Spin liquid to spin glass crossover in the random quantum Heisenberg magnet

Abstract

We study quantum SU($M$) spins with all-to-all and random Heisenberg exchange interactions of root-mean-square strength $J$. The $M\to \infty$ model has a 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 $S=1/2$ 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 $1/M$ expansion to describe the crossover from fractionalized fermionic spinons to a confining spin glass state with weak spin glass order $q_{EA}$. The SYK spin liquid behavior persists down to a frequency ${\omega }_{\ast }\sim J{q}_{EA}$, and for $\omega <{\omega }_{\ast }$, the spectral density is linear in $\omega$, thus quenching the extensive zero temperature entropy of the spin liquid. The linear $\omega$ spectrum is qualitatively similar to that obtained earlier using bosonic spinons for large $q_{EA}$. We argue that the extensive SYK spin liquid entropy is transformed as $T\to 0$ to an extensive complexity of the spin glass state.

26 pages, 5 figures

References in corpus (7)

• From a single-band metal to a high-temperature superconductor via two thermal phase transitions
• From a single-band metal to a high-temperature superconductor via two thermal phase transitions (Supporting Material)
• Fractional excitations in the square-lattice quantum antiferromagnet
• Zero-Temperature Magnetic Transition in an Easy-Axis Kondo Lattice Model
• Fermionic spinon theory of square lattice spin liquids near the Néel state
• Extended Mean Field study of complex ${\varphi }^4$-theory at finite density and temperature
• The quantum $p$-spin glass model: A user manual for holographers

Cited by in corpus (13)

• Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
• Electronic spectra with paramagnon fractionalization in the single band Hubbard model
• Critical metallic phase in the overdoped random $t$-$J$ model
• Towards a Comprehensive Theory of Metal-Insulator Transitions in Doped Semiconductors
• Equilibrium dynamics of infinite-range quantum spin glasses in a field
• Exact numerical solution of the fully-connected classical and quantum Heisenberg spin glass
• Superconductivity of non-Fermi liquids described by Sachdev-Ye-Kitaev models
• Bipartite Sachdev-Ye Models with Read-Saleur Symmetries
• Two-level systems and harmonic excitations in a mean-field anharmonic quantum glass
• $\mathcal{N}=2$ SYK models with dynamical bosons and fermions
• Information scrambling and butterfly velocity in quantum spin glass chains
• Spin-liquid and spin-glass behavior in quantum spin models with all-to-all p-spin interactions
• Searching for emergent spacetime in spin glasses