Failure of the large-N expansion in a Bosonic Tensor Model

TL;DR

This paper investigates a bosonic tensor model's large-N limit and finds that, despite similar expansion properties to disordered models, its ground state causes the large-N expansion to fail catastrophically at all scales.

Contribution

It reveals the failure of the large-N expansion in a bosonic tensor model due to superextensive ground states, challenging assumptions about its applicability.

Findings

Large-N expansion matches disordered models' expansion

Ground state is superextensive, contradicting expectations

Large-N expansion fails at all scales without perturbative signals

Abstract

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.