A two-tensor model with order-three

TL;DR

This paper introduces a novel two-tensor model of order three, deriving its $W$-representation, analyzing correlators and free energy, and connecting it to Fredkin spin chain entanglement scaling.

Contribution

It constructs a new two-tensor model with order three, provides its $W$-representation, and links tensor model correlators to spin chain entanglement properties.

Findings

Derived compact correlator expressions from the $W$-representation.

Analyzed the free energy behavior in the large $N$ limit.

Established a correspondence between Dyck walks and tree operators.

Abstract

We construct a two-tensor model with order-3 and present its $W$-representation. Moreover we derive the compact expressions of correlators from the $W$-representation and analyze the free energy in large $N$ limit. In addition, we establish the correspondence between two colored Dyck walks in the Fredkin spin chain and tree operators in the ring. Based on the classification Dyck walks, we give the number of tree operators with the given level. Furthermore, we show the entanglement scaling of Fredkin spin chain beyond logarithmic scaling in the ordinary critical systems from the viewpoint of tensor model.