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

@misc{swingle2026singleinstance,
  title = {{Single-Instance Observables in the Sachdev-Ye-Kitaev Model}},
  author = {Brian Swingle},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16130},
  eprint = {2609.16130},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16130},
}

TY  - UNPB
TI  - Single-Instance Observables in the Sachdev-Ye-Kitaev Model
AU  - Brian Swingle
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.16130
UR  - https://arxiv.org/abs/2609.16130
AB  - 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.
ER  -