Single-Instance Observables in the Sachdev-Ye-Kitaev Model

• URL: http://arxiv.org/abs/2609.16130v1
• Date: Mon, 14 Sep 2026 18:00:03 GMT
• Title: Single-Instance Observables in the Sachdev-Ye-Kitaev Model
• Abstract summary: We present a diagrammatic expansion for thermal expectation values of low-weight-anaana strings in a fixed realization of the $N$-fermion Sachdev-Ye-Qi Major (SYK) model.<n>For the four-body SYK model, we show that exact diagonalization results at sizes up to $N24$.<n>We also apply the method to the Maldacena--Qi Major (SYK) model formed from two identical copies of a fixed SYK realization.
• Score: 0.14504054468850666
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a diagrammatic expansion for thermal expectation values of low-weight Majorana strings in a fixed realization of the $N$-fermion Sachdev--Ye--Kitaev (SYK) model. At each order in the expansion, the observable is expressed as a finite sum of polynomials in the couplings multiplied by temperature-dependent kernels built from the large-$N$ melonic propagator. At fixed $βJ$, the expansion is organized in powers of $N^{-1/2}$, and each order can be efficiently evaluated with classical resources polynomial in $N$. The expansion also extends to correlations at arbitrary imaginary times and sufficiently short real times. For the four-body SYK model, we show that the diagrammatic predictions give an excellent account of exact diagonalization results at sizes up to $N=24$. We also apply the method to the Maldacena--Qi (MQ) model formed from two identical copies of a fixed SYK realization. This enables the identification of a nearby SYK-like Hamiltonian whose thermofield double state has higher fidelity with the Maldacena--Qi ground state than the thermofield double of the original SYK Hamiltonian.

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