The Large N Expansion

Ashok Chatterjee

Aidan Herderschee, Michael Winer

A bstract We study the tensor model generalization of the quantum p -spherical model in the large- N limit. While the tensor model has the same large- N expansion as the disordered quantum p -spherical model, its ground state is superextensive, in contradiction with large- N perturbation theory. Therefore, the large- N expansion of this model catastrophically fails at arbitrarily large- N , without any obvious signal in perturbation theory.

A. J. Berlinsky, Amanda Harris

Paolo Amore, Francisco Marcelo Fernández, Martin Rodriguez-Vega

Abstract We analyze the convergence properties of the connected moments expansion (CMX) for the Rabi Hamiltonian. To this end we calculate the moments and connected moments of the Hamiltonian operator to a sufficiently large order. Our large-order results suggest that the CMX is not reliable for most practical purposes because the expansion exhibits considerable oscillations.

A. Foussats, A. Greco

In the present work we have developed a large-$N$ expansion for the $t\ensuremath{-}J$ model based on the path integral formulation for Hubbard operators. Our large-$N$ expansion formulation contains diagrammatic rules, in which the propagators and vertex are written in term of Hubbard operators. Using our large-$N$ formulation we have calculated, for $J=0,$ the renormalized $O(1/N)$ boson propagator. We also have calculated the spin-spin and charge-charge correlation functions to leading order $1/N.$ We have compared our diagram technique and results with existing ones in the literature.

Peter Kopietz, Lorenz Bartosch, Florian Schütz