Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet

Abstract

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 $\barχ (ω) \sim \log(1/|ω|) + i (π/2) \mbox{sgn} (ω)$ at low frequencies. This form is identical to the phenomenological `marginal' spectrum proposed by Varma {\em et. al.\/} for the doped cuprates.