Crossover to Sachdev-Ye-Kitaev criticality in an infinite-range quantum Heisenberg spin glass
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910049688879104 |
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| author | Hosseinabadi, Hossein Sachdev, Subir Marino, Jamir |
| author_facet | Hosseinabadi, Hossein Sachdev, Subir Marino, Jamir |
| contents | We study the equilibrium dynamics of an infinite-range quantum Heisenberg model with random couplings, in which local magnetic moments arise from $\mathcal{N}_f$ flavors of spinful fermions. We employ an expansion in $\mathcal{N}_f$, which controls the strength of quantum fluctuations, and self-consistently include $1/\mathcal{N}_f$ corrections to the Luttinger-Ward functional. In the large-$\mathcal{N}_f$ limit, where quantum fluctuations are weak, the high- and low-temperature phases are respectively paramagnetic and spin glass ordered, with a transition temperature independent of $\mathcal{N}_f$. For small numbers of fermionic flavors, however, quantum fluctuations substantially suppress the ordering temperature. We show that this behavior reflects the proximity of the system to a Sachdev-Ye-Kitaev (SYK) phase, where both fermionic and spin spectral densities display critical behavior over a broad range of finite frequencies, with the latter exhibiting the scale-invariant form $χ''(ω)\sim \operatorname{sgn}(ω)$. At the lowest energies and temperatures, spin-glass dynamics ultimately take over, producing a universal sub-Ohmic dynamical spin susceptibility $χ''(ω)\sim \operatorname{sgn}(ω)\sqrt{|ω|}$. Our results establish a minimal framework for understanding dynamical crossovers between SYK criticality and spin-glass ordering. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11263 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Crossover to Sachdev-Ye-Kitaev criticality in an infinite-range quantum Heisenberg spin glass Hosseinabadi, Hossein Sachdev, Subir Marino, Jamir Strongly Correlated Electrons Disordered Systems and Neural Networks We study the equilibrium dynamics of an infinite-range quantum Heisenberg model with random couplings, in which local magnetic moments arise from $\mathcal{N}_f$ flavors of spinful fermions. We employ an expansion in $\mathcal{N}_f$, which controls the strength of quantum fluctuations, and self-consistently include $1/\mathcal{N}_f$ corrections to the Luttinger-Ward functional. In the large-$\mathcal{N}_f$ limit, where quantum fluctuations are weak, the high- and low-temperature phases are respectively paramagnetic and spin glass ordered, with a transition temperature independent of $\mathcal{N}_f$. For small numbers of fermionic flavors, however, quantum fluctuations substantially suppress the ordering temperature. We show that this behavior reflects the proximity of the system to a Sachdev-Ye-Kitaev (SYK) phase, where both fermionic and spin spectral densities display critical behavior over a broad range of finite frequencies, with the latter exhibiting the scale-invariant form $χ''(ω)\sim \operatorname{sgn}(ω)$. At the lowest energies and temperatures, spin-glass dynamics ultimately take over, producing a universal sub-Ohmic dynamical spin susceptibility $χ''(ω)\sim \operatorname{sgn}(ω)\sqrt{|ω|}$. Our results establish a minimal framework for understanding dynamical crossovers between SYK criticality and spin-glass ordering. |
| title | Crossover to Sachdev-Ye-Kitaev criticality in an infinite-range quantum Heisenberg spin glass |
| topic | Strongly Correlated Electrons Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2603.11263 |