.