Numerical study of fermion and boson models with infinite-range random interactions

By Wenbo Fu, S. Sachdev. 2016

184 citations recorded by the source corpus.

We present numerical studies of fermion and boson models with random all-to-all interactions (the SYK models). The high temperature expansion and exact diagonalization of the $N$-site fermion model are used to compute the entropy density: our results are consistent with the numerical solution of $N=\infty$ saddle point equations, and the presence of a non-zero entropy density in the limit of vanishing temperature. The exact diagonalization results for the fermion Green's function also appear to converge well to the $N=\infty$ solution. For the hard-core boson model, the exact diagonalization study indicates spin glass order. Some results on the entanglement entropy and the out-of-time-order correlators are also presented.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/65a3cdb5142d77c2dfa7beb3243d494e28e43807

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

In Nuclear and High Energy Physics

Citations in the corpus

Higher dimensional generalizations of the SYK model (2016, background): “This is simply the sum over the replicated action obtained for each site separately, for a direct comparison see for example the discussion in [6, 15].”
Notes on the complex Sachdev-Ye-Kitaev model (2019, background): “This has been examined numerically [1, 25, 4, 26, 27], and a consistent extrapolation exists for |μ| .”
Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models (2016, background): “[12, 27, 29], a complex fermion version of the SYK model can be defined, which has similar properties such as local critical two-point functions.”
Remarks on the Sachdev-Ye-Kitaev model (2016, result): “Further recent work in this or similar models includes [14, 15, 16, 17, 7, 18, 19].”
Black holes and random matrices (2016, methodology): “The theory also has a particle-hole symmetry under the operator [39, 32, 31]”
Uncolored random tensors, melon diagrams, and the Sachdev-Ye-Kitaev models (2016, unknown): “The procedure would be quite different from that in [48, 50] because there is no averaging over disorder.”
Pure states in the SYK model and nearly-$AdS_2$ gravity (2017, unknown): “Similar subsytem entanglement entropies were computed for the ground state in [22].”