This paper presents a study of the spin-S quantum Heisenberg magnet with Gaussian-random, infinite-range exchange interactions. The quantum-disordered phase is analyzed using $ SU(M) $ symmetry and the large M limit. For large S, the ground state is a spin-glass, while for small S, quantum fluctuations produce a spin-fluid state. The spin-fluid phase is generically gapless, with the average, zero temperature, local dynamic spin-susceptibility obeying $ \bar{\chi}(\omega) \sim \log(1/|\omega|) + i(\pi/2)\mathrm{sgn}(\omega) $ at low frequencies. This form is similar to the 'marginal' Fermi liquid susceptibility proposed for cuprates.
The model considered has infinite-range exchange interactions and is solvable, complementing spin chains. The spin-fluid phase is generically gapless, but the mechanism differs from that of random spin chains. The paper also discusses the transition to a spin-glass phase, though the nature of this transition remains unclear.
The model is analyzed using a coherent-state path-integral approach, leading to an integro-differential equation for the boson Green's function. The solution shows that the zero-temperature boson spectrum must be gapless. The low-frequency behavior of the spin-susceptibility is determined, showing it increases with 'spin' but has a maximum at $ \theta = \pi/4 $, suggesting a transition to the spin-glass phase at this point.
Numerical studies of the equations confirm the existence of physically sensible solutions for $ \theta < \pi/4 $, corresponding to the spin-fluid phase. The results are consistent with the conjecture that no such solutions exist for $ \theta > \pi/4 $, where a spin-glass phase is expected.
The paper also considers the large M limit (B), leading to a fermionic representation. The analysis shows that the dynamical susceptibility has the same low-frequency dependence as in the bosonic case, with a constant X that increases with $ n_b $.
The key unresolved issue is the validity of the dynamic susceptibility in Eqn (1) and its implications for experiments on random antiferromagnets. The paper also addresses questions about the upper-critical dimension and the effects of nonzero average $ J_{ij} $.This paper presents a study of the spin-S quantum Heisenberg magnet with Gaussian-random, infinite-range exchange interactions. The quantum-disordered phase is analyzed using $ SU(M) $ symmetry and the large M limit. For large S, the ground state is a spin-glass, while for small S, quantum fluctuations produce a spin-fluid state. The spin-fluid phase is generically gapless, with the average, zero temperature, local dynamic spin-susceptibility obeying $ \bar{\chi}(\omega) \sim \log(1/|\omega|) + i(\pi/2)\mathrm{sgn}(\omega) $ at low frequencies. This form is similar to the 'marginal' Fermi liquid susceptibility proposed for cuprates.
The model considered has infinite-range exchange interactions and is solvable, complementing spin chains. The spin-fluid phase is generically gapless, but the mechanism differs from that of random spin chains. The paper also discusses the transition to a spin-glass phase, though the nature of this transition remains unclear.
The model is analyzed using a coherent-state path-integral approach, leading to an integro-differential equation for the boson Green's function. The solution shows that the zero-temperature boson spectrum must be gapless. The low-frequency behavior of the spin-susceptibility is determined, showing it increases with 'spin' but has a maximum at $ \theta = \pi/4 $, suggesting a transition to the spin-glass phase at this point.
Numerical studies of the equations confirm the existence of physically sensible solutions for $ \theta < \pi/4 $, corresponding to the spin-fluid phase. The results are consistent with the conjecture that no such solutions exist for $ \theta > \pi/4 $, where a spin-glass phase is expected.
The paper also considers the large M limit (B), leading to a fermionic representation. The analysis shows that the dynamical susceptibility has the same low-frequency dependence as in the bosonic case, with a constant X that increases with $ n_b $.
The key unresolved issue is the validity of the dynamic susceptibility in Eqn (1) and its implications for experiments on random antiferromagnets. The paper also addresses questions about the upper-critical dimension and the effects of nonzero average $ J_{ij} $.