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arXiv:cond-mat/9212030 · Physical Review Letters

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

Subir Sachdev A, Jinwu Ye

Published May 24, 1993• 1,905 citations
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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 \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.

DOI
10.1103/physrevlett.70.3339

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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.
We study the Schwinger bosons SU(M) generalization of the spin-S (S\ensuremath{\equiv}\ensuremath{\kappa}M) quantum Heisenberg magnet with infinite-range, Gaussian-random exchange interactions. The spin-glass transition was accessed in the spherical limit M=\ensuremath{\infty} with fixed \ensuremath{\kappa}. The model is solved exactly in the spin-glass phase wthin the Parisi ansatz with a single step of the replica symmetry breaking. The physical consequences of this quantum spin-glass transition scenario are discussed.
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We study quantum SU(MMM) spins with all-to-all and random Heisenberg exchange interactions of root-mean-square strength JJJ. The $M\ensuremath{\rightarrow}\ensuremath{\infty}$ model has a quantum spin liquid ground state with the spinons obeying the equations of the Sachdev-Ye-Kitaev (SYK) model. Numerical studies of the SU(2) model with S=1/2S=1/2S=1/2 spins show spin glass order in the ground state, but also display SYK spin liquid behavior in the intermediate frequency spin spectrum. We employ a 1/M1/M1/M expansion to describe the crossover from fractionalized fermionic spinons to a confining spin glass state with weak spin glass order qEA{q}_{EA}qEA​. The SYK spin liquid behavior persists down to a frequency ${\ensuremath{\omega}}_{*}\ensuremath{\sim}J{q}_{EA}$, and for $\ensuremath{\omega}<{\ensuremath{\omega}}_{*}$, the spin spectral density is linear in $\ensuremath{\omega}$, thus quenching the extensive zero temperature entropy of the spin liquid. The linear $\ensuremath{\omega}$ spectrum is qualitatively similar to that obtained earlier using bosonic spinons for large qEA{q}_{EA}qEA​. We argue that the extensive SYK spin liquid entropy is transformed as $T\ensuremath{\rightarrow}0$ to an extensive complexity of the spin glass state. We comment on holographic connections of the confinement transition to the fragmentation of black holes with AdS2{\mathrm{AdS}}_{2}AdS2​ horizons.
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