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

TL;DR

This paper investigates a quantum Heisenberg magnet with random interactions, revealing a gapless spin-fluid ground state at small spins, characterized by a marginal spectrum similar to that observed in doped cuprates.

Contribution

It demonstrates the existence of a gapless spin-fluid phase in a disordered quantum magnet using large M limit analysis, connecting theoretical predictions to experimental spectra.

Findings

The spin-fluid phase is generically gapless.

The local dynamic spin susceptibility follows a logarithmic divergence at low frequencies.

The spectrum matches the marginal form proposed for doped cuprates.

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