Approximation of the Sachev-Ye-Kitaev Model by Free Fermion Variational States

Wenbo Fu, Yingfei Gu, Subir Sachdev A

Daniel Ish, Mark Srednicki

Through a mixture of analytic and numerical techniques, we explore the optimal approximation by a free Majorana state to individual disorder realizations of the Sachdev-Ye-Kitaev model, along with a generalization of it. We elucidate the properties of the known time-reversal symmetry breaking phase in the generalized model, finding strong evidence of "spin glass" order. For the Sachdev-Ye-Kitaev model itself, our results are inconclusive but suggest a similar order may be present at zero temperature.

Виктор Павлович Маслов

Arijit Haldar, Omid Tavakol, Thomas Scaffidi

Given a class of q-local Hamiltonians, is it possible to find a simple variational state whose energy is a finite fraction of the ground-state energy in the thermodynamic limit?Whereas product states often provide an affirmative answer in the case of bosonic (or qubit) models, we show that Gaussian states fail dramatically in the fermionic case, such as for the Sachdev-Ye-Kitaev (SYK) models.This prompts us to propose a new class of wave functions for SYK models inspired by the variational coupled cluster algorithm.We introduce a static "(0+0)-dimensional" large-N field theory to study the energy, two-point correlators, and entanglement properties of these states.Most importantly, we demonstrate a finite disorder-averaged approximation ratio of r ≈ 0.62 between the variational and ground-state energy of the SYK model for q = 4.Moreover, the variational states provide an exact description of spontaneous symmetry breaking in a related two-flavor SYK model.

Malvin H. Kalos, L. Reatto

Grigory Tarnopolsky

We consider the Sachdev-Ye-Kitaev (SYK) model, where interaction involves $q$ fermions at a time. We find the $1/{q}^{2}$ correction to the thermal two-point function in the large $q$ expansion. Using this result, we find the $1/{q}^{3}$ correction to the SYK free energy.